ME’scopeVES Reference Manual Volume IIB – Options

(February 2014)

Notice Information in this document is subject to change without notice and does not represent a commitment on the part of Vibrant Technology. Except as otherwise noted, names, companies, and data used in examples, sample outputs, or screen shots, are fictitious and are used solely to illustrate potential applications of the software.

Warranty Vibrant Technology, Inc. warrants that (a) the software in this product will perform substantially in accordance with the accompanying documentation, for a period of one (1) year from the date of delivery, and that (b) any hardware accompanying the software will be free from defects in materials and workmanship for a period of one (1) year from the date of delivery. During this period, if a defect is reported to Vibrant Technology, replacement software or hardware will be provided to the customer at no cost, excluding delivery charges. Any replacement software will be warranted for the remainder of the original warranty period or thirty (30) days, whichever is longer. This warranty shall not apply to defects resulting from improper or inadequate maintenance by the customer, customer supplied software or interfacing, unauthorized modification or misuse, operation outside of the environmental specifications for the product, or improper site preparation or maintenance. In the event that the software does not materially operate as warranted above, the sole remedy of the customer (and the entire liability of Vibrant Technology) shall be the correction or detour of programming errors attributable to Vibrant Technology. The software should not be relied on as the sole basis to solve a problem whose incorrect solution could result in injury to a person or property. If the software is employed in such a manner, it is at the entire risk of the customer, and Vibrant Technology disclaims all liability for such misuse. NO OTHER WARRANTY IS EXPRESSED OR IMPLIED. VIBRANT TECHNOLOGY SPECIFICALLY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANT ABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE REMEDIES PROVIDED HEREIN ARE THE CUSTOMER'S SOLE AND EXCLUSIVE REMEDIES. VIBRANT TECHNOLOGY SHALL NOT BE LIABLE FOR ANY DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS PRODUCT, WHETHER BASED ON CONTRACT, TORT, OR ANY OTHER LEGAL THEORY.

Copyright The software described in this document is copyrighted by Vibrant Technology, Inc. or its suppliers and is protected by United States copyright laws and international treaty provisions. Unauthorized reproduction or distribution of this program, or any portion of it, may result in severe civil and criminal penalties, and will be prosecuted to the maximum extent possible under the law. You may make copies of the software only for backup or archival purposes. No part of this manual may be reproduced or transmitted in any form or by any means for any purpose without the express written permission of Vibrant Technology. Copyright ďƒ“ 1992-2014 by Vibrant Technology, Inc. All rights reserved. Printed in the United States of America.

Vibrant Technology, Inc. 5 Erba Lane, Suite B Scotts Valley, CA 95066 phone: (831) 430-9045 fax: (831) 430-9057 E-mail: support@vibetech.com http://www.vibetech.com

Table of Contents Acquisition Window Commands ...................................................................................... 1 Graphics Areas & Spreadsheets ................................................................................. 1 Menu Commands ........................................................................................................ 2 Acquisition Mouse & Keyboard Operations ..................................................................... 2 Right Click Menus ........................................................................................................ 2 Ordering Spreadsheet Columns .................................................................................. 2 Scrolling Spreadsheets ................................................................................................ 2 Spreadsheet Text Size ................................................................................................ 2 Scrolling the Trace Display .......................................................................................... 2 Zooming....................................................................................................................... 2 Panning a Zoomed Display .......................................................................................... 2 Moving the Cursors...................................................................................................... 2 Line Cursor .............................................................................................................. 3 Peak or Band Cursor................................................................................................ 3 Moving an Edge of the Peak or Band Cursor ........................................................... 3 Selecting a Range of Traces ....................................................................................... 3 Toggle Trace Selection ................................................................................................ 3 Trace Values ............................................................................................................... 3 Cut, Copy & Paste Text ............................................................................................... 3 Graphics Scroll Bars........................................................................................................ 3 Vertical Scroll Bar ........................................................................................................ 3 Horizontal Scroll Bar .................................................................................................... 3 Toolbar Lists .................................................................................................................... 4 Traces Spreadsheet ........................................................................................................ 4 Channels Spreadsheet .................................................................................................... 5 Setup, Units, and DOFs Tabs ...................................................................................... 5 Active Column ............................................................................................................. 5 DOF Column ................................................................................................................ 6 Editing Channel Properties .......................................................................................... 6 Setup Tab .................................................................................................................... 6 Signal Level Column ................................................................................................ 6

iii

Reference Volume IIB - Options Label Column ........................................................................................................... 6 Input Output Column ................................................................................................ 6 ADC Coupling Column ............................................................................................. 7 Transducer Power Column ...................................................................................... 7 ADC Range Column................................................................................................. 7 Data Type Column ................................................................................................... 7 Window Type Column .............................................................................................. 7 Window Value Column ............................................................................................. 7 Units Tab ..................................................................................................................... 7 Units Column............................................................................................................ 8 Display Column ........................................................................................................ 8 Transducer Sensitivity, Sensitivity Units & Transducer Units Columns ................... 8 DOFs Tab .................................................................................................................... 8 Point Number & Direction Columns.......................................................................... 9 Manual Increment Column ....................................................................................... 9 Increment Point By and Increment Direction By Columns........................................ 9 Measurement Tab ........................................................................................................... 9 Time & Frequency Measurements ............................................................................. 10 Averaging .................................................................................................................. 10 Averaging Method...................................................................................................... 10 Increment DOFs ........................................................................................................ 11 Sampling Tab ................................................................................................................ 11 Display Limits ............................................................................................................ 12 Triggering Tab ............................................................................................................... 12 Auto Range Front End Channels ............................................................................... 12 Free Run.................................................................................................................... 13 Trigger ....................................................................................................................... 14 Trigger Channel ......................................................................................................... 14 +Slope, -Slope ........................................................................................................... 14 Trigger Level (% of Channel voltage) ........................................................................ 14 Trigger Lines .......................................................................................................... 14 Lock Lines .............................................................................................................. 14 Pre-Trigger Delay (samples)...................................................................................... 14 iv

Table of Contents Double Hit Line .......................................................................................................... 14 Overload .................................................................................................................... 14 Source Tab.................................................................................................................... 15 Random & Chirp Signals ........................................................................................... 16 Frequency Range ...................................................................................................... 16 Burst Width ................................................................................................................ 16 File Menu ...................................................................................................................... 17 Save Acquisition ........................................................................................................ 17 Save Acquisition As... ................................................................................................ 17 Save Graphics in File................................................................................................. 17 Copy to Clipboard | Trace Graphics........................................................................... 17 Copy to Clipboard | Traces Spreadsheet ................................................................... 17 Copy to Clipboard | Channels Spreadsheet ............................................................... 17 Print | Trace Graphics ................................................................................................ 17 Print | Traces Spreadsheet ........................................................................................ 18 Print | Channels Spreadsheet .................................................................................... 18 Acquisition Properties ................................................................................................ 18 Acquisition Options .................................................................................................... 18 File | Close Acquisition .............................................................................................. 18 Opening a Window .................................................................................................... 18 Edit Menu ...................................................................................................................... 19 Select Traces ............................................................................................................. 19 Sort Traces ................................................................................................................ 19 Display Menu ................................................................................................................ 19 Center Acquisition Window ........................................................................................ 19 Traces Spreadsheet .................................................................................................. 19 Acquisition Toolbars .................................................................................................. 19 Active Graph .............................................................................................................. 19 Real, Imaginary, Magnitude, Phase ........................................................................... 19 CoQuad, Bode, Nyquist ............................................................................................. 20 Cursor Menu .............................................................................................................. 20 Zoom, mooZ .............................................................................................................. 20 Maximize ................................................................................................................... 20 v

Reference Volume IIB - Options Windowed Traces ...................................................................................................... 20 Animate Menu ............................................................................................................... 21 Create Animation Equations (Assign M#s) ................................................................ 21 Animate Shapes ........................................................................................................ 21 Renumber M#s .......................................................................................................... 21 Format Menu ................................................................................................................. 22 Rows/Columns, Overlaid, Overlaid by DOF, Strip Chart, Cascade, Contour ............. 22 Overlay By DOF......................................................................................................... 22 Y-axis Scaling, X-axis Scaling ................................................................................... 22 Saving Traces Into a Data Block ................................................................................... 22 Tools Menu ................................................................................................................... 23 Save Shape ............................................................................................................... 23 Save Traces (F7) ....................................................................................................... 23 Save Traces As ......................................................................................................... 24 Save and Start (F8) ................................................................................................... 24 Acquire Menu ................................................................................................................ 24 Start (F5) ................................................................................................................... 24 Stop (F6).................................................................................................................... 25 Front End Scope ........................................................................................................ 25 Reject Impact (F9) ..................................................................................................... 25 Reject Overloads ....................................................................................................... 25 Measurement Sets Menu .............................................................................................. 25 What is a Measurement Set ...................................................................................... 25 Use Measurement Sets ............................................................................................. 25 Next Set (F4), Current Set, Previous Set (F3) ........................................................... 25 Add Measurement Sets ............................................................................................. 26 Delete Measurement Set ........................................................................................... 26 Show Channel DOFs ................................................................................................. 26 Assign Channel DOFs ............................................................................................... 26 Macro-Program Window Commands ............................................................................ 29 Commands & Parameters Spreadsheets .................................................................. 29 Menu Commands ...................................................................................................... 29 Program Menu in Each Window ................................................................................ 29 vi

Table of Contents Program Description...................................................................................................... 30 Commands Spreadsheet ........................................................................................... 30 Select Step Column ............................................................................................... 30 Execute Step Column ............................................................................................ 31 Delay After Column ................................................................................................ 31 Step Label Column................................................................................................. 31 Target Window Column .......................................................................................... 31 Target Window Command ..................................................................................... 31 Open Dialog Column .............................................................................................. 32 Parameters Spreadsheet ........................................................................................... 32 Parameter Name Column ...................................................................................... 32 Parameter Value Column ....................................................................................... 32 Program Mouse & Keyboard Operations....................................................................... 32 Right Click Menus ...................................................................................................... 32 Re-Ordering Spreadsheet Columns........................................................................... 32 Scrolling Spreadsheets .............................................................................................. 32 Spreadsheet Text Size .............................................................................................. 32 Cut, Copy & Paste Text ............................................................................................. 32 File Menu ...................................................................................................................... 32 Save Program ............................................................................................................ 33 Save Program As....................................................................................................... 33 Copy to Clipboard Menu ............................................................................................ 33 Print Menu ................................................................................................................. 33 Program Options........................................................................................................ 33 Display Tab ............................................................................................................ 34 Delay Tab ............................................................................................................... 34 Show/Hide Tab....................................................................................................... 34 Close Program ........................................................................................................... 34 Opening a Window .................................................................................................... 34 Edit Menu ...................................................................................................................... 35 Undo .......................................................................................................................... 35 Redo .......................................................................................................................... 35 Select Steps Menu..................................................................................................... 35 vii

Reference Volume IIB - Options Select All ................................................................................................................ 35 Invert Selection ...................................................................................................... 35 Select None ........................................................................................................... 35 Cut selected Steps..................................................................................................... 35 Copy selected Steps .................................................................................................. 35 Paste Steps ............................................................................................................... 36 Insert selected Steps ................................................................................................. 36 Delete selected Steps ................................................................................................ 36 Move Selected Steps Up/Down ................................................................................. 36 All Window Commands.............................................................................................. 36 Display menu ................................................................................................................ 36 Center Program Window ........................................................................................... 36 Program Toolbars ...................................................................................................... 36 Split............................................................................................................................ 36 Parameters ................................................................................................................ 37 Target Window .......................................................................................................... 37 Run Menu...................................................................................................................... 37 Run Once .................................................................................................................. 37 Run Continuous ......................................................................................................... 37 Stop ........................................................................................................................... 37 Continue .................................................................................................................... 37 Continue to selected Step.......................................................................................... 37 Single Step ................................................................................................................ 38 Program Menu .............................................................................................................. 38 Sleep ......................................................................................................................... 38 User Dialog ................................................................................................................ 38 Question Box ............................................................................................................. 38 Parameters ............................................................................................................ 39 Variable | Var_1 = Var_2 ........................................................................................... 39 Variable | Var_1 = Var_2 [operator] Var_3................................................................. 39 [ + ] add ................................................................................................................. 39 [ - ] subtract ............................................................................................................ 39 [ x ] multiply ............................................................................................................ 39 viii

Table of Contents [ / ] divide ................................................................................................................ 39 Variable | If (Var_1 [compare] Var_2) Then GoTo Step Label ................................... 40 [ = ] equal to ........................................................................................................... 40 [ <> ] not equal to ................................................................................................... 40 [ < ] less than.......................................................................................................... 40 [ <= ] less than or equal to ...................................................................................... 40 [ > ] greater than..................................................................................................... 40 [ >= ] greater than or equal to ................................................................................. 40 Variable | Variable Dialog .......................................................................................... 40 Parameters ............................................................................................................ 40 Variable | Show Variable ........................................................................................... 40 Parameter .............................................................................................................. 40 Variable | Var_1 = Var_2 from Program..................................................................... 40 Parameters ............................................................................................................ 40 Variable | Var_1 = Var_2 from Program..................................................................... 41 Parameters ............................................................................................................ 41 GoTo Line .................................................................................................................. 41 Close All Other Windows ........................................................................................... 41 Program Running Banner.............................................................................................. 41 Stop All Programs Button .......................................................................................... 41 ME'scope Window Program Menu ................................................................................ 41 Window | Minimize ..................................................................................................... 42 Parameter .............................................................................................................. 42 Window | Restore ...................................................................................................... 42 Parameter .............................................................................................................. 42 Window | Maximize .................................................................................................... 42 Parameter .............................................................................................................. 42 Window | Position ...................................................................................................... 42 Parameters ............................................................................................................ 42 Window | Bring to the Front ....................................................................................... 42 Parameter .............................................................................................................. 42 Window | Send to the Back ........................................................................................ 43 Parameter .............................................................................................................. 43 ix

Reference Volume IIB - Options Auto Start Program .................................................................................................... 43 New Data Block Menu ............................................................................................... 43 Structure Window Program Menu ................................................................................. 43 Objects | Select.......................................................................................................... 43 Parameters ............................................................................................................ 44 Objects | Hide ............................................................................................................ 44 Parameter .............................................................................................................. 44 Objects | Label ........................................................................................................... 44 Parameter .............................................................................................................. 44 Objects | Color ........................................................................................................... 44 Parameter .............................................................................................................. 44 Objects | Bold ............................................................................................................ 44 Parameter .............................................................................................................. 44 Data Block Program Menu ............................................................................................ 44 Display | Cursor ......................................................................................................... 44 Parameters ............................................................................................................ 44 Display | Zoom ........................................................................................................... 45 Parameters ............................................................................................................ 45 Display | Sine Dwell Cycles per Shape ...................................................................... 45 Parameter .............................................................................................................. 45 Traces | Select ........................................................................................................... 45 Parameters ............................................................................................................ 45 Traces | Color ............................................................................................................ 45 Parameter .............................................................................................................. 45 Traces | Label ............................................................................................................ 45 Parameter .............................................................................................................. 45 Traces | DOFs ........................................................................................................... 46 Parameter .............................................................................................................. 46 Traces | Units............................................................................................................. 46 Parameters ............................................................................................................ 46 Traces | Measurement Type ...................................................................................... 46 Parameter .............................................................................................................. 46 Traces | Input Output ................................................................................................. 46 x

Table of Contents Parameter .............................................................................................................. 46 Traces | Visibility ........................................................................................................ 46 Parameter .............................................................................................................. 46 Traces | Linear/Power ................................................................................................ 46 Parameter .............................................................................................................. 46 Traces | SubShape .................................................................................................... 46 Parameter .............................................................................................................. 46 Tools | Damping Decay Constant .............................................................................. 46 Parameters ............................................................................................................ 47 Tools | ODS Correlation ............................................................................................. 47 Parameters ............................................................................................................ 47 Tools | Trace Correlation ........................................................................................... 47 Parameters ............................................................................................................ 48 Tools | Save Cursor Values ....................................................................................... 48 Tools | Save Statistics ............................................................................................... 48 Parameters ............................................................................................................ 48 Math | Trace Matrix Add (or Subtract)........................................................................ 48 Parameters ............................................................................................................ 48 Math | Trace Matrix Multiply ....................................................................................... 49 Parameters ............................................................................................................ 49 Math | Trace Matrix Inverse ....................................................................................... 49 Parameters ............................................................................................................ 49 Curve Fit | Number of Modes ..................................................................................... 49 Parameter .............................................................................................................. 49 Curve Fit | Mode Indicator Noise Threshold............................................................... 49 Parameter .............................................................................................................. 49 Curve Fit | Count Peaks ............................................................................................. 49 Parameters ............................................................................................................ 49 Curve Fit | Frequency and Damping .......................................................................... 50 Parameters ............................................................................................................ 50 Curve Fit | Residues .................................................................................................. 50 Parameter .............................................................................................................. 50 Curve Fit | Stability Button ......................................................................................... 50 xi

Reference Volume IIB - Options Parameters ............................................................................................................ 50 Curve Fit | Stability Reset .......................................................................................... 50 Curve Fit | Save Stable Groups ................................................................................. 50 Shape Table Program Menu ......................................................................................... 50 Display | Dwell Cycles per Sweep Step ..................................................................... 51 Parameter .............................................................................................................. 51 Shapes | Select.......................................................................................................... 51 Parameter .............................................................................................................. 51 Shapes | Color ........................................................................................................... 51 Parameter .............................................................................................................. 51 Shapes | Label ........................................................................................................... 51 Parameter .............................................................................................................. 51 Shapes | Frequency................................................................................................... 51 Parameter .............................................................................................................. 52 Shapes | Damping ..................................................................................................... 52 Parameter .............................................................................................................. 52 Shapes | Copy Shapes data to Clipboard .................................................................. 52 Parameters ............................................................................................................ 52 Shapes | Paste Clipboard data into Shapes .............................................................. 52 Parameters ............................................................................................................ 52 Shapes | Copy Shapes data to Variable .................................................................... 52 Parameters ............................................................................................................ 52 Shapes | Paste Variable into Shapes ........................................................................ 52 Parameters ............................................................................................................ 53 DOFs | Select ............................................................................................................ 53 Parameters ............................................................................................................ 53 DOFs | Color .............................................................................................................. 53 Parameter .............................................................................................................. 53 DOFs | Label.............................................................................................................. 53 Parameter .............................................................................................................. 53 DOFs | DOF ............................................................................................................... 53 Parameter .............................................................................................................. 53 DOFs | Units .............................................................................................................. 53 xii

Table of Contents Parameter .............................................................................................................. 53 DOFs | Measurement Type........................................................................................ 53 Parameter .............................................................................................................. 53 DOFs | Copy DOFs data to Clipboard ....................................................................... 53 Parameters ............................................................................................................ 54 DOFs | Paste Clipboard data into DOFs .................................................................... 54 Parameters ............................................................................................................ 54 DOFs | Copy DOFs data to Variable.......................................................................... 54 Parameters ............................................................................................................ 54 DOFs | Paste Variable into DOFs .............................................................................. 54 Parameters ............................................................................................................ 54 Math | Add an Offset .................................................................................................. 54 Parameter .............................................................................................................. 55 Math | Invert DOFs .................................................................................................... 55 Math | Scale by Mag Phs ........................................................................................... 55 Parameters ............................................................................................................ 55 Math | Square DOFs .................................................................................................. 55 Math | Square Root of DOFs ..................................................................................... 55 Math | Add DOFs ....................................................................................................... 55 Parameters ............................................................................................................ 55 Math | Subtract DOFs ................................................................................................ 55 Parameters ............................................................................................................ 55 Math | Multiply DOFs ................................................................................................. 55 Parameters ............................................................................................................ 56 Math | Divide DOFs ................................................................................................... 56 Parameters ............................................................................................................ 56 Acquisition Window Program Menu............................................................................... 56 Display | Cursor ......................................................................................................... 56 Parameters ............................................................................................................ 56 Display | Zoom ........................................................................................................... 56 Parameters ............................................................................................................ 56 Display | Dwell Cycles per Sweep Step ..................................................................... 57 Parameter .............................................................................................................. 57 xiii

Reference Volume IIB - Options Traces | Select ........................................................................................................... 57 Parameters ............................................................................................................ 57 Traces | Color ............................................................................................................ 57 Parameter .............................................................................................................. 57 Traces | Label ............................................................................................................ 57 Parameter .............................................................................................................. 57 Traces | DOFs ........................................................................................................... 57 Parameter .............................................................................................................. 57 Traces | Units............................................................................................................. 57 Parameters ............................................................................................................ 57 Traces | Measurement Type ...................................................................................... 57 Parameter .............................................................................................................. 58 Traces | Input Output ................................................................................................. 58 Parameter .............................................................................................................. 58 Traces | Visible .......................................................................................................... 58 Parameter .............................................................................................................. 58 Tools | Save Statistics ............................................................................................... 58 Tools | Connected Structure ...................................................................................... 58 Parameter .............................................................................................................. 58 Tools | Connected Data Block ................................................................................... 58 Parameter .............................................................................................................. 58 Signal Processing Commands ...................................................................................... 59 Data Block Signal Processing Commands .................................................................... 59 File Menu ................................................................................................................... 59 Tools Menu ................................................................................................................ 59 Transform Menu ........................................................................................................ 59 Traces Spreadsheet Columns ................................................................................... 59 Linear Power Column ................................................................................................ 60 Input Output Column.................................................................................................. 60 Peak RMS Pk-Pk Column.......................................................................................... 61 FFT Column ............................................................................................................... 61 Window Column......................................................................................................... 61 Window Value Column .............................................................................................. 61 xiv

Table of Contents Window Correction Column ....................................................................................... 61 Windowing Examples ................................................................................................ 61 Z-Axis Column ........................................................................................................... 63 File | Export to VSI Rotate ............................................................................................. 63 Edit | Cut Traces to File ................................................................................................. 63 Data in the Cursor Band ............................................................................................ 64 M#s and Animation Equations ................................................................................... 64 Edit | Copy Traces to File .............................................................................................. 64 Data in the Cursor Band ............................................................................................ 64 Edit | Paste Traces from File ......................................................................................... 64 Edit | Paste Trace Data at Cursor.................................................................................. 65 Edit | Delete selected Traces ........................................................................................ 65 M#s and Animation Equations ................................................................................... 65 Tools | Integrate ............................................................................................................ 65 Integration Errors Due To DC Offset.......................................................................... 66 Integration Errors Due To Leakage............................................................................ 66 Removing Lower Frequencies Before Integration ...................................................... 66 Tools | Differentiate ....................................................................................................... 66 Tools | Remove DC ....................................................................................................... 67 Tools | Statistics ............................................................................................................ 67 Minimum Value .......................................................................................................... 67 Maximum Value ......................................................................................................... 68 Mean Value ............................................................................................................... 68 Mean Squared (MS) Value ........................................................................................ 68 Root Mean Squared (RMS) Value ............................................................................. 68 Variance .................................................................................................................... 68 Standard Deviation .................................................................................................... 68 Power ........................................................................................................................ 69 Linear Power ............................................................................................................. 69 Crest Factor ............................................................................................................... 69 Absolute Deviation ..................................................................................................... 69 Skew .......................................................................................................................... 69 Kurtosis...................................................................................................................... 70 xv

Reference Volume IIB - Options Tools | Math Menu......................................................................................................... 70 Math | Scale By Mag Phs .......................................................................................... 70 Math | Add an Offset .................................................................................................. 70 Math | Add Random Noise ......................................................................................... 71 Math | Conjugate Traces ........................................................................................... 71 Math | Invert Traces ................................................................................................... 71 Math | Square Traces ................................................................................................ 71 Math | Square Root of Traces .................................................................................... 71 Math | Smooth Traces ............................................................................................... 71 Math | Re-Sample Traces .......................................................................................... 71 Math | Sum Traces .................................................................................................... 71 Math | Average Traces .............................................................................................. 71 Math | Add (Subtract, Multiply by, Divide by) a selected Trace .................................. 72 Transform | Block Size .................................................................................................. 72 Increasing the Block Size ....................................................................................... 72 Decreasing the Block Size ..................................................................................... 72 The FFT and DFT.......................................................................................................... 72 1. Sampled Time Domain Waveform ......................................................................... 72 2. Digital Fourier Transform (DFT) ............................................................................. 72 3. Shannon's (Nyquist) Sampling Criterion ................................................................ 73 Fundamental Sampling Rule ..................................................................................... 73 Sampling Rate and Frequency Resolution ................................................................ 73 Anti-Aliasing Filter ...................................................................................................... 73 Transform | FFT ............................................................................................................ 73 Prime Number FFT .................................................................................................... 74 One Sided Versus Two Sided FFT ............................................................................ 75 Transform | Inverse FFT ................................................................................................ 75 Time Domain Windows ................................................................................................. 75 Non-Periodic Signals ................................................................................................. 75 Time Domain Windowing to Reduce Leakage ........................................................... 75 Hanning Window for Broad Band Signals .................................................................. 75 Flat Top Window for Narrow Band Signals ................................................................ 76 Exponential Window for Transient Response Signals ............................................... 76 xvi

Table of Contents Rectangular Window for Periodic Signals .................................................................. 77 Transform | Window Traces .......................................................................................... 77 Notch Window ........................................................................................................... 78 Band Pass Window.................................................................................................... 78 Interpolation Window ................................................................................................. 79 Exponential Window .................................................................................................. 80 Decreasing Exponential Removes Noise and Leakage ............................................. 80 Increasing Exponential Narrows Resonance Peaks .................................................. 80 Modal Damping.......................................................................................................... 80 Damping Removal Following Curve Fitting ................................................................ 81 Transform | Spectra....................................................................................................... 81 Fourier spectrum........................................................................................................ 81 Auto spectrum ........................................................................................................... 82 Cross spectrum.......................................................................................................... 82 Power Spectral Density (PSD) ................................................................................... 82 Energy Spectral Density (ESD) ................................................................................. 82 Time Domain Source ................................................................................................. 82 Spectrogram .............................................................................................................. 82 Spectrum Averaging ...................................................................................................... 82 Number of Averages .................................................................................................. 83 Overlap Processing ................................................................................................... 83 Linear Averaging........................................................................................................ 84 Peak Hold Averaging ................................................................................................. 84 Transform | ODS FRFs ................................................................................................. 84 What is an ODS FRF? ............................................................................................... 84 Advantages of ODS FRFs ......................................................................................... 85 ODS's from a Set of ODS FRFs ................................................................................ 85 What is Transmissibility? ........................................................................................... 85 Difficulty with Transmissibility's .................................................................................. 85 Scaled Cross Spectra ................................................................................................ 86 Advantages of Scaled Cross Spectra ........................................................................ 86 Operating Mode Shapes ............................................................................................ 86 Setting Up Your Data ................................................................................................. 86 xvii

Reference Volume IIB - Options Measurement Sets..................................................................................................... 87 Transform | Scale ODS FRFs........................................................................................ 87 Overlaid Reference Auto Spectra .............................................................................. 87 Scale Factor .............................................................................................................. 88 Transform | Order Tracked ODS's. ................................................................................ 88 What is an Order?...................................................................................................... 88 What is Order Tracking? ............................................................................................ 88 Non-Stationary Signal ................................................................................................ 89 Order Tracked ODS's ................................................................................................ 89 1. Simultaneous Method ...................................................................................... 89 2. Measurement Set Method ................................................................................ 89 Processing Multiple Measurement Sets..................................................................... 90 Editing Trace DOFs for Multiple Measurement Sets .................................................. 90 1. Phase Correction ............................................................................................. 91 2. Magnitude Correction ....................................................................................... 91 Shape Table Signal Processing Commands ................................................................. 91 Edit Menu .................................................................................................................. 91 Display Menu ............................................................................................................. 92 Tools Menu ................................................................................................................ 92 DOFs Spreadsheet Columns ..................................................................................... 92 Shape Table Edit Menu ................................................................................................. 92 Edit | Add Shapes ...................................................................................................... 92 Edit | Delete Selected Shapes ................................................................................... 92 Edit | Copy Shapes to File ......................................................................................... 92 Edit | Paste Shapes from File .................................................................................... 92 Edit | Add DOFs ......................................................................................................... 93 Edit | Delete Selected DOFs ...................................................................................... 93 Display | Shape DOFs | Accel, Vel, Disp ....................................................................... 93 Shape Table Tools Menu .............................................................................................. 94 Tools | Multiply Shapes By......................................................................................... 94 Tools | Integrate ......................................................................................................... 95 Tools | Differentiate.................................................................................................... 95 Tools | Shape Product ............................................................................................... 95 xviii

Table of Contents Basic Modal Analysis Commands ................................................................................. 97 Data Block Basic Modal Analysis Commands ............................................................... 97 Modes Menu .............................................................................................................. 97 Curve Fitting Menu .................................................................................................... 97 Special Mouse & Keyboard Commands .................................................................... 97 Single Reference Modal Test ........................................................................................ 97 MIMO Model .............................................................................................................. 98 Roving Response Test .............................................................................................. 98 Roving Impact Test .................................................................................................... 98 Maxwell's Reciprocity ................................................................................................ 98 Single Reference Modal Test .................................................................................... 98 What is FRF Curve Fitting? ........................................................................................... 98 Curve Fitting Steps .................................................................................................... 99 FRFs in Terms of Modal Parameters ............................................................................ 99 Partial Fraction Expansion of the FRF Matrix ............................................................ 99 Local versus Global Curve Fitting ............................................................................ 100 Residue Matrix ......................................................................................................... 100 Parameter Estimation .............................................................................................. 100 Damped Natural Frequency..................................................................................... 100 Undamped Natural Frequency ................................................................................. 100 Damping Ratio or Percent of Critical Damping ........................................................ 101 Damping Decay Constant ........................................................................................ 101 Half Power Point (3 dB bandwidth) Damping........................................................... 101 Conclusions: ............................................................................................................ 102 Quality Factor and Loss Factor ................................................................................ 102 Frequency & Damping Plot ...................................................................................... 102 Frequency & Damping Terminology ............................................................................ 103 Mode Shapes From Residues ..................................................................................... 104 Fundamental Modal Testing Criterion ...................................................................... 104 Mode Shape Node Points ........................................................................................ 105 Global Versus Local Modes ..................................................................................... 105 Curve Fitting Guidelines .............................................................................................. 105 1. Overlay the FRFs................................................................................................. 105 xix

Reference Volume IIB - Options 2. Inspect the Impulse Response Functions (IRFs) ................................................. 105 3. Use the Mode Indicator........................................................................................ 106 4. Use the Band cursor ............................................................................................ 106 5. Verify Fundamental Mode Shapes....................................................................... 106 6. Compare Results from Different Curve Fitting Methods ...................................... 106 Modes | Modal Parameters ......................................................................................... 106 Curve Fitting Splitter Bars ........................................................................................... 107 Vertical Splitter Bars............................................................................................. 107 Horizontal Splitter Bars ........................................................................................ 108 Modal Parameters Spreadsheet .................................................................................. 108 Select Mode Column ............................................................................................... 109 Frequency & Damping Columns .............................................................................. 109 Residue Magnitude & Phase Columns .................................................................... 109 Methods Column...................................................................................................... 109 Cursor Columns ....................................................................................................... 109 Showing & Hiding Spreadsheet Columns ................................................................ 110 Reset Spreadsheet Column Widths ......................................................................... 110 Editing Cells ............................................................................................................. 110 Mode Indicator Tab ..................................................................................................... 110 Mode Indicator ......................................................................................................... 111 Frequency & Damping Methods .................................................................................. 111 Polynomial Method .................................................................................................. 112 Curve Fitting Assumptions ....................................................................................... 112 Non-Stationary Data ................................................................................................ 112 Global Versus Local Curve Fitting ........................................................................... 112 Frequency & Damping Tab ......................................................................................... 112 Global Polynomial Method ....................................................................................... 113 Local Polynomial Method......................................................................................... 113 Extra Numerator Polynomial Terms ......................................................................... 113 Vertical Frequency Lines ......................................................................................... 113 Horizontal Damping Lines........................................................................................ 113 Residue Methods ........................................................................................................ 114 Lightly Coupled Modes ............................................................................................ 114 xx

Table of Contents Peak Method ........................................................................................................... 115 Closely Coupled Modes ........................................................................................... 115 Polynomial Method .................................................................................................. 115 Extra Numerator Polynomial Terms ......................................................................... 115 Residues & Save Shapes Tab .................................................................................... 116 Residues Button ...................................................................................................... 116 Fit Function .............................................................................................................. 116 Save Shapes Button ................................................................................................ 116 Removing Exponential Window Damping ................................................................ 116 Residue Mode Shapes ............................................................................................ 117 Curve Fit | Delete All Fit Data ...................................................................................... 117 Curve Fit | Quick Fit..................................................................................................... 117 Quick Fit Steps ........................................................................................................ 117 Improving Quick Fit Results ..................................................................................... 118 Fixed Number of Modes .......................................................................................... 118 Curve Fit | Sort Modes by Frequency .......................................................................... 119 Curve Fit | Delete Selected Modes .............................................................................. 119 Curve Fit | Clear Fit Functions ..................................................................................... 119 Curve Fit | Fit Function Synthesis................................................................................ 119 Curve Fit | Mode Indicator Menu ................................................................................. 119 Clear (Clear In Band) ............................................................................................... 119 Smooth .................................................................................................................... 120 Curve Fit | Shapes Menu ............................................................................................. 120 Animate Shapes ...................................................................................................... 120 MAC......................................................................................................................... 120 Save Shapes ........................................................................................................... 120 Curve Fit | Close.......................................................................................................... 120 Modes | Display Traces Menu ..................................................................................... 120 Measurements ......................................................................................................... 120 Fit Functions ............................................................................................................ 120 CMIFs ...................................................................................................................... 121 MMIFs ...................................................................................................................... 121 Modes | Copy Traces Menu ........................................................................................ 121 xxi

Reference Volume IIB - Options Fit Functions ............................................................................................................ 121 CMIFs ...................................................................................................................... 121 MMIFs ...................................................................................................................... 121 Modes | Synthesize FRFs ........................................................................................... 121 Residue Mode Shapes ............................................................................................ 122 UMM Mode Shapes ................................................................................................. 122 Comparing Synthesized & Measured FRFs ............................................................. 123 Shape Table Basic Modal Analysis Commands .......................................................... 124 Display Menu ........................................................................................................... 124 Tools Menu .............................................................................................................. 124 Display | MAC.............................................................................................................. 124 What is MAC? .......................................................................................................... 125 What is CoMAC? ..................................................................................................... 125 What is a Shape Difference Indicator (SDI)? ........................................................... 125 MAC Window Commands........................................................................................ 126 File | Copy Graphics to Clipboard ........................................................................ 126 File | Print ............................................................................................................. 126 File | Close ........................................................................................................... 126 Display | Spreadsheet .......................................................................................... 126 Display | 3D Bar Chart ......................................................................................... 126 Display | Values ................................................................................................... 127 Display | MAC, CoMAC, SDI ................................................................................ 127 Display | Real Scale Factor, Imaginary Scale Factor, Scale Factor Magnitude.... 127 Structure Options Animation Tab ............................................................................. 127 Show MAC ........................................................................................................... 128 Show SDI ............................................................................................................. 128 Animate | Compare Shapes | Synchronize MAC ..................................................... 128 What is a Modal Model? .............................................................................................. 129 Uses of a Modal Model ............................................................................................ 129 Tools | Scaling Menu ................................................................................................... 129 Residue to UMM Shapes ......................................................................................... 129 Multiple Reference Shapes .................................................................................. 129 MAC Column ........................................................................................................ 130 xxii

Table of Contents UMM to Residue Shapes ......................................................................................... 130 Residue Mode Shapes ............................................................................................ 131 Residue Mode Shape Units ..................................................................................... 131 Editing Residue Units .............................................................................................. 131 UMM Mode Shapes ................................................................................................. 131 UMM Displacement Response Units ....................................................................... 132 Compatibility Between UMM and Structure Units for SDM ...................................... 132 Tools | Synthesize FRFs ............................................................................................. 132 Multi-Reference Modal Analysis Commands............................................................... 133 Data Block Multi-Reference Modal Commands ........................................................... 133 Multi-Reference Methods......................................................................................... 133 Stability Tab ............................................................................................................. 133 Animate Menu ......................................................................................................... 133 Display Menu ........................................................................................................... 133 Modes Menu ............................................................................................................ 133 Special Mouse & Keyboard Operations ................................................................... 133 When Is Multi-Reference Modal Analysis Necessary? ................................................ 133 Single Reference versus Multi-Reference FRFs ...................................................... 134 Mult-Reference Modal Test ......................................................................................... 134 Multiple Shaker Test ................................................................................................ 134 Multiple Reference Roving Impact Test ................................................................... 135 Multi-Reference Mode Indicators ................................................................................ 135 Multi-Reference CMIF.............................................................................................. 135 Multi-Reference MMIF ............................................................................................. 135 Modal Participation Factors ..................................................................................... 135 Multi-Reference Parameter Estimation........................................................................ 136 Multi-Reference Polynomial ..................................................................................... 136 Stability Diagram Methods ....................................................................................... 136 Alias Free Polynomial .......................................................................................... 136 Complex Exponential ........................................................................................... 136 Z Polynomial ........................................................................................................ 136 Methods Column...................................................................................................... 136 Stability Diagram ......................................................................................................... 136 xxiii

Reference Volume IIB - Options Why Use a Stability Diagram? ................................................................................. 137 Stable Group of Poles.............................................................................................. 137 Poles Diagram ......................................................................................................... 138 Changing the Stable Group Tolerances................................................................... 139 Percentage of Critical Damping or 3 dB Bandwidth Damping.................................. 139 Displaying Pole Values ............................................................................................ 139 Save Groups Button ................................................................................................ 139 Stability | Pole Selection Box ................................................................................... 140 Stability | Clear Stability Diagram............................................................................. 140 Display | Complexity Plot (Data Block) ........................................................................ 140 Animate | Normalize Shapes (Data Block) .................................................................. 140 Display | Magnitude Ranking (Data Block) .................................................................. 141 Which Magnitudes Are Ranked? ............................................................................. 141 Magnitude Values .................................................................................................... 141 Modes Modal Decomposition ...................................................................................... 141 Shape Table Multi-Reference Modal Commands........................................................ 142 Animate Menu ......................................................................................................... 142 Display Menu ........................................................................................................... 142 Tools menu .............................................................................................................. 142 MPC (Modal Phase Colinearity) Column ................................................................. 142 Display | Shape DOFs | M,C,K .................................................................................... 143 Animate | Normalize Shapes (Shape Table) ............................................................... 143 Display | Poles............................................................................................................. 143 Display | Complexity Plot (Shape Table) ..................................................................... 144 Normal Shape .......................................................................................................... 144 Complex Shape ....................................................................................................... 144 Normalized Shapes ................................................................................................. 145 MPC (Modal Phase Colinearity) .............................................................................. 145 Flipping the Sign of a Shape .................................................................................... 146 Display | Magnitude Ranking (Shape Table) ............................................................... 146 Which Magnitudes Are Ranked? ............................................................................. 146 Magnitude Values .................................................................................................... 146 Tools | Shape Expansion ............................................................................................ 146 xxiv

Table of Contents Draw or Animate | Normalize Shapes ......................................................................... 147 Operational Modal Analysis (OMA) Commands .......................................................... 149 Data Block OMA Commands ...................................................................................... 149 Transform Menu ...................................................................................................... 149 Curve Fitting OMA Measurements .............................................................................. 149 Fourier Spectra .................................................................................................... 149 Cross Spectra ...................................................................................................... 149 ODS FRFs ........................................................................................................... 149 Flat Force Spectrum ................................................................................................ 150 Transform | Increase Resolution ................................................................................. 150 Transform | Window Traces | (DeConvolution window) ............................................... 151 Shape Table OMA Commands ................................................................................... 152 Three Types of Mode Shapes ................................................................................. 152 UMM Mode Shapes ............................................................................................. 152 FEA Mode Shapes ............................................................................................... 153 Residue Mode Shapes ......................................................................................... 153 Scaling Operational Mode Shapes or ODS's ........................................................... 153 Tools | Scaling | Unscaled to Scaled Shapes .......................................................... 153 Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands .......................... 155 Data Block MIMO Commands ..................................................................................... 155 Transform | MIMO Menu .......................................................................................... 155 What is a MIMO (Multi-Input Multi-Output) Model? ..................................................... 155 MIMO Calculations .................................................................................................. 155 Transfer Function..................................................................................................... 155 Frequency Response Function (FRF)...................................................................... 156 Transmissibility ........................................................................................................ 156 Trace DOFs and Input Output ..................................................................................... 156 DOF Format ............................................................................................................. 156 MIMO DOFs ............................................................................................................ 157 Measurement Set Number....................................................................................... 157 Editing Trace DOFs ................................................................................................. 157 Transform | MIMO | Transfer Functions....................................................................... 157 Using Auto & Cross Spectra .................................................................................... 158 xxv

Reference Volume IIB - Options Using Time Waveforms ........................................................................................... 158 Triggering ................................................................................................................ 159 Trigger Level & Pre-Trigger Delay ........................................................................... 160 Time Domain Windowing ......................................................................................... 160 Calculating Outputs From Inputs ................................................................................. 160 Time Domain Outputs or Fourier Spectra ................................................................ 160 Cross Spectra .......................................................................................................... 161 Output Auto Spectra ................................................................................................ 162 Transform | MIMO | Outputs ........................................................................................ 162 Time Domain Inputs................................................................................................. 163 FRFs from Modal Parameters ................................................................................. 163 Transfer Function Matrix .......................................................................................... 163 Calculating Inputs From Outputs ................................................................................. 164 Time Domain Inputs or Fourier spectra ................................................................... 164 Input Auto spectra From Cross spectra ................................................................... 164 Input Auto spectra from Output Auto spectra........................................................... 164 Transform | MIMO | Inputs........................................................................................... 165 Transform | MIMO | Sinusoidal ODS ........................................................................... 166 Animating the ODS .................................................................................................. 166 Shape Table MIMO Command .................................................................................... 166 Tools | Sinusoidal ODS ............................................................................................ 167 Acoustics Commands.................................................................................................. 169 Data Block Acoustics Commands ............................................................................... 169 Display Menu ........................................................................................................... 169 Tools | Animate Using | Sources.............................................................................. 169 Acoustics Menu ....................................................................................................... 169 Acoustics | Calculate Menu .................................................................................. 169 Acoustics | Intensity to Power .............................................................................. 169 Acoustics | Source Ranking menu ....................................................................... 169 Acoustics | Tone Calibration menu....................................................................... 169 Trace Spreadsheet Columns ................................................................................... 169 dB Reference Value Column ................................................................................ 169 Weight Column..................................................................................................... 169 xxvi

Table of Contents Source Column .................................................................................................... 169 Acoustic Surfaces........................................................................................................ 170 Display | Display Objects | Points | Acoustic Normals.............................................. 170 Display Menu .............................................................................................................. 170 Display | Real........................................................................................................... 170 Octave Band Data ................................................................................................... 171 Real Part in dB Reference Units .............................................................................. 171 Display | Magnitude ................................................................................................. 171 Linear, Log or dB ..................................................................................................... 172 dB Units for Linear Versus Power Quantities........................................................... 172 Magnitude in dB Reference Units ............................................................................ 172 Tools | Animate Using | Sources (Data Block)............................................................. 173 Acoustics | ABC Weighting .......................................................................................... 173 Acoustics | Narrow to Octave Band ............................................................................. 173 Acoustics | Calculate | SPL ......................................................................................... 174 Time Responses ...................................................................................................... 175 Fourier Spectra or Auto Spectra .............................................................................. 175 Acoustics | Calculate | Intensity ................................................................................... 175 Time Responses ...................................................................................................... 176 Cross Spectra .......................................................................................................... 176 SPL and P-I Index.................................................................................................... 176 Acoustics | Calculate | P-I Index .................................................................................. 177 Acoustics | Intensity to Power...................................................................................... 177 Animating Sound Power & Intensity......................................................................... 177 Acoustics | Source Ranking | Chart ............................................................................. 178 Values at Cursor Position ........................................................................................ 178 Which Magnitudes Are Ranked? ............................................................................. 178 Status Bar ................................................................................................................ 178 Source Ranking ....................................................................................................... 178 Naming Acoustic Sources ........................................................................................ 179 Source Ranking | Save Shape By Source ................................................................... 179 Acoustics | Tone Calibration Menu .............................................................................. 179 Tone Calibration | Calculate..................................................................................... 179 xxvii

Reference Volume IIB - Options Tone Calibration | Apply .......................................................................................... 180 Shape Table Acoustics Commands ............................................................................ 180 Display | Source Ranking ........................................................................................ 180 Tools | Animate Using | Sources.............................................................................. 180 DOFs Spreadsheet Columns ................................................................................... 180 Weight Column..................................................................................................... 180 Source Column .................................................................................................... 180 Display | Source Ranking ............................................................................................ 180 Which Magnitudes Are Ranked? ............................................................................. 181 Status Bar ................................................................................................................ 181 Source Ranking ....................................................................................................... 181 Naming Acoustic Sources ........................................................................................ 181 Tools | Animate Using | Sources (Shape Table).......................................................... 182 Structural Dynamics Modification (SDM) Commands.................................................. 183 Structure Window SDM Commands ........................................................................... 183 SDM Menu ............................................................................................................... 183 FEA Menu ................................................................................................................ 183 FEA Objects ............................................................................................................ 183 What is SDM? ............................................................................................................. 183 FEA Objects ................................................................................................................ 184 FEA Mass ................................................................................................................ 184 FEA Spring & FEA Damper ..................................................................................... 184 FEA Rod .................................................................................................................. 184 FEA Bar ................................................................................................................... 185 FEA Triangle & FEA Quad Plate ............................................................................. 185 Plate Stiffness Multiplier ....................................................................................... 185 FEA Tetra, FEA Prism & FEA Brick ......................................................................... 186 Adding FEA Objects to a Structure Model ................................................................... 186 Validating UMM Mode Shapes .................................................................................... 187 Round Trip Check .................................................................................................... 187 SDM | Calculate New Modes....................................................................................... 187 UMM Mode Shape and Structure Units ................................................................... 187 FEA Objects ............................................................................................................ 188 xxviii

Table of Contents SDM | Modal Sensitivity .............................................................................................. 188 Upper Spreadsheet .............................................................................................. 189 Lower Spreadsheet .............................................................................................. 190 Error Function .......................................................................................................... 190 Solution Space ........................................................................................................ 190 Solution Space Example ...................................................................................... 190 Calculation Process ................................................................................................. 191 Before Starting a Calculation ................................................................................... 191 STOP Calculation .................................................................................................... 191 Solution Scroll Bar ................................................................................................... 192 Bar Graphics ........................................................................................................ 192 Calculating New Modes ........................................................................................... 192 SDM | Add Tuned Absorber ........................................................................................ 192 Before Adding The Absorber ................................................................................ 193 SDM | Interpolate Source ............................................................................................ 194 FEA | Materials List ..................................................................................................... 194 File Menu ................................................................................................................. 195 File | Import .......................................................................................................... 195 File | Print Spreadsheet ........................................................................................ 195 Edit Menu ................................................................................................................ 195 Edit | Add.............................................................................................................. 195 Edit | Delete.......................................................................................................... 195 Display Menu ........................................................................................................... 195 Display | Center window ....................................................................................... 195 Display | Toolbar .................................................................................................. 195 FEA | Properties List ................................................................................................... 196 File Menu ................................................................................................................. 196 File | Import .......................................................................................................... 196 File | Print Spreadsheet ........................................................................................ 196 Edit Menu ................................................................................................................ 197 Edit | Add.............................................................................................................. 197 Edit | Delete.......................................................................................................... 197 Display Menu ........................................................................................................... 197 xxix

Reference Volume IIB - Options Display | Center window ....................................................................................... 197 Display | Toolbar .................................................................................................. 197 FEA | FEA Objects List................................................................................................ 197 FEA | Calculate FEA Modes ........................................................................................ 198 Normal Modes ......................................................................................................... 198 Number of Modes .................................................................................................... 198 Rigid Body Offset (Hz) ............................................................................................. 198 Maximum Iterations ................................................................................................. 198 Include Damping ...................................................................................................... 198 Compute from Mode Shapes ............................................................................... 198 Experimental Finite Element Analysis (FEA) Commands............................................ 201 Structure Window Experimental FEA Commands ....................................................... 201 FEA Menu ................................................................................................................ 201 FEA Objects ............................................................................................................ 201 FEA Objects ................................................................................................................ 201 FEA Mass ................................................................................................................ 201 FEA Spring & FEA Damper ..................................................................................... 201 FEA Rod .................................................................................................................. 202 FEA Bar ................................................................................................................... 202 FEA Triangle & FEA Quad Plate ............................................................................. 202 Plate Stiffness Multiplier ....................................................................................... 202 FEA Tetra, FEA Prism & FEA Brick ......................................................................... 203 FEA | Materials List ..................................................................................................... 203 File Menu ................................................................................................................. 204 File | Import .......................................................................................................... 204 File | Print Spreadsheet ........................................................................................ 204 Edit Menu ................................................................................................................ 204 Edit | Add.............................................................................................................. 204 Edit | Delete.......................................................................................................... 204 Display Menu ........................................................................................................... 204 Display | Center window ....................................................................................... 204 Display | Toolbar .................................................................................................. 204 FEA | Properties List ................................................................................................... 205 xxx

Table of Contents File Menu ................................................................................................................. 205 File | Import .......................................................................................................... 205 File | Print Spreadsheet ........................................................................................ 205 Edit Menu ................................................................................................................ 206 Edit | Add.............................................................................................................. 206 Edit | Delete.......................................................................................................... 206 Display Menu ........................................................................................................... 206 Display | Center window ....................................................................................... 206 Display | Toolbar .................................................................................................. 206 FEA | FEA Objects List................................................................................................ 206 FEA | FEA Assistant .................................................................................................... 207 Add FEA Objects Tab .............................................................................................. 207 Rules for Adding FEA Objects ................................................................................. 207 FEA | Calculate FEA Modes ........................................................................................ 208 Normal Modes ......................................................................................................... 208 Number of Modes .................................................................................................... 208 Rigid Body Offset (Hz) ............................................................................................. 208 Maximum Iterations ................................................................................................. 208 Include Damping ...................................................................................................... 208 Compute from Mode Shapes ............................................................................... 209 FEA | Point Matching................................................................................................... 209 Point Matching Steps ............................................................................................... 210 Creating Two SubStructures .................................................................................... 210 Aligning the SubStructures ...................................................................................... 210 FEA | Export the Model ............................................................................................... 211 FEA Model Updating Commands ................................................................................ 213 Structure Window FEA Model Updating Commands ................................................... 213 Targeted FEA Model Updating ................................................................................ 213 Difference Between SDM and Model Updating ....................................................... 213 FEA Objects ................................................................................................................ 213 FEA Mass ................................................................................................................ 213 FEA Spring & FEA Damper ..................................................................................... 214 FEA Rod .................................................................................................................. 214 xxxi

Reference Volume IIB - Options FEA Bar ................................................................................................................... 214 FEA Triangle & FEA Quad Plate ............................................................................. 214 Plate Stiffness Multiplier ....................................................................................... 215 FEA Tetra, FEA Prism & FEA Brick ......................................................................... 215 FEA | Model Updating ................................................................................................. 216 Command Requirements ......................................................................................... 216 Upper Spreadsheet.................................................................................................. 218 Error Function .......................................................................................................... 218 Lower Spreadsheet.................................................................................................. 218 Solution Space Example ...................................................................................... 218 Calculating Solutions ............................................................................................... 218 Solution Scroll Bar ................................................................................................... 219 Bar Graphics ............................................................................................................ 219 Saving a Solution ..................................................................................................... 220 FEA | Calculate Updated FEA Modes ......................................................................... 220 Glossary ...................................................................................................................... 223 Index ........................................................................................................................... 237

xxxii

Acquisition Window Commands

Acquisition Window. This chapter contains descriptions of all of the commands in an Acquisition window. NOTE: The Acquisition window is optional. This window is only provided in ME'scope if one of the VES7xx Data Acquisition options is authorized in your software. Check Help | About to verify authorization of this option. The Acquisition window is used for; •

Setting up a third party multi-channel hardware acquisition front end and acquiring fixed length blocks of digitized time domain data from it.

•

Post-processing the blocks of time domain data and calculating most of the popular singlechannel and cross-channel measurement functions.

•

Displaying Operating Deflection Shapes (ODS's) directly from measurement data on a 3D model in a connected Structure window.

Graphics Areas & Spreadsheets The Acquisition window contains a Trace graphics area on the left, and tabs and spreadsheets on the right. •

A vertical blue splitter bar separates the Trace graphics area from the Traces spreadsheet.

•

A vertical red splitter bar separates the Trace graphics & spreadsheet on the left from Control tabs and a Channels spreadsheet on the right.

•

A horizontal blue splitter bar separates the upper & lower Trace graphics areas on the left side.

•

The upper Trace graphics displays the time domain waveforms acquired from an acquisition front end.

•

The lower Trace graphics displays calculated waveforms such as FRFs, Coherences, etc.

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Reference Volume IIB - Options •

Click & drag the vertical blue splitter bar horizontally in the window to make the Trace graphics or the Traces spreadsheet larger.

Menu Commands Menu command descriptions are ordered by command menu (from left to right), and then by the commands in each menu (from top to bottom). •

Each command is executed by choosing it from its command menu, or by clicking on its Tool if it is on a Toolbar.

•

See the Command Toolbars section in the Tutorial - Introduction to ME'scopeVES chapter for details on customizing the Toolbars in this window.

Acquisition Mouse & Keyboard Operations NOTE: To enlarge this text, click on it, hold down the Ctrl key and spin the mouse wheel. Right Click Menus •

Right click on a spreadsheet to display a menu of frequently used spreadsheet commands.

•

Right click on the graphics area to display a menu of frequently used window commands.

Ordering Spreadsheet Columns •

Click on a spreadsheet column header and drag it to its new position.

Scrolling Spreadsheets If a vertical scroll bar is displayed next to a spreadsheet, •

Click on the spreadsheet and spin the mouse wheel to scroll the spreadsheet vertically.

Spreadsheet Text Size •

To change the text size, click on the spreadsheet, hold down the Ctrl key, and spin the mouse wheel.

Scrolling the Trace Display •

Click on the vertical scroll bar, and spin the mouse wheel.

•

Following a Zoom operation, click on the horizontal scroll bar and spin the mouse wheel.

Zooming •

Click in the Trace graphics area, and spin the mouse wheel.

Panning a Zoomed Display •

Hold down the Shift key, and click & drag to Pan the display of Zoomed Trace data.

•

Or use the horizontal scroll bar displayed below the Traces.

Moving the Cursors

2

Acquisition Window Commands Line Cursor •

Position the mouse pointer in the Trace graphics area, and click, or click & drag the mouse.

Peak or Band Cursor •

Position the mouse pointer inside the band, and click & drag the mouse.

Moving an Edge of the Peak or Band Cursor •

Position the mouse pointer outside the band, and click & drag the mouse.

Selecting a Range of Traces •

Click on a Select Trace button in the Traces spreadsheet of the first Trace.

•

Hold down the Shift key, and click on the Select Trace button of the last Trace of the range of Traces.

Toggle Trace Selection •

Hold down the Ctrl key and click in the Trace graphics area to toggle the selection of a Trace.

NOTE: A selected Trace has a shaded background in the graphics area, and its Select Trace button will change from No to Yes in the Traces spreadsheet. Trace Values •

Hold down the Alt key to display cursor values at the nearest sample to the mouse pointer.

•

Left click to display the values permanently.

•

Right click to erase all permanent values.

Cut, Copy & Paste Text •

Select one or more spreadsheet text cells.

•

Hold down the Ctrl key and press the X key to Cut the selected text to the Clipboard.

•

Hold down the Ctrl key and press the C key to Copy the selected text to the Clipboard.

•

Hold down the Ctrl key and press the V key to Paste text from the Clipboard into the selected cells.

Graphics Scroll Bars Under certain conditions, both vertical & horizontal scroll bars will be displayed on the right side and below the graphics area in an Acquisition window. Vertical Scroll Bar If the number of displayed Traces is less than the total number of Traces, a scroll bar is displayed on the right side of the Trace graphics area. •

Click on the scroll bar and spin the mouse wheel to scroll through the Traces.

Horizontal Scroll Bar

3

Reference Volume IIB - Options When the Trace display is Zoomed, not all of the Trace samples are displayed, and a scroll bar is displayed below the Trace graphics area. •

Click & drag on the scroll bar to scroll through the Trace samples.

•

Or hold down the Shift key and drag in the graphics area to scroll through the Trace samples.

•

Or click on the scroll bar and spin the mouse wheel.

Toolbar Lists Two lists of Data Block and Structure files are listed on the Acquisition window Toolbar. •

Choose a Data Block for saving (and accumulating) measurements acquired with the Acquisition window.

•

Choose a Structure for assigning channel DOFs in Measurement Sets, or for creating Animation equations using the M#s in the lower Traces of the Acquisition window.

Traces Spreadsheet The Traces spreadsheet displays the Trace properties of either the upper or lower Traces in the Acquisition window, whichever are active. •

Click on the graphics area of the upper or lower Traces to make them active.

•

Or execute Display | Active Graph to toggle the active Traces between the upper & lower Traces.

•

Drag the Vertical Blue Splitter Bar to the left to view the Traces spreadsheet.

•

Or execute Display | Traces Spreadsheet.

Acquisition Window Showing Lower Traces Spreadsheet.

4

Acquisition Window Commands See the Traces Spreadsheet section in the Data Block Window Commands chapter for details regarding the Traces spreadsheet.

Channels Spreadsheet All of the properties associated with the front end data acquisition channels are listed in the Channels spreadsheet. •

Each row in the Channels spreadsheet contains the properties of one channel.

•

Each column of the spreadsheet contains a property of all front end channels.

•

Drag the Vertical Red Splitter Bar to the left to display more of the Channels spreadsheet.

Acquisition Window Showing Channels Spreadsheet. Setup, Units, and DOFs Tabs The Channels spreadsheet contains three (lower) tabs (Setup, Units, and DOFs), which define the properties of each front end channel. The Select Channel, Active, and DOF columns are common to all three spreadsheet tabs. Active Column Used to make channels active. If a channel is active, data will acquired on the channel when either Acquire | Start or Acquire | Front End Scope is executed. •

To make a channel active, click on its Active button until it reads Yes.

•

To make two or more channels active, select them in the Select Channel column and double click on the Active column heading.

5

Reference Volume IIB - Options NOTE: When data is acquired from the front end, a time domain Trace is displayed in the upper Trace graphics area for each active Channel. DOF Column Used to define the channel DOF. A DOF is typically the Point number & direction of the transducer location on the test article. NOTE: Using channel DOFs is optional, but it is strongly recommended as a convenient way of identifying where measurements were made on a test article. •

For example, a DOF = 1X means the transducer is located at Point No. 1 on the structure and senses motion in the X direction.

Editing Channel Properties •

Click on the channel property cell to toggle its button, edit its text contents, or select one of the choices from a drop down list.

•

Or double click on a property column heading to change the property of all (or selected) channels.

Setup Tab

Acquisition Window Setup Tab. Signal Level Column Indicates the signal level for each channel during acquisition. Label Column Used to enter a text description of each channel. Input Output Column Defines the signal on a channel as either an Input, Output, or Both. •

6

An Output is the numerator of an FRF, or the (moving) Roving transducer of a set of measurements.

Acquisition Window Commands •

An Input is the denominator of an FRF, or the (fixed) Reference transducer of a Cross channel measurement.

ADC Coupling Column Applies either AC or DC coupling to each acquisition channel. •

AC coupling removes the lower frequencies from a signal by applying a high pass analog filter to the signal before digitizing it.

•

AC coupling should be applied to all dynamic signals, like vibration or acoustics signals.

•

DC coupling does not remove the lower frequencies from a signal.

•

DC coupling should be applied to all static or quasi-static signals like temperature, pressure, voltage or current.

Transducer Power Column Turns the power ON/OFF to the transducer connected to each channel. •

Many types of transducers have built-in electronics and therefore must be supplied with power in order to operate.

ADC Range Column Defines the input voltage range analog to digital converter (ADC) for each channel. Data Type Column Defines the data type for each acquisition channel. Data type can be Translational (vibration), Scalar (temperature, pressure), or Machine Rotation (torsional vibration). Window Type Column Defines the type of time domain window to be applied to each channel signal before and frequency domain signal processing is applied to it. Refer to the Signal Processing Commands chapter for more details on the use of these windows. Window Value Column Used to specify a numerical value for either a Force or an Exponential window NOTE: Only the Force and Exponential windows use the values in this column. Units Tab

7

Reference Volume IIB - Options

Acquisition Window Units Tab. Units Column Defines the acquired data in engineering units for each channel. •

Typical Output units are displacement, velocity, or acceleration units.

•

Typical Input units are excitation force units (for an FRF calculation) .

Display Column Displays the upper (time domain) Traces in either engineering units or volts. •

If Units is chosen, each upper Trace is displayed in the units specified in the Units column.

•

If Volts is chosen, each upper Trace is displayed as the voltage of the signal acquired on its channel.

Transducer Sensitivity, Sensitivity Units & Transducer Units Columns These three columns are used together to scale the data on each channel into the Transducer Units. •

Sensitivity units are either Unit/V (engineering units per volt), V/Unit (volts per engineering unit), Unit/mV (engineering units per millivolt), or mV/Unit (millivolts per engineering unit)

NOTE: If the channel Units (entered into the Units column) are different from the Transducer Units, the channel data will be integrated or differentiated from the Transducer Units to the channel Units, if possible. DOFs Tab

8

Acquisition Window Commands

Acquisition Window DOFs Tab. Point Number & Direction Columns These two columns are used to select the Point number & direction of measurement for each acquisition channel. •

Point numbers can be incremented or decremented by using the arrows in each cell, or they can be typed into each cell.

•

Point directions are chosen from the drop down list next to each cell.

NOTE: Using channel DOFs is optional, but it is strongly recommended as a convenient way of identifying where measurements were made on a test article. Manual Increment Column Increments the Point number & direction (in their respective columns), according to the Increment Point By and Increment Direction By columns. Increment Point By and Increment Direction By Columns These two columns are used to specify how the Point number & direction are to be incremented when the Manual Increment button is pressed for each channel.

Measurement Tab The Acquisition window acquires finite length blocks of time domain data from all front end channels that are active in the Channels spreadsheet. •

The acquired time domain data is displayed in the upper Trace graphics area on the left side of the Acquisition window.

The Measurement tab is used for the following purposes; •

Choosing the measurement functions to be calculated from the upper Traces, and displayed in the lower Traces graphics area of the window.

9

Reference Volume IIB - Options •

Choosing the type of averaging and the number of averages to be used to calculate the lower Traces.

•

Enabling Increment Roving DOFs to increment the Roving DOFs between successive acquisitions (Measurement Sets).

Measurement Tab. Time & Frequency Measurements •

Click on the Time or Frequency button in the Domain section to choose either time domain or frequency domain calculations for the lower Traces,

If Time is chosen, •

Check Time waveforms, Auto or Cross Correlations, Impulse Responses, Inverse Coherences, or Inverse ODS FRFs to calculate any of these time domain functions

If Frequency is chosen, •

Check Fourier spectra, Auto or Cross spectra, FRFs (Transfer functions), Coherences, or ODS FRFs to calculate any of these frequency domain functions.

If Remove DC is checked, •

DC components are removed from all acquired channel signals.

Averaging Defines the number of spectrum averages to be calculated during the calculation of measurement functions for the lower Traces. •

For impact testing, between 3 & 5 averages are recommended.

•

For shaker testing using random signals, between 25 &100 averages are recommended.

Averaging Method Linear averaging (also called stable averaging) is the same as summing together all of the spectral estimates and dividing by the number of averages. •

10

th

The N stable average is calculated with the formula,

Acquisition Window Commands Average (N) = (1 / N) x New Spectrum + (1 - (1 / N)) x Average (N-1) Peak Hold averaging retains the peak value at each sample from all spectral estimates in the final spectrum. •

th

th

The J sample of the N average is determined with the formula, Average (N,J) = maximum (New Spectrum, Average (N-1,J) )

Increment DOFs •

If Increment Roving DOFs is checked, DOFs are incremented each time Acquire | Save Traces (F7) or Acquire | Save & Start (F8) is executed.

•

If Increment Roving DOFs is checked and Roving DOFs are Inputs, all of the Roving DOFs for the Input channels will be incremented with each new acquisition (each new Measurement Set).

•

If Increment Roving DOFs is checked and Roving DOFs are Outputs, all of the Roving DOFs for the Output channels will be incremented with each new acquisition (each new

•

DOFs are incremented according to the Increment Point By and Increment Direction settings on the DOFs tab in the Channels spreadsheet.

•

DOFs are also incremented when each a new Measurement Set is created using the Measurement Set | Add command.

Sampling Tab The Acquisition window acquires finite length blocks of time domain data from all front end channels that are active in the Channels spreadsheet. •

The acquired time domain data is displayed in the upper Trace graphics area on the left side of the Acquisition window.

The Sampling tab is used to setup two front end data acquisition parameters ; •

The Number of Samples of the upper (time domain) Traces.

•

The frequency domain Span (or frequency range) of the lower (calculated) Traces.

•

The front end sampling rate (1 / increment between time domain samples) is twice the frequency Span of the lower Traces.

NOTE: All other Time and Frequency parameters displayed on this tab are calculated from the Number of (time domain) Samples and the (frequency domain) Span. See the DFT and FFT section in the Signal Processing Commands chapter for details.

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Reference Volume IIB - Options

Acquisition Window Showing the Sampling Tab. Display Limits Defines the display limits of the lower Traces. The display limits can be entered in units of; 1. Percent of the frequency Span 2. Samples 3. X-axis units NOTE: Most multi-channel acquisition front ends band limit vibration signals using anti-aliasing filters with a cutoff frequency equal to 80% of the frequency Span, or 40% of the sampling rate. Data at frequencies greater than the cutoff frequency and less than the sampling rate is not alias-free and therefore should not be displayed or used for further analysis.

Triggering Tab Used to setup triggering for data acquisition on the active front end channels. •

When Free Run is chosen, data is acquired as quickly as possible from the front end.

•

When Trigger is chosen, a defined trigger condition must be met before data is acquired.

Auto Range Front End Channels Enables Auto Ranging of the channel voltage on all active acquisition channels. •

When checked, execute Acquisition | Front End Scope to initiate Auto Ranging.

Auto Ranging works in the following way;

12

•

Acquisition begins using the current voltage range on each acquisition channel.

•

The voltage range is decreased on each channel until an overload occurs.

•

When an overload occurs on a channel, its voltage range is increased until no overload occurs.

Acquisition Window Commands Free Run When Free Run is chosen, data is acquired as quickly as possible. â€˘

Choose Free Run when the test article is excited using a shaker, or to acquire operating (output only) data.

Acquisition Showing Trigger Lines Before Acquisition.

Acquisition After Triggered Acquisition Has Occurred.

13

Reference Volume IIB - Options Trigger When Trigger is chosen, data is acquired when the Trigger condition is met on the Trigger Channel. Trigger Channel The channel in the Channels spreadsheet on which the Trigger condition must be met before data acquisition will occur. •

For Impact Testing, the Trigger Channel should be the channel on which the impact force is acquired.

•

When Trigger Lines is checked, the Trigger lines are displayed on the Trigger Channel Trace in the upper Traces, as shown above.

+Slope, -Slope •

If +Slope is chosen, the trigger condition will occur when the signal is greater than the % of channel voltage on the Trigger Channel.

•

If -Slope is chosen, the trigger condition will occur when the signal is less than the % of channel voltage on the Trigger Channel.

Trigger Level (% of Channel voltage) •

The signal must exceed the % of Channel voltage on the Trigger Channel for acquisition to occur.

Trigger Lines •

When Trigger Lines is checked, the blue horizontal & green vertical Trigger lines are displayed on the Trigger Channel Trace, as shown above.

Lock Lines •

When Lock Lines is unchecked, click & drag the horizontal line vertically to change the trigger level.

•

When Lock Lines is checked, the horizontal line position can still be changed by changing the % of Channel voltage in the box provided.

Pre-Trigger Delay (samples) The number of samples of data to acquire before the trigger condition occurs. •

Pre-trigger delay is the number of samples that occur before the vertical Trigger line on the Trigger Channel Trace, as shown above.

Double Hit Line When a double hit condition is detected, the acquired data is rejected. When Double Hit Detection is enabled, a double hit condition will be signaled if more than one peak is detected above the red horizontal line. •

When Double Hit Line is checked, the red horizontal line is displayed on the Trigger Channel Trace (as shown above), and Double Hit Detection is enabled.

•

The vertical position of the Double Hit Line can be edited as a % of Channel voltage in the box provided.

Overload

14

Acquisition Window Commands When Overload is checked, and the Overload line is displayed, if any acquired data exceeds the overload level, the entire acquisition block is not used. NOTE: This function is only enabled when the Acquisition window is connected to front end acquisition hardware.

Source Tab NOTE: This tab is displayed if the VES-7610, VES-7620, or VES-3500 option is authorized in your software. (Check the Help | About box details to verify authorization of these options.) This tab is used to setup one or more output signals from the acquisition front end hardware to one or more shakers. •

Output signals are used to drive one or more shakers, and provide more controlled excitation of the test article.

•

Broad band random or chirp signals are used to excite structural resonances over the frequency Span of the acquired measurements.

Source Tab Showing Burst Random Output from Source Channel 1. To setup a Source signal, •

In the Signal Type section, choose a signal type.

•

Select a Burst Width percentage.

•

In the Active column, make one or more channels active.

•

In the DOF column, select a DOF on the test article to which the signal will be applied by a shaker.

•

in the Range column, select a voltage range for the signal.

15

Reference Volume IIB - Options Random & Chirp Signals Random & Chirp source signals are synthesized over the Frequency Span selected in the Sampling tab, and output to the front end hardware. •

A random signal is synthesized with a constant magnitude and random phase.

•

A chirp signal is a fast sine sweep signal, that is synthesized with a constant magnitude and random starting time.

Frequency Range Defines the frequency range of the Source signals as percentages of the Frequency Span selected in the Sampling tab. Burst Width Defines the percentage of the sampling window samples over which the synthesized Source signals are non-zero, followed by zeros for the remainder of the sampling window. •

Burst width is chosen so that the response signals will decay essentially to zero within the sampling window.

NOTE: Signals that decay within the sampling window are completely contained within the window, and therefore their spectra are leakage-free and don't require special time domain windowing. •

The amount of damping in the structure determines how quickly the structural responses will decay to zero in the sampling window.

To determine the required burst width, •

Choose a Burst Width percentage.

•

Execute Acquire | Front End Scope.

•

Scroll through the upper Traces to display the response channels of data.

If the response signals decay to zero within the window, the Burst Width of the source signal is correct, as shown below.

16

Acquisition Window Commands

Correct Burst Random Output Showing Responses Contained In The Window.

File Menu Save Acquisition Saves the Acquisition file into the current Project file on disk. Save Acquisition As... Saves a copy of the Acquisition file with a new name into the current Project file on disk. Save Graphics in File Saves the upper and lower Trace graphics areas into a disk file. NOTE: Graphics files can be saved in the JPG, GIF, PNG or BMP file formats. Copy to Clipboard | Trace Graphics Copies the upper and lower Trace graphics area to the Windows Clipboard. Copy to Clipboard | Traces Spreadsheet Copies the active Traces spreadsheet to the Windows Clipboard. Copy to Clipboard | Channels Spreadsheet Copies the Channels spreadsheet to the Windows Clipboard. Print | Trace Graphics

17

Reference Volume IIB - Options NOTE: The installed Windows printer must be a graphics printer to use these commands. Prints the upper and lower Trace graphics area to the Windows printer. Print | Traces Spreadsheet Prints the Traces spreadsheet to the Windows printer. Print | Channels Spreadsheet Prints the Channels spreadsheet to the Windows printer. Acquisition Properties Opens the Acquisition window Properties box, showing the properties of the active Traces. •

See File | Data Block Properties in the Data Block Window Commands chapter for details.

Acquisition Options Opens the Acquisition Options box. •

See File | Data Block Options in the Data Block Window Commands chapter for details.

Acquisition Options Dialog Box. File | Close Acquisition Closes the Acquisition window. •

The window can also be closed by clicking on the close button the window.

Opening a Window To open an Acquisition window in the Work Area,

18

in the upper right corner of

Acquisition Window Commands •

Double click on its name in either pane of the Project Panel.

•

Or right click on its name in either pane of the Project Panel, and execute Open from the menu.

Edit Menu Select Traces The commands in this menu are used to select or un-select Traces among the active Traces. •

A selected Trace has a shaded background, and its Select button is depressed in the Traces spreadsheet.

•

See Edit | Select Traces in the Data Block Window Commands chapter for details on selecting Traces.

Sort Traces Opens the Sort Traces dialog box that contains several options for sorting the active Traces. •

See Edit | Sort Traces | Sort By in the Data Block Window Commands chapter for details on sorting Traces.

Display Menu Center Acquisition Window Centers the Acquisition window in the Work Area of the ME'scope window. NOTE: Repeated execution of this command alternately centers the window and returns it to its former position. Traces Spreadsheet Moves the vertical blue splitter bar either to the left to display the Traces spreadsheet, or to the right to hide the spreadsheet. Acquisition Toolbars If checked, the Toolbars are displayed in the Acquisition window. Active Graph Toggles the active graph between the upper and lower Traces in the graphics area. NOTE: The Trace properties of the active graph are shown in the Traces spreadsheet. •

Click on the upper or lower Trace graphics area to make those Traces active.

•

Or click on the command tool to make the upper Traces active

or the lower Traces active

. Real, Imaginary, Magnitude, Phase Displays the Real part, Imaginary part, Magnitude, or Phase of the Traces on the active graph.

19

Reference Volume IIB - Options •

See Display | Magnitude in the Data Block Window Commands chapter for more details on these commands.

CoQuad, Bode, Nyquist Displays the Traces on the active graph in CoQuad, Bode, or Nyquist format. •

See Display | CoQuad, Bode, etc. in the Data Block Window Commands chapter for more details on these commands.

Cursor Menu The commands in this menu are used for displaying the Line, Band, and Peak cursors on the active Traces graph. •

See Display | Cursor in the Data Block Window Commands chapter for more details on these commands.

Zoom, mooZ Initiates a Zoom operation on the active Traces, or restores the display of all samples on the active Traces (reverses the Zoom). •

See Display | Zoom, mooZ in the Data Block Window Commands chapter for more details.

Maximize Maximizes the vertical (y-axis) display of each active Trace to make the data more visible. •

See Display | Maximize in the Data Block Window Commands chapter for more details.

Windowed Traces Displays the upper Traces following the application of a time domain window to them. •

20

The time domain window is chosen in the Window Type column of the Channels spreadsheet.

Acquisition Window Commands

Upper Traces Showing Hanning Window Applied.

Animate Menu Create Animation Equations (Assign M#s) Creates Measured animation equations on the model in a connected Structure window. •

Animation equations are created to retrieve data using the M#s in the lower Traces of the Acquisition window.

•

See Animate | Create Animation Equations (Assign M#s) in the Data Block Commands chapter for details.

Animate Shapes Initiates animation of shapes on the model in the connected Structure window using data from the lower Traces. •

To display the shape data correctly, the Animation equations on the structure model must contain the proper M#s for the lower Traces in the Acquisition window.

NOTE: If shapes do not display correctly during animation, new Animation equations may be required. Execute Create Animation Equations (Assign M#s) to create new Measured animation equations. Renumber M#s Renumbers the M#s of the active Traces in the Acquisition window. NOTE: Each Trace has a unique M#. M#s are used by the Animation equations in a Structure window to retrieve shape data from the current cursor location in an Acquisition window.

21

Reference Volume IIB - Options •

If the M#s of the lower Traces are renumbered, new Animation equations must be created by executing Animate | Create Animation Equations (Assign M#s).

Format Menu Rows/Columns, Overlaid, Overlaid by DOF, Strip Chart, Cascade, Contour Displays the active Traces in the Row/Column, Overlaid, Strip Chart, or Cascade format, respectively. •

See Format | Rows/Columns, etc. in the Data Block Window Commands chapter for more details.

Overlay By DOF If checked, all active Traces with the same DOFs are displayed together in Overlaid format. Y-axis Scaling, X-axis Scaling These two commands open dialog boxes for changing the Y-axis (vertical) and X-axis (horizontal) scaling on the active Traces. •

See Format | X-axis Scaling or Format | Y-axis Scaling in the Data Block Window Commands chapter for more details.

Saving Traces Into a Data Block The active Traces can be saved from the Acquisition window into a destination Data Block. •

Execute Display | Active Graph to make the desired upper or lower Traces active.

•

Execute Tools | Save Traces As.

A dialog box will open listing all of the available Data Blocks in the Project.

22

•

Only the destination Data Blocks that match the type of data (time or frequency) to be saved will be listed.

•

Once a destination Data Block has been chosen, it is listed in the destination Data Block list on the Toolbar, as shown below.\

Acquisition Window Commands

NOTE: If Tools | Save Traces is executed and no destination Data Block has been chosen, Tools | Save Traces As is executed. •

After each new Measurement Set of data is acquired, execute Tools | Save Traces to add the active Traces to the destination Data Block.

•

Once a destination Data Block has been chosen, Tools | Save and Start can also be used.

Tools Menu Save Shape Saves the Trace data at the current cursor location for all (or selected) active Traces into a Shape Table. •

If Display | Real

•

If Display | Imaginary

•

For all other data formats, the complex Trace data is saved.

•

If the Peak cursor is displayed, the peak value in each Trace is saved.

•

If the Band cursor is displayed, the average of the Trace data in the band is saved.

•

If the Order cursor is displayed, values for all visible orders in each Trace are saved as multiple shapes.

•

See Tools | Save Shape in the Data Block Window Commands chapter for details on this command.

is checked, only the Real part of the Trace data is saved. is checked, only the Imaginary part of the Trace data is saved.

Save Traces (F7)

23

Reference Volume IIB - Options Saves all (or selected) active Traces into the Data Block that is listed on the destination Data Block box on the Toolbar. This command can be used to accumulate measurements from multiple Measurement Sets into a Data Block. •

Traces are added to the Traces already in the destination Data Block.

NOTE: If no destination Data Block has been chosen, Tools | Save Traces As is automatically executed. Save Traces As Saves all (or selected) active Traces into a new Data Block. •

When executed, a dialog box will open for entering the name the new Data Block file.

Save and Start (F8) Saves the active Traces in the destination Data Block, and starts another acquisition. •

Executes Tools | Save Traces (F7) followed by Acquire | Start (F5).

Acquire Menu Start (F5) Initiates data acquisition from the acquisition front end.

24

•

The status of the acquisition process is reported in the message box on the Toolbar.

•

The acquired time domain Traces are displayed on the upper Traces, and calculated functions are displayed on the lower Traces of the graphics area.

•

Calculated functions are chosen on the Measurements tab.

Acquisition Window Commands Acquisition Window During Data Acquisition. Stop (F6) Terminates data acquisition from the acquisition front end. Front End Scope Initiates continuous acquisition from the acquisition front end. NOTE: If Free Run is selected on the Trigger tab, acquisition will continue until Acquire | Stop (F6) is executed. Reject Impact (F9) During an Impact test (if a Trigger has been enabled for acquiring data), executing this command will reject the last acquired block of data. Reject Overloads When checked, if an overload occurs on any active acquisition channel, the currently acquired block of time data will be rejected, and another average of data acquired.

Measurement Sets Menu What is a Measurement Set To calculate cross-channel functions like FRFs or Cross spectra, or to animate shapes from time waveforms, all active channels of data must be simultaneously acquired. When all measurements cannot be simultaneously acquired, Measurement Sets should be used to calculate cross-channel functions.

Each Measurement Set contains the Channel spreadsheet parameters required to simultaneously acquire a set of data with a multi-channel acquisition front end.

The current Measurement Set number is added to the DOFs of all acquired and calculated Traces.

Creating Measurement Sets before doing any data acquisition is a convenient way of defining all of the parameters necessary for each acquisition.

Measurement Sets are numbered, from 1 to the total number of Measurement Sets.

All Measurement Sets are saved as part of the Acquisition file when it is saved.

Use Measurement Sets When checked, Measurement Sets can be used during acquisition. •

When checked, the current Measurement Set number and total number of Measurement Sets is shown in the Active channel header of the Channels spreadsheet.

•

For example, MS 1 (of 5) indicates that Measurement Set 1 is current, and that 5 Measurement Sets have been created.

Next Set (F4), Current Set, Previous Set (F3) Changes the current Measurement Set to the Next Set (F4) or the Previous Set (F3), or allows you to enter the Current Set number.

25

Reference Volume IIB - Options •

All Channel spreadsheet values are changed to those for the current Measurement Set.

Add Measurement Sets Opens a dialog box for adding Measurement Sets to the Acquisition window. NOTE: New Measurement Sets are inserted following the current Measurement Set. Delete Measurement Set Deletes the current Measurement Set, and reduces the number of Measurement Sets by one. Show Channel DOFs Displays the channel DOFs of the current Measurement Set on the structure model in a connected Structure window. •

The connected Structure is displayed in the list box on the Toolbar.

•

Input DOFs are displayed in RED on the structure model.

•

Output DOFs are displayed in BLUE on the structure model.

•

Input & Output (Both) DOFs are displayed in GREEN on the structure model.

•

Repeatedly execute Next Set (F4) or Previous Set (F3) to display the channel DOFs of all Measurement Sets.

Channel DOFs Showing 1 Input DOF (15Z) and 9 Output DOFs (1X to 3Z). Assign Channel DOFs Enables the DOF creation operation for creating DOFs for each channel in the Channels spreadsheet. •

Channel DOFs are created by selecting Points & directions on the model in the connected Structure window.

Before executing this command,

26

Acquisition Window Commands •

Number each test Point on the structure model in the connected Structure window. (See Draw | Points | Point Numbering in the Structure Window Commands chapter for details.)

•

Orient the Measurement Axes at each test Point to coincide with the transducer measurement directions.

Execute this command to enable DOF creation, and execute the following steps; •

Click near a Point on the structure model to select it.

•

Click on an axis at the Point to create a DOF for the current channel (highlighted) in the Channels spreadsheet.

When finished creating all Channel DOFs for the current Measurement Set, •

Execute Next Set (F4) or Previous Set (F3), and repeat the steps above.

•

Execute this command again to terminate DOF creation.

Assigning Channel DOFs.

27

Macro-Program Window Commands

Program Window. This window is used for creating, editing, and running Macro-Programs in ME'scope. NOTE: The Program window and its commands described in this chapter are only available if the VES7000 Macro-Programming option is authorized for use in your software. Check Help | About to verify authorization of this option. •

Macro-Programs are useful for executing repetitive tasks in ME'scope.

•

Each row in the Commands spreadsheet contains a Program Step.

•

Each Step executes a command in a Target Window in the currently open Project.

Commands & Parameters Spreadsheets A Macro-Program window is divided into two spreadsheets, separated by a blue splitter bar. •

The Commands spreadsheet is (above or left of) the blue splitter bar.

•

The Parameters spreadsheet is (below or right of) the blue splitter bar.

•

Drag the blue splitter bar in the window to make either spreadsheet larger.

Menu Commands Menu command descriptions in this chapter are ordered by command menu (from left to right), and then by the commands in each menu (from top to bottom). •

Each command is executed by choosing it from its command menu, or by clicking on its Tool if it is on a Toolbar.

•

See the Command Toolbars section in the Tutorial - Introduction to ME'scope chapter for details on customizing the Toolbars in this window.

Program Menu in Each Window

29

Reference Volume IIB - Options When the VES-7000 Programming option in enabled, a Program menu is added to each window in ME'scope. •

Each command in the Program menu is executed in the same manner as any other command.

•

All Program menu commands are documented in this chapter.

Program Description

Program Window. •

A Program window is used to execute a sequence of ME'scope commands.

•

A Program window contains a list of Steps in its Commands (upper or left) spreadsheet.

•

Additional Program commands are provided in the Program menu in each window within ME'scope.

Commands Spreadsheet •

Each row in the Commands spreadsheet is a Program Step.

•

When the Program is run, the Steps in the Commands spreadsheet are executed in sequence, from top to bottom.

•

Each Step executes a command in one of the windows in the currently open Project.

The Program Commands spreadsheet contains the following columns; Select Step Column Used for selecting a Program Step. Selected steps can be duplicated, cut or copied (to the Program paste buffer), deleted, and pasted into Programs (from the Program paste buffer). •

Click on a Select Step button to select (green) or un-select (gray) the Step.

Toggling Step selection,

30

Macro-Program Window Commands •

Hold down the Ctrl key and click on a Select Step button to toggle its selection (select or unselect it).

Selecting a sequence of Steps, •

Click on the Select Step button on the first Step to select it.

•

Hold down the Shift key and click on the last Step in the sequence to select all of the Steps between the first & last steps.

Execute Step Column Used to execute (if Yes), or skip over (if No) a Program Step. Delay After Column Used for delaying the Program execution after a Program Step. NOTE: The amount of delay (in seconds) is entered on the Delay tab in the File | Program Options box. •

If Yes is chosen in this column, the Program execution will be delayed (in seconds) after the step has been executed and before the next command is executed.

Step Label Column Used for labeling a Step. Step Labels can be used as GoTo parameters in certain Program commands. Target Window Column The name of the ME'scope window where the current Step will be executed. •

Double click on this column and choose a Target Window from the drop down list of windows.

NOTE: Each Target Window must exist in the currently open Project. If a new Window is created by a Program Step, commands in the new Window can be executed in Program Steps that follow the creation of the new Window. Target Window Command The command to be executed in the Target Window of the current Step. After a Target Window is chosen, •

Double click in this column and choose a command from the command menu.

31

Reference Volume IIB - Options Open Dialog Column Used during execution of a Program to open a dialog box for entering parameters for the command in the current Step. •

If Yes, a dialog box will open for selecting or entering the parameters required by the command in the current Step.

•

If No, the parameters required by the command must be entered in the Parameters spreadsheet.

Parameters Spreadsheet Each row in the Parameters spreadsheet includes the following columns; Parameter Name Column A description of the command parameter. Parameter Value Column A value for the command parameter.

Program Mouse & Keyboard Operations NOTE: To enlarge this text, click on it, hold down the Ctrl key and spin the mouse wheel. Right Click Menus •

Right click on a spreadsheet to display a menu of frequently used commands.

Re-Ordering Spreadsheet Columns •

Click on a spreadsheet column header and drag it to its new position.

Scrolling Spreadsheets If a vertical scroll bar is displayed next to a spreadsheet, •

Click on the spreadsheet and spin the mouse wheel to scroll the spreadsheet vertically.

Spreadsheet Text Size •

To change the text size, click on the spreadsheet, hold down the Ctrl key, and spin the mouse wheel.

Cut, Copy & Paste Text •

Select one or more spreadsheet text cells.

•

Hold down the Ctrl key and press the X key to Cut the selected text to the Clipboard.

•

Hold down the Ctrl key and press the C key to Copy the selected text to the Clipboard.

•

Hold down the Ctrl key and press the V key to Paste text from the Clipboard into the selected cells.

File Menu

32

Macro-Program Window Commands

Save Program Saves the Macro-Program file into the currently open Project file on disk. Save Program As Saves a copy of the Macro-Program file with a new name into the currently open Project file on disk. Copy to Clipboard Menu These commands copy either the Commands spreadsheet (upper or left) or the Parameters spreadsheet (lower or right) to the Windows Clipboard. â€˘

Right click on the Column Heading of the Commands or Parameters spreadsheet to execute these commands.

Print Menu NOTE: The installed Windows printer must be a graphics printer to use these commands. These commands print either the Program spreadsheet (upper or left) or the Parameters spreadsheet (lower or right) on the attached Printer. â€˘

Right click on the Column Heading of the Commands or Parameters spreadsheet to execute these commands.

Program Options Opens the Program Options dialog box, where different options can be chosen for the Macro-Program window. Options are grouped under Tabs.

33

Reference Volume IIB - Options

Display Tab •

If Display Together is checked, when a Program Step is clicked on, its Target Window is displayed next to the Program window, in either Left-Right or Top-Bottom format.

•

If Suspend while running is checked, the Target Window will not be displayed when the Macro-Program is executing Steps.

Delay Tab •

If Delay after each Step is checked, execution of the Macro-Program is delayed after each Step by this time delay.

•

If Delay at the end of Program is checked, and Program | Run Continuous is executed, execution of the Program is delayed by this time delay before starting over at the beginning.

•

If Re-start Program after Delay is checked, execution of the Program is re-started after this time delay.

Show/Hide Tab All of the columns in a Program window (except the Select Step or Select Parameter column) can be hidden or shown. •

Right click on a spreadsheet and execute Show/Hide Columns to open the File | Program Options box.

•

On the Show/Hide tab, check columns to show them, un-check columns to hide them. .

Close Program Closes the Program window. •

Any window can also be closed by clicking on the close button the window.

Opening a Window To open a Macro-Program window in the Work Area,

34

in the upper right corner of

Macro-Program Window Commands •

Double click on the window name in either pane of the Project Panel.

•

Or right click on the window name in either pane of the Project Panel, and execute Open from the menu.

Edit Menu

Undo Restores the Program window to the state it was in before the last operation. •

This command can be used repeatedly to undo the last N operations, N = Number of edits saved.

•

The Number of edits saved is changed on the General tab in the Project | ME'scope Options dialog box.

Redo Restores the Program window to the state it was in before the last execution of the Edit | Undo command. Select Steps Menu Used for selecting Program Steps. Select All Selects all Program Steps. Invert Selection Inverts the Step selection. All selected Steps are un-selected, and all un-selected Steps are selected. Select None Un-selects all Program Steps. Cut selected Steps Removes the selected Steps from the Program and puts them in the Program paste buffer. Copy selected Steps

35

Reference Volume IIB - Options Copies the selected Steps of the Program into the Program paste buffer. Paste Steps Pastes Steps from the Program paste buffer into the Program following the last selected Step. Insert selected Steps Inserts the selected Steps into the Program following the last selected Step. •

All Steps are then un-selected, and the inserted Steps are selected.

•

If no Steps are selected, the last Program Step is duplicated at the end of the Program.

Delete selected Steps Deletes (removes) all selected Steps from the Program. Move Selected Steps Up/Down Moves the selected Steps either up or down in the Program spreadsheet. All Window Commands Adds all the programmable commands in a Target Window to the Program window. •

A dialog box will open from which a currently open Target Window can be chosen.

NOTE: This command is convenient for listing the Descriptions of all programmable commands in a Target Window.

Display menu

Center Program Window Centers the Program window in the Work Area of the ME'scope window. •

Repeated execution centers the window and returns it to its former position.

Program Toolbars If checked, the Toolbars are displayed in the Program window. Split

36

Macro-Program Window Commands Displays the two spreadsheets in side-by-side or upper-lower format. •

In side-by-side format, the Commands spreadsheet is on the left and the Parameters spreadsheet is on the right of the blue splitter bar.

•

In upper-lower format, the Commands spreadsheet is above and the Parameters spreadsheet is below the blue splitter bar.

Parameters If checked, the Parameters spreadsheet is displayed. Target Window If checked, the Target window for each Program step is displayed next to the Program window. •

See the Display tab under File | Program Options for details.

Run Menu

All of these commands execute Steps (except those with Execute Step = No) in sequence, from the top to the bottom of the Commands spreadsheet in the Program window. Run Once Executes all Steps with Execute Step = Yes in sequence, starting on the first Step and stopping after execution of the last Step in the Commands spreadsheet. Run Continuous Executes all Steps with Execute Step = Yes in sequence without stopping, starting on the first Step in the Commands spreadsheet. After the last Step is executed, execution resumes starting at the first Step. Stop Stops execution of the Macro-Program. Continue Executes all Steps with Execute Step = Yes in sequence, starting from the current Step and stopping after execution of the last Step in the Commands spreadsheet. Continue to selected Step

37

Reference Volume IIB - Options Executes all Steps with Execute Step = Yes in sequence, starting from the current Step and stopping after execution of the first selected Step in the Commands spreadsheet. Single Step Executes the current Step in the Commands spreadsheet.

Program Menu

This menu contains commands that can be added to any Macro-Program. The Target Window for each command is the Program (PGM) window in which the command is to be executed, usually the current (PGM) window. Sleep Causes the Program to pause execution on the current Step for a user-specified period of time (in seconds). User Dialog Opens a dialog box containing a user-specified message, as shown below. •

If the OK button is pressed, the Program continues execution on the next Step.

•

If the Cancel button is pressed, execution of the Program is stopped.

Program User Dialog. Question Box Opens a dialog box containing two user-specified messages, and Yes, No & Cancel buttons, as shown below. •

38

The Yes & No buttons can each have a user-defined text message associated with them.

Macro-Program Window Commands â€˘

If the Yes button is pressed, the Program branches to the Yes label.

â€˘

If the No button is pressed, the Program branches to the No label.

â€˘

If the Cancel button is pressed, execution of the Program is stopped.

Parameters 1. Question text for the Yes button. 2. Label to branch to if Yes button is pressed. 3. Question text for the No button. 4. Label to branch to if No button is pressed. 5. Default pressed button. 6. Variable to hold the pressed button (Yes = 1, No = 0).

Program Question Box. Variable | Var_1 = Var_2 Assigns the contents of variable Var_2 to variable Var_1. NOTE: Var_2 can be a constant or a named variable. Variable | Var_1 = Var_2 [operator] Var_3 Assigns the result of the operation between variable Var_2 and variable Var_3 to variable Var_1. The [operator] can be one of the following operations; [ + ] add Adds Var_3 to Var_2 and stores the result in Var_1. [ - ] subtract Subtracts Var_3 from Var_2 and stores the result in Var_1. [ x ] multiply Multiplies Var_3 by Var_2 and stores the result in Var_1. [ / ] divide

39

Reference Volume IIB - Options Divides Var_2 by Var_3 and stores the result in Var_1. Variable | If (Var_1 [compare] Var_2) Then GoTo Step Label Compares the value of variable Var_1 with the value of variable Var_2. Depending on the outcome of the [compare] operation, jumps to the Step with Step Label. The [compare] operator can be one of the following comparisons; [ = ] equal to If Var_1 is equal to Var_2, then go to the Step with Step Label and continue executing Steps. [ <> ] not equal to If Var_1 is not equal to Var_2, then go to the Step with Step Label and continue executing Steps. [ < ] less than If Var_1 is less than Var_2,then go to the Step with Step Label and continue executing Steps. [ <= ] less than or equal to If Var_1 is less than or equal to Var_2,then go to the Step with Step Label and continue executing Steps. [ > ] greater than If Var_1 is greater than Var_2,then go to the Step with Step Label and continue executing Steps. [ >= ] greater than or equal to If Var_1 is greater than or equal to Var_2,then go to the Step with Step Label and continue executing Steps. Variable | Variable Dialog Opens a dialog box for entry of a numerical value for a named Variable in the Program. Parameters 1. Variable Name 2. Instruction text Variable | Show Variable Opens a dialog box displaying the value of a named Variable in the Program. Parameter 1. Variable Name Variable | Var_1 = Var_2 from Program Sets a named Variable (Var_1) in the current Program equal to a named Variable (Var_2) from another Program. Parameters 1. Var_1 Name 2. Program Name

40

Macro-Program Window Commands 3. Var_2 Name Variable | Var_1 = Var_2 from Program Sets a named Variable (Var_1) in another Program equal to a named Variable (Var_2) in the current Program. Parameters 1. Program Name 2. Var_1 Name 3. Var_2 Name GoTo Line Causes the Program execution to go to a Line number or Step Label in the Commands spreadsheet. Close All Other Windows Closes all open windows in ME'scope except the Target window.

Program Running Banner When a Program is running in ME'scope, the Program Running banner is displayed on the Toolbar, as shown below.

Program Running Banner. Stop All Programs Button This button appears on the left side of the Program Running Banner. â€˘

Press this button to terminate execution in all Macro-Programs that may be currently running in the Work Area.

ME'scope Window Program Menu

41

Reference Volume IIB - Options

NOTE: This menu of commands is added to the ME'scope window when the VES-7000 MacroProgramming option is authorized for use in your software. Window | Minimize Minimizes a window (changes it to an Icon) in the Work Area. Parameter 1. File name of the window to minimize. Window | Restore Restores a window from its minimized state in the Work Area. Parameter 1. File name of the window to restore. Window | Maximize Maximizes a window in the Work Area. Parameter 1. File name of the window to maximize in the Work Area. Window | Position Places a window in a specific position in the Work Area. Parameters 1. Left side (0 to 1), percentage of the Work Area. 2. Top (0 to 1), percentage of the Work Area. 3. Right side (0 to 1), percentage of the Work Area. 4. Bottom (0 to 1), percentage of the Work Area. 5. The File name of the window to Position. Window | Bring to the Front Displays a window in front of all other windows in the Work area. Parameter 1. File name of the window to bring to the front on all other windows in the Work Area.

42

Macro-Program Window Commands Window | Send to the Back Displays a window in back of all other windows in the Work Area. Parameter 1. File name of the window to place behind all other windows in the Work Area. Auto Start Program Automatically starts a Macro-Program running when the Project containing the Program is opened from disk storage. •

If this command is executed when it is un-checked, the following dialog box will open,

•

Choose a Program from the drop down list of available Macro-Programs in the Project, and click on OK to enable the Auto Start Program function.

•

If this command is executed when it is checked, the Auto Start Program function is disabled.

New Data Block Menu

The two commands in this menu, New Data Block | Sinusoidal and New Data Block | Auto Spectrum implement the same functions are the Sinusoidal and Auto spectrum tabs in the File | New | Data Block dialog box. See the File | New | Data Block command reference for more details. Structure Window Program Menu

NOTE: This menu of commands is added to a Structure window when the VES-7000 MacroProgramming option is authorized for use in your software. Objects | Select Selects (or un-selects) Objects in the current Objects spreadsheet by row number.

43

Reference Volume IIB - Options Parameters 1. A list of row numbers in the Objects spreadsheet (Examples; 1,2,3; 1-3; all) 2. Select (yes or no). Objects | Hide Hides (or shows) all (or selected) Objects in the current Objects spreadsheet. Parameter 1. Hide (yes or no). Objects | Label Changes the label of all (or selected) Objects in the current Objects spreadsheet. Parameter 1. Label (text). Objects | Color Changes the color of all (or selected) Objects in the current Objects spreadsheet. Parameter 1. Color (text). Objects | Bold Displays as bold all (or selected) Objects in the current Objects spreadsheet. Parameter 1. Bold (yes or no).

Data Block Program Menu

NOTE: This menu of commands is added to a Data Block window when the VES-7000 MacroProgramming option is authorized for use in your software. Display | Cursor Displays and positions the cursor in the Data Block window. Parameters

44

Macro-Program Window Commands 1. (Line, Band, Peak, None) 2. Position •

Percentage (1 to 100) of the Block Size

•

Sample (1 to the Block Size)

•

Horizontal Axis Units (Hz, RPM, CPM, Sec, Milli-sec, micro-sec)

3. Bandwidth •

(Percentage, Sample, Horizontal Axis Units)

Display | Zoom Zooms the display in the Data Block. Parameters 1. Zoom start •

Percentage (1 to 100) of the Block Size

•

Samples (1 to the Block Size)

•

X-Axis Units (Hz, RPM, CPM, Sec, milli-sec, micro-sec)

2. Zoom end 3. Percent, Samples, X-Axis Units) Display | Sine Dwell Cycles per Shape Sets the number of Sine Dwell Cycles per Shape during Sweep Animation from a Data Block. •

During Sweep animation from a Data Block, the specified number of Dwell Cycles per shape is carried out before displaying the next sample of shape data.

Parameter 1. Number of Cycles Traces | Select Selects (or un-selects) Traces by measurement number (M#) in the Traces spreadsheet. Parameters 1. M#s (1,2,3,,,; 1-3; all) 2. Select (yes or no). Traces | Color Changes the color of all (or selected) Traces in the Data Block. Parameter 1. Trace Color (from color pallet) Traces | Label Changes the label of all (or selected) Traces in the Data Block. Parameter

45

Reference Volume IIB - Options 1. Label (text) Traces | DOFs Changes the DOFs of all (or selected) Traces in the Data Block. Parameter 1. DOFs (1X , 1Y, 1Z ,...) Traces | Units Changes the units of all (or selected) Traces in the Data Block. Parameters 1. Units (g, N, lbs,...) 2. Re-scale Traces (yes or no) Traces | Measurement Type Changes the Measurement Type of all (or selected) Traces in the Data Block. Parameter 1. Type (FRF, Auto spectrum,...) Traces | Input Output Changes the Input Output of all (or selected) Traces in the Data Block. Parameter 1. Input Output (Input, Output, Both, Cross) Traces | Visibility Makes all (or selected) Traces visible (or invisible) in the Data Block. Parameter 1. Visible (yes or no). Traces | Linear/Power Changes the Linear/Power property of all (or selected) Traces in the Data Block. Parameter 1. Linear or Power. Traces | SubShape Gives a SubShape name to all (or selected) Traces in the Data Block. Parameter 1. SubShape text name. Tools | Damping Decay Constant

46

Macro-Program Window Commands Calculates the damping decay constant for each Trace in a time domain Data Block. The damping decay constant is the coefficient of the exponential decay envelope on a decaying sinusoidal response. The Logarithmic Decrement method is used to calculate the damping decay constant. A straight line is curve fit to the Log Magnitude of each Trace, and its slope is damping decay constant. For a single resonance, the damping decay constant is the same as the modal damping in Hz obtained by curve fitting FRFs using one of the Modal Analysis options. Parameters 1. Destination Data Block 2. Save method (Add To, Replace) Tools | ODS Correlation Calculates two measures for comparing ODS's from two different Data Blocks, the Modal Assurance Criterion (MAC) and the Shape Difference (SDI). MAC & SDI are calculated between the ODS at each sample in one Data Block and the ODS at the same sample in a second Data Block. The results are saved as two Traces in a new Data Block. •

MAC is a measure of the co-linearity of two shapes. Two shapes are co-linear if they "lie on the same straight line".

•

MAC has values between 0 & 1.

•

If MAC = 1, the ODS in one Data Block is co-linear with the ODS at the same sample in the other Data Block.

•

If MAC < 1, the ODS in one Data Block is different from the ODS at the same sample in the other Data Block.

SDI is a measure of the difference between two shapes. •

SDI has values between 0 & 1.

•

If SDI = 1, the ODS in one Data Block is the same as the ODS at the same sample in the other Data Block.

•

If SDI < 1, the ODS in one Data Block is different from the ODS at the same sample in the other Data Block.

Parameters 1. Destination Data Block 2. Save method (Add To, Replace) 3. Comparison Data Block Tools | Trace Correlation Calculates the Modal Assurance Criterion (MAC) and the Shape Difference Indicator (SDI) between matching Traces in two Data Blocks. The results are saved as two shapes in a destination Shape Table. •

Two Traces match if they have matching DOFs.

•

If MAC = 1 the Trace data in one Data Block is co-linear with the Trace data of the matching Trace in the other Data Block.

•

If MAC < 1, the Trace data in one Data Block is different from the Trace data for the matching Trace in the other Data Block.

•

If SDI = 1 the Trace data in one Data Block is the same as the Trace data of the matching Trace in the other Data Block.

47

Reference Volume IIB - Options •

If SDI < 1, the Trace data in one Data Block is different from the Trace data for the matching Trace in the other Data Block.

Parameters 1. Destination Shape Table 2. Save method (Add To, Replace) 3. Comparison Data Block Tools | Save Cursor Values Saves the cursor value (for the Line, Band, or Peak cursor) for all (or selected) Traces in a Data Block as a constant value Trace in a separate Data Block. Tools | Save Statistics Saves the statistics for all (or selected) Traces into a Shape Table. •

See the Tools | Statistics command description in the Signal Processing Commands chapter for details.

Parameters 1. Destination Data Block 2. Save method (Add To, Replace) 3. Save RMS (yes or no) 4. Save Min (yes or no) 5. Save Max (yes or no) 6. Save Mean (yes or no) 7. Save MS (yes or no) 8. Save Crest (yes or no) 9. Save Var (yes or no) 10. Save Std Dev (yes or no) 11. Save Abs Dev (yes or no) 12. Save Kurt (yes or no) 13. Save Power (yes or no) 14. Save Lin Pwr (yes or no) Math | Trace Matrix Add (or Subtract) Adds the Trace Matrix in a Data Block to the Trace Matrix in the host Data Block or subtracts the Trace Matrix in a Data Block from the Trace Matrix in the host Data Block. The host Data Block is the one from which this command is executed. NOTE: A Trace Matrix is defined by the Roving & Reference DOFs of the Traces, •

A Trace Roving DOF designates its row in the Trace Matrix.

•

A Trace Reference DOF designates its column in the Trace Matrix.

Parameters 1. Destination Data Block

48

Macro-Program Window Commands 2. Save method (Add To, Replace) 3. Operator Data Block Math | Trace Matrix Multiply Multiplies the Trace Matrix in the host Data Block by the Trace Matrix in another Data Block. The host Data Block is the one from which this command is executed. NOTE: A Trace Matrix is defined by the Roving & Reference DOFs of the Traces, •

A Trace Roving DOF designates its row in the Trace Matrix.

•

A Trace Reference DOF designates its column in the Trace Matrix.

Parameters 1. Destination Data Block 2. Save method (Add To, Replace) 3. Operator Data Block Math | Trace Matrix Inverse Calculates the inverse of the Trace Matrix in the host Data Block. NOTE: A Trace Matrix is defined by the Roving & Reference DOFs of the Traces, •

A Trace Roving DOF designates its row in the Trace Matrix.

•

A Trace Reference DOF designates its column in the Trace Matrix.

Parameters 1. Destination Data Block 2. Save method (Add To, Replace) Curve Fit | Number of Modes Sets the number of modes to be used by the Frequency & Damping curve fitting methods. Parameter 1. Number of Modes Curve Fit | Mode Indicator Noise Threshold Sets the noise threshold level on the Mode Indicator graph. Parameter 1. Threshold (10 to 90) Curve Fit | Count Peaks Calculates a Mode Indicator, counts the peaks above the noise threshold on the Mode Indicator graph, and sets the number of modes equal to the peaks counted. Parameters 1. Mode Indicator (CMIF or MMIF)

49

Reference Volume IIB - Options 2. Data used to calculate Indicator (real, imaginary, magnitude) Curve Fit | Frequency and Damping Estimates modal frequency & damping using all (or cursor band) data from all (or selected) Traces in the Data Block. Parameters 1. Method (global polynomial, local polynomial) 2. Extra numerator terms (0 to 8) Curve Fit | Residues Estimates modal residues using all (or selected) modes using data from all (or selected) Traces in the Data Block. Parameter â€˘

Method (polynomial, peak, AF polynomial)

Curve Fit | Stability Button Creates a stability diagram using data from all (or selected) Traces in the Data Block. Parameters 1. Method (AF polynomial, complex exponential, Z polynomial) 2. Damping (yes =>percent, no => Hz) 3. Maximum damping 4. Frequency tolerance 5. Damping tolerance 6. Min No. of Poles 7. Show all (yes or no) 8. Poles diagram (yes or no) Curve Fit | Stability Reset Resets all of the stability diagram parameters to default values. Curve Fit | Save Stable Groups Saves all of the stable pole groups into the modal parameters spreadsheet. The frequencies & damping of all of the poles in a stable group are averaged together, and the average values are saving in the modal parameters spreadsheet.

Shape Table Program Menu

50

Macro-Program Window Commands

NOTE: This menu of commands is added to a Shape Table window when the VES-7000 Programming option is authorized for use in your software. Display | Dwell Cycles per Sweep Step Sets the number of Dwell Cycles per shape during Sweep animation from a Shape Table. â€˘

During Sweep animation from a Shape Table, the specified number of Dwell Cycles per shape is carried out before displaying the next shape in animation.

Parameter 1. Number of Cycles Shapes | Select Selects (or un-selects) shapes in the Shape Table. Parameter 1. Select (yes or no). Shapes | Color Changes the color of all (or selected) shapes in the Shape Table. Parameter 1. Shape Color (from color pallet) Shapes | Label Changes the label of all (or selected) shapes in the Shape Table. Parameter 1. Label (text) Shapes | Frequency Changes the frequency of all (or selected) shapes in the Shape Table.

51

Reference Volume IIB - Options Parameter 1. Frequency value (in Hz) Shapes | Damping Changes the damping of all (or selected) shapes in the Shape Table. Parameter 1. Damping (in Hz) Shapes | Copy Shapes data to Clipboard Copies rows & columns of data from the Shapes spreadsheet to the Windows Clipboard. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Top Left Row 2. Top Left Column 3. Bottom Right Row 4. Bottom Right Column Shapes | Paste Clipboard data into Shapes Pastes data from the Windows Clipboard into the Shapes spreadsheet NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Top Left Row 2. Top Left Column 3. Bottom Right Row 4. Bottom Right Column Shapes | Copy Shapes data to Variable Copies a cell (row & column) of data from the Shapes spreadsheet in a Shape Table to a Program Variable. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Row 2. Column 3. Variable Name Shapes | Paste Variable into Shapes Pastes a Program Variable value into a cell (row & column) of the Shapes spreadsheet in a Shape Table.

52

Macro-Program Window Commands NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Row 2. Column 3. Variable Name DOFs | Select Selects (or un-selects) DOFs by measurement number (M#) in the DOFs spreadsheet. Parameters 1. M#s (1,2,3,,,; 1-3; all) 2. Select (yes or no). DOFs | Color Changes the color of all (or selected) DOFs in the Shape Table. Parameter 1. DOFs Color (from color pallet) DOFs | Label Changes the label of all (or selected) DOFs in the Shape Table. Parameter 1. Label (text) DOFs | DOF Changes the DOF of all (or selected) DOFs in the Shape Table. Parameter 1. DOF (point & direction) DOFs | Units Changes the units of all (or selected) DOFs in the Shape Table. Parameter 1. Units (g, N, lbs,...) DOFs | Measurement Type Changes the Measurement Type of all (or selected) DOFs in the Shape Table. Parameter 1. Measurement Type (drop down list) DOFs | Copy DOFs data to Clipboard

53

Reference Volume IIB - Options Copies rows & columns of data from the DOFs spreadsheet in a Shape Table to the Windows Clipboard. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Top Left Row 2. Top Left Column 3. Bottom Right Row 4. Bottom Right Column DOFs | Paste Clipboard data into DOFs Pastes data from the Windows Clipboard into rows & columns of the DOFs spreadsheet of a Shape Table. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Top Left Row 2. Top Left Column 3. Bottom Right Row 4. Bottom Right Column DOFs | Copy DOFs data to Variable Copies a cell (row & column) of data from the DOFs spreadsheet in a Shape Table to a Program Variable. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Row 2. Column 3. Variable Name DOFs | Paste Variable into DOFs Pastes a Program Variable value into a cell (row & column) of the DOFs spreadsheet in a Shape Table. NOTE: Row & Column numbers start at "1", and do not include the Select columns Parameters 1. Row 2. Column 3. Variable Name Math | Add an Offset

54

Macro-Program Window Commands Adds an offset to the DOF values of all (or selected) DOFs, for all (or selected) shapes in the Shape Table. Parameter 1. Offset value Math | Invert DOFs Inverts the DOF values of all (or selected) DOFs, for all (or selected) shapes in the Shape Table. Math | Scale by Mag Phs Scales the Magnitude & Phase of the DOF values of all (or selected) DOFs, for all (or selected) shapes in the Shape Table. Parameters 1. Magnitude value 2. Phase values Math | Square DOFs Squares the DOF values of all (or selected) DOFs, for all (or selected) shapes in the Shape Table. Math | Square Root of DOFs Takes the square root of the DOF values of all (or selected) DOFs, for all (or selected) shapes in the Shape Table. Math | Add DOFs Adds first and second DOF values and stores the sum in a result DOF, for all (or selected) shapes in the Shape Table. Parameters 1. First DOF 2. Second DOF 3. Result DOF Math | Subtract DOFs Subtracts the second from first DOF values and stores the difference in a result DOF, for all (or selected) shapes in the Shape Table. Parameters 1. First DOF 2. Second DOF 3. Result DOF Math | Multiply DOFs Multiplies first and second DOF values together and stores the result in a result DOF, for all (or selected) shapes in the Shape Table.

55

Reference Volume IIB - Options Parameters 1. First DOF 2. Second DOF 3. Result DOF Math | Divide DOFs Divides the first by the second DOF values and stores the result in a result DOF, for all (or selected) shapes in the Shape Table. Parameters 1. First DOF 2. Second DOF 3. Result DOF

Acquisition Window Program Menu

NOTE: This menu of commands is added to a Acquisition window when the VES-7000 Programming option is authorized for use in your software. Display | Cursor Displays and positions the cursor in the Acquisition window. Parameters 1. (Line, Band, Peak) 2. Position •

Percentage (1 to 100) of the Block Size

•

Sample (1 to the Block Size)

•

Horizontal Axis Units (Hz, RPM, CPM, Sec, Milli-sec, micro-sec)

3. Bandwidth 4. (Percentage, Sample, Horizontal Axis Units) Display | Zoom Zooms the display in the Acquisition window. Parameters 1. Zoom start •

56

Percentage (1 to 100) of the Block Size

Macro-Program Window Commands â€˘

Samples (1 to the Block Size)

â€˘

Horizontal Axis Units (Hz, RPM, CPM, Sec, milli-sec, micro-sec)

2. Zoom end 3. Percent, Samples, Horizontal Axis Units) Display | Dwell Cycles per Sweep Step Sets the number Dwell Cycles per Sweep step in the Acquisition window. During Sweep animation from an Acquisition window, the number of Dwell Cycles per Sweep step is carried out before stepping to the next time or frequency value. Parameter 1. Number of Cycles Traces | Select Selects (or un-selects) active Traces by measurement number (M#) in the Traces spreadsheet. Parameters 1. M#s (1,2,3,,,; 1-3; all) 2. Select (yes or no). Traces | Color Changes the color of all (or selected) active Traces in the Acquisition window. Parameter 1. Trace Color (from color pallet) Traces | Label Changes the label of all (or selected) active Traces in the Acquisition window. Parameter 1. Label (text) Traces | DOFs Changes the DOFs of all (or selected) active Traces in the Acquisition window. Parameter 1. DOFs (1X, 1Y, 1Z,...) Traces | Units Changes the units of all (or selected) active Traces in the Acquisition window. Parameters 1. Units (g, N, lbs,...) 2. Re-scale Traces (yes or no) Traces | Measurement Type

57

Reference Volume IIB - Options Changes the Measurement Type of all (or selected) active Traces in the Acquisition window. Parameter 1. Measurement Type (FRF, Auto spectrum,...) Traces | Input Output Changes the Input Output of all (or selected) active Traces in the Acquisition window. Parameter 1. Input Output (Input, Output, Both, Cross) Traces | Visible Makes all (or selected) active Traces visible (or invisible) in the Acquisition window. Parameter 1. Visible (or Invisible). Tools | Save Statistics Saves the statistics for all (or selected) active Traces into a Shape Table. â€˘

See the Tools | Statistics command description in the Signal Processing Commands chapter for details.

Tools | Connected Structure Defines the Structure window that is connected to the Acquisition window. Parameter 1. Structure window name Tools | Connected Data Block Defines the destination Data Block window for storing Traces from the Acquisition window. Parameter 1. Destination Data Block window name

58

Signal Processing Commands Data Block Signal Processing Commands NOTE: If the VES-3000 Signal Processing option is authorized, the following Data Block commands, and spreadsheet columns are enabled in your software. Check Help | About to verify authorization of this option. File Menu •

File | Export to VSI Rotate

Tools Menu •

Tools | Integrate

•

Tools | Differentiate

•

Tools | Remove DC

•

Tools | Statistics

•

Tools | Math

Transform Menu •

Transform | Block Size

•

Transform | FFT

•

Transform | Inverse FFT

•

Transform | Window Traces

•

Transform | Spectra

•

Transform | ODS FRFs

•

Transform | Scale ODS FRFs

•

Transform | Order Tracked ODS's.

Traces Spreadsheet Columns •

Linear Power

•

Input Output

•

Peak RMS Pk-Pk

•

FFT

•

Window, Window Value, Window Correction

•

Z-Axis

59

Reference Volume IIB - Options

Extra Traces Spreadsheet Column With Signal Processing Option. Linear Power Column Converts all (or selected) Traces between Linear and Power engineering units (EU & EU^2). â€˘

All Traces with Linear engineering units (EU) are converted to Power engineering units (EU^2), and the Trace values are re-scaled using the formula,

â€˘

All Traces with Power engineering units (EU^2) are converted to Linear engineering units (EU), and the Trace values are re-scaled using the formula,

Input Output Column Defines a Trace as an Input signal, an Output signal, or Both an Input and an Output to a test structure. Also designates a Trace as a Cross channel measurement, between two DOFs of a structure, such as an FRF. IMPORTANT: Input, Output, Cross, and Both designations are required by the Transform | Spectra, Transform | MIMO and Transform | ODS FRFs commands.

60

Signal Processing Commands Peak RMS Pk-Pk Column Scales all (or selected) Traces using the following scale factors. Amplitude Scaling Choice

Trace Is Multiplied By

Peak

1.0

Pk-Pk

2.0

RMS

0.707

FFT Column Defines the FFT (or DFT spectrum) of each Trace as either One Sided or Two Sided. •

The FFT calculates a Two Sided spectrum, where half of a signal is represented by the negative frequency half and half by the positive frequency half of the spectrum.

•

The frequency spectrum of a real valued time signal is symmetric about zero frequency (DC), so only the positive frequency half of the spectrum is displayed.

•

The amplitude and power values for a Two Sided FFT are only half of the values of the original time domain signal.

•

The amplitude and power values for a One Sided FFT are the same values as its corresponding time domain signal.

Window Column Describes the type of time domain window applied to all (or selected) Traces. •

A Time domain window is applied by executing the Transform | Window Traces command.

Window Value Column Contains the window value corresponding to the window listed in the Window column. •

The Exponential window value is the amount of damping added by the window (in Hz).

•

The Force window value is the number of samples following the beginning of signal where the Force window transitions to zero.

Window Correction Column Used together with the Window and Window Value columns to correct the effects of time domain windowed from calculated spectra. •

For each Trace containing a narrow band signal, choose Narrow Band in the Window Correction column before applying a time domain window and calculating its spectrum.

•

For each Trace containing a wide band signal, choose Wide Band in the Window Correction column before applying a time domain window and calculating its spectrum.

Windowing Examples The figure below contains the spectra of 3 sine wave (narrow band) signals, and three random (wide band) signals.

61

Reference Volume IIB - Options â€˘

Each Trace was windowed using Rectangular, Hanning, and Flat Top windows before its Auto spectrum was calculated.

Notice that all of the magnitudes of the Sine Wave spectra (on the left side) are the same, even though each has been windowed with a different time domain window. Notice also that all of the magnitudes of the Random spectra (on the right side) are approximately the same, even though each has been windowed with a different time domain window.

Narrow Band and Wide Band Spectra Amplitude Corrected for Windowing. The figure below shows that the Power in all of the Sine Wave spectra is the same, since they have been Narrow Band corrected. Likewise, the Power in all of the Random spectra is the same, since they have been Wide Band corrected.

62

Signal Processing Commands

Narrow Band and Wide Band Spectra Power Corrected for Windowing. Z-Axis Column Used to enter a Z-Axis text label for all (or selected) Traces. •

Traces can be selected by Z-Axis label using Edit | Select Traces | Select By so that all of the data with the same label is displayed together in animation.

File | Export to VSI Rotate Exports a time domain Data Block in binary UFF format. •

This file can then be imported by the VSI Rotate™ package for performing computed order tracking.

•

The VSI Rotate™ package is used together with ME'scopeVES for animating order tracked ODS's.

Edit | Cut Traces to File Cuts (deletes) selected Traces from the Data Block and puts them into another Data Block file.

63

Reference Volume IIB - Options Data in the Cursor Band If the Band cursor is displayed, you are given the choice of copying only the Trace data in the cursor band. •

Press Yes to cut only the samples in the cursor band.

•

Press No, to cut all samples of the selected Traces.

M#s and Animation Equations NOTE: Trace Measurement numbers (M#s) are used in the Animation equations when animating from a Data Block. If Traces are cut from a Data Block, new Animation equations may have to created in the connected Structure window in order to animate shapes from the Data Block.

Edit | Copy Traces to File Copies all (or selected) Traces from the Data Block into another Data Block file. Data in the Cursor Band If the Band cursor is displayed, you are given the choice of copying only the Trace data in the cursor band. •

Press Yes to copy the samples in the cursor band.

•

Press No, to copy all samples of all (or selected) Traces.

Edit | Paste Traces from File Pastes Traces from another Data Block file into the Data Block in which it is executed. •

The pasted Traces are added to the end of the Traces currently in the Data Block.

•

If Traces are selected in the paste from Data Block, only the selected Traces are pasted.

When this command is executed, a dialog box will open listing all of the open Data Blocks of the same type (time or frequency domain) as the Paste To Data Block. •

Choose a Paste From Data Block, and press the Paste button.

NOTE: If the X-axis in the Paste From Data Block does not match the X-axis values of the Paste To Data Block, each Paste From Trace is interpolated so that its X-axis values match those of the Paste To Data Block.

64

Signal Processing Commands

Edit | Paste Trace Data at Cursor Pastes Trace data from another Data Block file into the Data Block in which it is executed. •

The pasted Trace data is added to the samples of each Trace in the Data Block, starting at the Line cursor position.

•

If Traces are selected in the Paste From Data Block, then only data from the selected Traces is pasted.

Edit | Delete selected Traces Deletes (removes) selected Traces from a Data Block file. M#s and Animation Equations NOTE: Trace Measurement numbers (M#s) are used in the Animation equations when animating from a Data Block. If Traces are deleted from a Data Block, new Animation equations may have to created in the connected Structure window in order to animate shapes from the Data Block.

Tools | Integrate Performs Integration on all (or selected) Traces in a Data Block. •

All integration is done in the frequency domain.

•

Time domain Traces are transformed to the frequency domain, integrated, and transformed back to the time domain.

Frequency domain Traces are integrated by using the following frequency domain operation,

where:

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Reference Volume IIB - Options i = 1 to Block Size Xi(2πf i) = linear spectrum (FFT) of the signal for the ith sample. th

2πf i = frequency of the i sample (radians/second). th

f i = frequency of the i sample (Hz). j - denotes the imaginary operator. Time domain integration of a signal is equivalent to dividing each sample of its frequency spectrum X i (2πf i ) by its sampled frequency 2πf i . Integration Errors Due To DC Offset If a time domain Trace has any DC Offset (or bias) in it, integration of the DC Offset will result in a ramp function. •

To minimize errors due to any DC Offset, Tools | Remove DC is automatically executed before integration is performed,

Integration Errors Due To Leakage The FFT assumes that the signals to be transforming are periodic, or completely contained within their sampling window. The sampling window is the range of samples in each Trace. •

If a time domain Trace is non-periodic, or not completely contained within its sampling window, smearing (called leakage) of its spectrum will occur when it is transformed to the frequency domain.

If a frequency domain waveform is non-periodic, or not completely contained within its sampling window, leakage (called wrap around error) of the time waveform will occur when it is transformed to the time domain. Removing Lower Frequencies Before Integration Integration amplifies the lower frequencies in a signal. To reduce the harmful effects of all nonessential lower frequencies in a signal, they should be removed from its spectrum before integrating it. •

Execute Transform | FFT to transform time domain Traces to the frequency domain.

•

Set up the Band cursor to include all non-essential low frequencies.

•

Execute Transform | Window Traces and apply the Notch window to remove the low frequencies (zero the Trace values).

•

Execute Tools| Integrate to integrate the Traces.

•

Execute Transform | Inverse FFT to transform the integrated signals back to the time domain.

Tools | Differentiate Performs differentiation on all (or selected) Traces in a Data Block. •

All differentiation is done in the frequency domain.

•

Time domain Traces are transformed to the frequency domain, differentiated, and transformed back to the time domain.

Frequency domain Traces are differentiated using the following equivalent operation,

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Signal Processing Commands

where: x(t) = continuous time waveform. th

X i (2πf i ) = linear spectrum (FFT) of the signal for the i sample. th

2πf i = frequency of the i sample (radians/second). th

f i = frequency of the i sample (Hz). j - denotes the imaginary operator. Time domain differentiation of a signal is equivalent to multiplying each sample of its frequency spectrum X i (2πf i ) by its sampled frequency 2πf i .

Tools | Remove DC Removes the DC offset (or bias) from all (or selected) Traces in a Data Block. The following steps are automatically carried out on time domain Traces, 1. Execute Transform | FFT to transform all Traces to the frequency domain. 2. Zero the DC component (at frequency = 0) of the spectrum. 3. Execute Transform | Inverse FFT to transform all Traces back to the time domain.

Tools | Statistics Calculates a variety of statistical measures and displays them on the right side of each Trace, as shown below. NOTE: If the Band cursor is displayed, the statistics are calculated only for data in the band.

Sine Wave Statistics Minimum Value

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Reference Volume IIB - Options The minimum value of the Trace data in the format displayed, in vertical axis units. Maximum Value The maximum value of the Trace data in the format displayed, in vertical axis units. Mean Value The mean (or average) value of the Trace data in the format displayed, in the vertical axis units. For N samples of data x i , the mean value is calculated with the following formula,

Mean Squared (MS) Value The mean squared value of the Trace data in the format displayed, in the vertical axis units. For N samples of data x i , the mean squared value is calculated with the following formula,

Root Mean Squared (RMS) Value The square root of the mean squared value of the Trace data in the format displayed, in the vertical axis units. For N samples of data x i , RMS is calculated with the following formula,

Variance For N samples of data x i , the variance is calculated with the following formula, in vertical axis units squared.

Standard Deviation The standard deviation is calculated with the following formula, in vertical axis units.

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Signal Processing Commands

Power The power value of the Trace data in the format displayed, in vertical axis units. For data with Power Units (EU^2), power is calculated for N samples of data x i with the formula,

For data with Linear Units (EU), power is calculated with the formula,

Linear Power Linear power is calculated with the formula,

Crest Factor The crest factor of the Trace data in the format displayed is calculated with the formula,

Absolute Deviation For N samples of data x i , in the format displayed, the absolute deviation is calculated with the formula,

Skew Skew is a measure of how asymmetrical (or skewed) a distribution of values is. â€˘

If the skew is positive, the asymmetry is above the mean value.

â€˘

If skew is negative, the asymmetry is below the mean value.

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Reference Volume IIB - Options •

A Normal (Gaussian) distribution is symmetrical about its mean, with a skew of "0".

For N samples of data x i , the skew is calculated with the formula,

Kurtosis Kurtosis is a measure of the width of the distribution of values compared to a Normal (Gaussian) distribution. •

If Kurtosis is negative, the distribution is wider than the Normal distribution.

•

If Kurtosis is positive, the distribution is narrower than the Normal distribution.

•

A Normal (Gaussian) distribution has a Kurtosis of "0".

For N samples of data x i , Kurtosis is calculated with the formula,

Tools | Math Menu Math | Scale By Mag Phs Multiplies all (or selected) Traces by a magnitude & phase Scale Factor.

•

The Use Shape Table button scales each Trace with a different scale factor from a Shape Table.

•

The magnitude & phase of each DOF (M#).of the first shape in the Shape Table is used to scale each matching Trace (M#).

Math | Add an Offset Adds a complex (real & imaginary) offset value to all (or selected) Traces.

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Signal Processing Commands

â€˘

The Use Shape Table button adds a different offset from a Shape Table to each Trace.

â€˘

The complex value for each DOF (M#).of the first shape in the Shape Table is used to offset each matching Trace ( M#).

Math | Add Random Noise Adds random noise to each Trace. The amount of random noise is a percentage of the maximum magnitude of each Trace. Math | Conjugate Traces Replaces each complex Trace value with its complex conjugate. The Real part remains the same and the Imaginary part is multiplied by "-1". Math | Invert Traces Replaces each Trace with its inverse. Math | Square Traces Replaces each Trace with its value squared. Math | Square Root of Traces Replaces each Trace with the square root of its value. Math | Smooth Traces Performs multi-point smoothing of the Traces in a Data Block. Replaces each Trace sample with the average value of N samples of data surrounding that sample. For example, for N = 3, Trace (sample) = ( Trace (sample) + Trace(sample-1) + Trace (sample +1) ) / 3 Math | Re-Sample Traces Changes the number of samples in a Data Block without changing the X-Axis span. Math | Sum Traces Sums the Trace values at each sample, and stores the result into a single Trace. Math | Average Traces

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Reference Volume IIB - Options Divides the sum of the Trace values at each sample by the number of Traces, and stores the result into a single Trace. Math | Add (Subtract, Multiply by, Divide by) a selected Trace Performs the indicated operation between the Traces in a Data Block and a selected Trace in the same of a different Data Block.. NOTE: If two Data Blocks have the same number of Traces in them, you can choose to perform the operation between Trace pairs in the two Data Blocks.

Transform | Block Size Changes the Block Size of the Traces in a Data Block file. Opens the File | Data Block Properties dialog box where the Block Size can be changed. NOTE: Block Size is the number of samples (time or frequency) in each Trace of a Data Block. In order to support animation of shapes from a Data Block, all Traces must have the same Block Size. Increasing the Block Size If the Block Size is increased, more samples are added to the end (right side) of each Trace, and the Yaxis of each Trace is filled with zero values for the new samples. Decreasing the Block Size If the Block Size is decreased, samples are deleted from the end (right side) of each Trace.

The FFT and DFT The FFT is a computer algorithm that calculates the Digital Fourier Spectrum (DFT) of a uniformly sampled time domain signal. Three different equations govern the use of the FFT algorithm; 1. An equation for a uniformly sampled time domain waveform. 2. An equation for its corresponding uniformly sampled Digital Fourier Transform (DFT). 3. Shannon's sampling criterion, also called the Nyquist sampling criterion. 1. Sampled Time Domain Waveform •

The FFT assumes that the sampled time waveform contains N uniformly spaced samples.

•

The spacing (or resolution) between time samples is denoted as delta t (in seconds).

•

The sampling time period (also called the sampling window), spans the time period (t = 0 to T) (in seconds).

These sampled time waveform parameters are related by the equation,

T = N x delta t (in seconds) 2. Digital Fourier Transform (DFT)

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•

The DFT contains (N/2) uniformly spaced samples of complex (magnitude & phase) data.

•

The spacing (or resolution) between frequency samples is denoted as delta f (in Hz).

•

The DFT is calculated over the frequency span (f = 0 to Fmax) (in Hz).

Signal Processing Commands These DFT parameters are related by the equation,

Fmax = (N/2) x delta f (in Hz) 3. Shannon's (Nyquist) Sampling Criterion Shannon's Sampling Criterion says that to calculate an accurate DFT over the span (f = 0 to Fmax), •

The time waveform must be sampled at least at a rate of twice Fmax.

•

This is called the Nyquist sampling rate.

Therefore, Fmax and the time domain sampling rate are related by the equation,

2 x Fmax = 1 / delta t (in Hz) Fmax = (1/2) x (Nyquist sampling rate)

(in Hz)

Fundamental Sampling Rule The following equation is derived from the three equations above.

delta f = 1/T

(in Hz)

This equation says that the resolution (delta f) of the DFT equals the length of the time domain sampling window (T). Sampling Rate and Frequency Resolution To increase the frequency resolution in a DFT (reduce delta f), the time domain signal must be sampled over a longer time period (T). NOTE: Increasing the time domain sampling rate does not increase the frequency resolution (delta f). Anti-Aliasing Filter When an analog (continuous) signal is sampled, higher frequencies in the signal will fold back and appear as lower frequencies in the DFT. These aliased high frequency components are not part of the lower frequency spectrum of the original signal. •

To insure that no frequencies higher than the Nyquist frequency are contained in a DFT, higher frequencies must be removed from the time waveform before it is sampled.

•

Frequencies higher than the Nyquist sampling frequency are removed using an analog low pass anti-aliasing filter.

Passing a time domain signal through an anti-aliasing filter before sampling insures that all high frequency components are removed from the frequency span (0 to Fmax) of the DFT. •

All anti-aliasing filters have a finite roll off frequency band.

•

If the cutoff frequency (start of the filter roll off) is set to 80% of Fmax, (or 40% of the sampling frequency), then 80% of a frequency span (0 to Fmax) will be alias-free.

•

Most FFT analyzers have anti-aliasing filters with a cutoff frequency set to 80% of Fmax, or 40% of the sampling frequency.

Transform | FFT Applies the Fast Fourier Transform (FFT) algorithm to all time domain Traces in a Data Block to transform them into their frequency domain spectrum (DFT).

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Reference Volume IIB - Options NOTE: The FFT is a loss-less (also called one-to-one and onto) transformation from one domain to the other, meaning that the original time domain waveform can always be recovered by executing Transform | IFFT, applying the Inverse FFT. Prime Number FFT ME'scope uses a prime number FFT, which doesn't required that the Block Size (number of Trace samples) does not have to be a power of 2.

Data Block Before FFT.

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Signal Processing Commands Data Block After FFT. One Sided Versus Two Sided FFT All of the energy in a time domain signal is spread of all frequencies, including both positive & negative frequencies. The FFT always calculates a Two Sided FFT, where half of a signal is represented by positive frequencies, and half by negative frequencies. Therefore, a One Sided FFT yields spectrum values that are twice the values of a Two Sided FFT. The frequency spectrum of a real valued time signal is symmetric about zero frequency (DC), so only the positive frequency half of the spectrum is displayed. •

The amplitude and power values for a Two Sided FFT are only half of the values of the its corresponding time domain signal.

•

The amplitude and power values for a One Sided FFT are the same values as its corresponding time domain signal.

Transform | Inverse FFT Applies the Inverse Fast Fourier Transform (IFFT) to all frequency domain Traces in a Data Block yielding their corresponding time domain waveforms. NOTE: The original frequency spectrum data can always be recovered by executing Transform | FFT, or by executing Edit | Undo.

Time Domain Windows The FFT assumes that the time domain waveform to be transformed is periodic in its sampling window. A signal is periodic in its sampling window if it satisfies one of the following criteria, •

An integer number of cycles of the signal are contained within its sampling window.

•

Or the signal has no discontinuity between the beginning or ending in its sampling window.

•

Or the signal is completely contained within its sampling window.

Non-Periodic Signals Many signals are never periodic in the sampling window. For example, a purely random signal is never completely contained within a finite length sampling window. Therefore, it is non-periodic in the window. Time Domain Windowing to Reduce Leakage If a time signal is non-periodic in its sampling window, a smearing of its spectrum (called leakage) will occur when it is transformed to the frequency domain. NOTE: If a time domain signal is non-periodic in its sampling window, leakage cannot be eliminated, but it can be reduced. •

Leakage distorts the spectrum, especially around resonance peaks.

•

Leakage is reduced by multiplying the time domain data by a special weighting function (called a window), before the FFT is applied.

Hanning Window for Broad Band Signals •

Effective for reducing leakage in the spectrum of a broad band signal such as a random signal.

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Reference Volume IIB - Options •

Reduces leakage (the spread of the spectrum surrounding resonance peaks), which is important for modal parameter estimation.

Hanning Window. Flat Top Window for Narrow Band Signals •

Effective for reducing the effects of leakage in the spectrum of a narrow band signal such as a sinusoidal signal.

•

Makes the magnitude values of a sinusoidal signal more accurate, but also makes its peaks wider.

Flat Top Window. Exponential Window for Transient Response Signals NOTE: A decreasing Exponential window should be applied to transient (or impulse response) signals that do not decay completely within the sampling window.

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•

A decreasing Exponential window artificially damps the signal toward zero before the end of the window, thus making it nearly periodic in the window.

•

(See Transform | Window Traces section for more details.)

Signal Processing Commands

Exponential Window. Rectangular Window for Periodic Signals •

Used on signals that are periodic, or nearly periodic, in the sampling window.

•

This window (also called the Box Car or No window), does not reduce leakage.

•

All the values of a rectangular window are "1".

Rectangular Window.

Transform | Window Traces This command is used to multiply all (or selected) Traces by various window functions. When it is executed, the following window is opened,

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Reference Volume IIB - Options

Window Traces Dialog Box. Notch Window The Notch window is useful for removing (zeroing) unwanted samples of data. It uses a Cosine function to transition the Trace data smoothly to zero inside the cursor band. The Notch window is defined as, •

Notch = 1.0 outside the cursor band.

•

Notch = Cos(0) =1.0 to Cos(90) = 0.0 from 0% to 5% of the cursor band.

•

Notch = 0.0 from 5% to 95% of the cursor band.

•

Notch = Cos(90) = 0.0 to Cos(0) = 1.0 from 95% to 100% of the cursor band.

Notch Window. To apply the Notch window, •

Select the Traces to be windowed.

•

Display the Band cursor, and position the band to enclose the data to be notched (or zeroed).

•

Execute Transform | Window Traces, select the Notch window, and press Apply.

Band Pass Window

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Signal Processing Commands The Band Pass window is useful for preserving certain samples of Trace data and setting the rest to zero. It uses a Cosine function to transition the Trace data smoothly to zero outside the cursor band. The Band Pass window is defined as, •

Band Pass = 1.0 inside the cursor band.

•

Band Pass = Cos(90) = 0.0 to Cos(0) = 1.0 for 5% of the cursor band prior to the lower edge.

•

Band Pass = Cos(0) = 1.0 to Cos(90) = 0.0 for 5% of the cursor band following the upper edge.

•

Band Pass = 0.0 otherwise.

Band Pass Window. To apply the Band Pass window, •

Select the Traces to be windowed.

•

Display the Band cursor, and position the band to enclose the data to be preserved.

•

Execute Transform | Window Traces, select the Band Pass window, and press Apply.

Interpolation Window This window is useful for replacing unwanted data with smooth data in a band of samples. •

Replaces Trace data in the cursor Band with a straight line of data between the Trace values at the ends of the band.

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Reference Volume IIB - Options Interpolation Window. Exponential Window This window is only applied to time domain Traces. Each time domain Trace is multiplied by a decreasing (or increasing) exponential curve. •

The beginning value of the exponential window is "1".

•

For a decreasing exponential, the ending value of the window should be less than "1" but greater than "0".

•

For an increasing exponential window, the ending value should be greater than "1".

Exponential Window. The following steps are carried out when this window is applied to frequency domain Traces; •

All (or selected) Traces are transformed to the time domain using the Inverse FFT.

•

The Exponential window is applied.

•

The Traces are transformed back to the frequency domain using the FFT.

Decreasing Exponential Removes Noise and Leakage •

A deceasing exponential has the effect of truncating the noise in each Trace, and also making a signal more periodic or completely contained within the window".

•

When the signal is transformed to the frequency domain, its spectrum will have less leakage.

Increasing Exponential Narrows Resonance Peaks •

If an increasing exponential window is applied to impulse response function (IRF) Traces, it will artificially decrease the amount of damping in all of the modes by a known amount.

•

When these windowed Traces are transformed into frequency response functions (FRFs), the resonance peaks will be narrower, and closely coupled modes will be more widely separated from one another.

•

An increasing exponential window will also amplify the noise in experimental Traces.

Modal Damping Applying an exponential window to Traces that contain responses due to resonant vibration adds a known amount of damping to each of the modes represented in the Trace data.

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Signal Processing Commands •

A decreasing exponential window adds the same amount of damping to each mode.

•

An increasing exponential window subtracts the same amount of damping from each mode.

•

The amount of damping added to modes by applying an Exponential window is listed in the Transform | Window Traces dialog box, and also in the Window Value column of the Traces spreadsheet.

The amount of modal damping added by the Exponential window is cumulative. •

If the Exponential window is applied several times to the same Trace data, the amount of damping is the sum of the damping amounts added with each application of the window.

Damping Removal Following Curve Fitting During modal parameter estimation (or curve fitting), the artificial damping added to the modes by the Exponential window is removed when mode Shapes are saved into a Shape Table. The artificial damping added by the Exponential window is removed from each modal damping estimate, •

When the Save Shapes button on the Residues & Save Shapes tab is pressed and modal parameters are saved into a Shape Table.

•

Or when Curve Fit | Shapes | Save Shapes is executed.

Transform | Spectra Calculates Fourier spectra, Auto & Cross spectra, PSD's or ESD's from time or frequency domain waveforms. When this command is executed, the a dialog box is opened.

All of the Data Blocks open in the Work Area are listed in this window. Only certain data can be used for calculating each type of spectrum. •

Time domain Traces are required to calculate Fourier Spectra, Cross Spectra, or a Spectrogram.

•

Single channel (Input, Output, or Both) Traces are required to calculate Auto Spectra, PSD's, or ESD's.

Fourier spectrum •

A Fourier spectrum is calculated by averaging together a number of DFTs of a time domain Trace.

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Reference Volume IIB - Options •

The FFT calculates the Digital Fourier Spectrum (DFT) of a time domain Trace.

•

See The FFT and DFT section for details.

Auto spectrum •

An Auto spectrum is calculated by averaging together a number of Auto spectrum estimates.

•

Each Auto spectrum estimate is calculated by multiplying a DFT by its complex conjugate.

•

The DFT is complex valued, but the Auto spectrum is only Real valued (magnitude only).

Cross spectrum •

A Cross spectrum is calculated by averaging together a number of Cross spectrum estimates.

•

Each Cross spectrum estimate is calculated by multiplying the DFT of one Trace by the complex conjugate of the DFT of a different Trace.

•

The Cross spectrum is complex valued.

Power Spectral Density (PSD) •

A PSD is an Auto spectrum that has been "normalized" by dividing it by the frequency resolution of the Auto spectrum.

•

If the units of an Auto spectrum are g^2, the units of its corresponding PSD are g^2 / Hz.

Energy Spectral Density (ESD) •

ESD's are used to characterize transient signals.

•

An ESD is a PSD multiplied by the time length (T) of the time domain signal used to create the ESD.

•

If the units of a PSD are g^2 / Hz, the units of its corresponding ESD are (g^2 - sec) / Hz.

Time Domain Source If you choose a Source File with time domain Traces in it, time domain windowing, overlap processing, and spectrum averaging can be used to calculate spectral estimates. •

If Spectrum Averaging is chosen, a dialog box will open for choosing several spectrum averaging options.

Spectrogram •

A Spectrogram is a series of spectra that are calculated from short time portions of a long time domain Trace.

•

If the Number of Averages = 10 during Spectrum Averaging, 10 individual spectrum estimates are retained as a Spectrogram instead of averaging the 10 spectral estimates together.

Spectrum Averaging Spectrum averaging is used to, •

Remove extraneous random noise from the frequency spectrum of a signal.

•

Or remove randomly excited non-linearities (that appear as random noise in a spectrum).

The following steps are carried out during spectrum averaging, as shown in the diagram below.

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Signal Processing Commands 1. Each time domain Trace is divided into several smaller sampling windows. NOTE: The number of samples in each sampling window = 2 x Spectrum Block Size. 2. Each sampling window is windowed (multiplied by a time domain window) to reduce leakage in its spectral estimates. 3. Each windowed Trace is transformed to its Digital Fourier Spectrum (DFT) using the FFT. 4. An Auto spectrum are calculated from each Fourier spectrum. 5. The Auto spectral estimates are averaged together to yield a single estimate for each Trace.

Number of Averages NOTE: The Spectrum Block Size (number of DFT samples) equals one half the time domain Block Size. Depending on the Block Size of the Source time domain Data Block file, two cases can occur, 1. Spectrum Block Size = 1/2 (Time Domain Block Size) In this case, no spectrum averaging can be performed. Only one spectral estimate can be calculated using all of the Trace samples of the Source file. 2.

Spectrum Block Size < 1/2 (Time Domain Block Size)

In this case, a large time domain Trace can be divided into many smaller sampling windows, and spectrum averaging can be performed. Overlap processing can also be performed. Overlap Processing Overlap processing divides each Trace time waveform into a series of smaller overlapping sampling windows. The amount of overlap of the sampling windows depends on the total number of samples

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Reference Volume IIB - Options available, the number of samples per sampling window, and the Number Of Averages. Increasing the Number Of Averages in the spectrum averaging dialog box increases the percentage of overlap processing. 2. 50 % Overlap means that half of the time waveform samples are used over again in each successive sampling window. 3. 0% Overlap means that unique time domain Trace data is used for each new sampling window. Linear Averaging Linear averaging is the same as summing together all of the spectral estimates and dividing by the number of estimates. th

The N stable average is calculated with the following formula,

Average (N) = (1 / N) x Spectrum (N) + (1 - (1 / N)) x Average(N-1) Peak Hold Averaging Peak Hold averaging retains the maximum value at each sample from all spectral estimates. th

th

The I sample of the N average is determined with the formula,

Average (N , I) =Maximum (Spectrum (I) , Average(N-1 , I))

Transform | ODS FRFs Calculates a set of ODS FRFs from operating (or output only) data. See the Tutorial - Signal Processing chapter for an illustrative example. What is an ODS FRF?

84

â€˘

An ODS FRF is formed by combining the Auto spectrum of each Roving response with the phase of the Cross spectrum between the Roving response and a (fixed) Reference response.

â€˘

An ODS FRF is complex valued frequency domain function that is like an FRF.

Signal Processing Commands A Typical ODS FRF. Advantages of ODS FRFs •

The ODS FRF provides the true response (in displacement, velocity or acceleration units) at each DOF of a machine or structure, together with a phase relative to a Reference response.

•

An ODS FRF contains peaks at resonant frequencies.

•

A set of ODS FRFs can be used to display ODS's, and to obtain operating mode shapes.

ODS's from a Set of ODS FRFs If shape data from the cursor position in two or more ODS FRFs is displayed in animation on a model of a test structure, the resulting ODS is the true overall response of the structure at each DOF, with the correct phase relative to all other DOFs. What is Transmissibility? Transmissibility is defined as the spectrum of a Roving response divided by the spectrum of a Reference response. It is the traditional measurement that is calculated when no excitation forces are measured. Transmissibility is calculated in the same way as an FRF, but a (fixed) Reference response is used instead of the unmeasured force. An advantage of the Transmissibility is that if the excitation force level varies from one Measurement Set to the next during data acquisition, its effect on both the Roving and Reference responses is assumed to be the same, so its effect will be "canceled out" in the Transmissibility calculation. Difficulty with Transmissibility's A Transmissibility has a ”flat spot” instead of a peak in the vicinity of each resonant frequency, as shown below.

Roving Auto Spectrum & Transmissibility.

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Reference Volume IIB - Options Scaled Cross Spectra •

If a set of Transmissibility's is multiplied by a single Reference response Auto spectrum, the resulting set of Scaled Cross Spectra can be used like a set of ODS FRFs.

•

A set Cross Spectra does not have to be re-scaled, even if the excitation force level changes between Measurement Sets.

Scaled Cross Spectrum = Transmissibility x Reference Auto Spectrum Advantages of Scaled Cross Spectra •

A scaled Cross Spectrum contains peaks at resonant frequencies.

•

No re-scaling is required if multiple Measurement Sets of data are used.

•

A set of Scaled Cross Spectra can be curve fit to obtain operating mode shapes.

Operating Mode Shapes •

At or near a resonant frequency, the ODS obtained either from a set of ODS FRFs or Scaled Cross Spectra is often dominated by the mode shape of that resonance.

•

A set of ODS FRFs or Scaled Cross Spectra can be curve fit to obtain operating modal parameters (frequency, damping, and mode shape) for each resonance.

Setting Up Your Data The Transform | ODS FRFs command can process multiple Measurement Sets of three different types of Source data; •

Multiple time domain Roving responses, plus a Reference time domain response.

•

Roving response Auto spectra, plus Cross spectra between each Roving response and a Reference response.

•

Transmissibility's between each Roving response and a Reference response, plus the Reference response Auto spectrum.

To calculate ODS FRFs from time waveforms, •

All Roving response Traces must be defined as Outputs in the Input Output column of the Traces spreadsheet.

•

All Reference response Traces must be defined as Inputs in the Input Output column of the Traces spreadsheet.

•

Each response Trace should contain the DOF (point & direction) at which it was acquired.

To calculate ODS FRFs from Auto & Cross spectra, •

All Auto spectrum Traces must be defined as Outputs in the Input Output column of the Traces spreadsheet.

•

All Cross spectrum Traces must be defined as Cross Traces in the Input Output column of the Traces spreadsheet.

•

Each Auto spectrum DOF must match the Roving DOF of a Cross spectrum.

To calculate Scaled Cross Spectra from multiple Measurement Sets of Transmissibility data,

86

•

Each Measurement Set must include the same an Auto spectrum for the same Reference response, defined as an Input in the Input Output column of the Traces spreadsheet.

•

All Transmissibility Traces must be defined as Cross Traces in the Input Output column of the Traces spreadsheet.

Signal Processing Commands •

Each Transmissibility Reference DOF must match the Roving DOF of the Auto spectrum of the Reference response for that Measurement Set.

When this command is executed, the following dialog box is opened.

NOTE: The Source Traces can be stored either in the same Data Block, or in two different Data Blocks. Measurement Sets •

If the Trace DOFs also contain Measurement Set numbers, then all data in each Measurement Set is processed independently of the other Measurement Sets.

•

If the Reference Auto spectra are different between Measurement Sets (indicating the force levels have changed), a set of ODS FRFs must be re-scaled using Transform | Scale ODS FRFs.

Transform | Scale ODS FRFs Re-scales a set of ODS FRFs to correct for changes in the response levels between multiple Measurement Sets. Overlaid Reference Auto Spectra If there was any change of response level between Measurement Sets, it can be observed by overlaying the Reference Auto Spectra from all Measurement Sets, as shown below.

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Reference Volume IIB - Options

Overlaid Reference Auto Spectra From Multiple Measurement Sets. Scale Factor The ODS FRFs are re-scaled by first calculating an average Reference Auto Spectrum for all on the Measurement Sets. Then, a scale factor for re-scaling the ODS FRFs in each Measurement Set is calculated using the following formula,

where: N = Number of Measurement Sets. ARM(i) = Average Magnitude of the Reference Auto spectrum for Measurement Set [ i ], and all ODS FRFs in Measurement Set [ i ] are multiplied by the Scale Factor ( i ). •

If the Line cursor is displayed, ARM(i) is calculated at the Line cursor position.

•

If the Band or Peak cursor is displayed, the ARM(i) is calculated using all the samples in the band.

•

If no cursors are displayed, the ARM(i) is calculated using all samples of the Reference Auto spectrum.

Transform | Order Tracked ODS's. Creates a new Data Block of ODS Order Tracks that are suitable for displaying Order Tracked ODS's in animation. What is an Order? A multiple of a rotational speed of a machine. What is Order Tracking?

88

Signal Processing Commands Order tracking is a filtering process that tracks spectral components as a function of an instantaneous rotational speed. •

Tracking the 2 order means tracking the frequency that is 2 x (the rotational speed) of a rotating machine.

•

An accurate measure of rotational speed is required in order to perform order tracking.

•

This requires that a tachometer (Tach) signal must be simultaneously acquiring along with the vibration response signals.

nd

Non-Stationary Signal A signal is non-stationary if frequency spectra are different from successive measurements of the signal. Vibration signals measured from rotating machinery are often non-stationary because the dominant excitation forces vary with the rotational speeds the machine. Order Tracked ODS's To display Order Tracked ODS's, a set of order tracked time domain responses that have the correct magnitudes & phases relative to one another is required. There are two ways to acquire data for order tracking, 1.

Simultaneous Method 2. Simultaneously acquires all Roving responses, plus a Tach signal. 3. This method requires a multi-channel data acquisition system with enough channels to simultaneously acquire all of the Roving responses and the Tach signal. 4. For most applications, this approach is usually too costly. 2. Measurement Set Method

3.

Data is acquired in multiple Measurement Sets.

4. Simultaneously acquires a small number of Roving responses, a Reference response, and a Tach signal in each Measurement Set. 5. As few as 3 channels need be simultaneously acquired (one Roving response, one Reference response, and one Tach signal). 6.

The Measurement Set Method is more economical and is more commonly used.

When this command is executed, a dialog box is opened.

NOTE: All Source Traces must be in the same Source Data Block file.

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Reference Volume IIB - Options Processing Multiple Measurement Sets To display order tracked ODS's from multiple measurement sets, the following steps are required, 1. Perform Computed Order Tracking on each Measurement Set. •

This will yield a new set of time waveforms for each order tracked.

•

These complex order tracked waveforms can be functions of either time or RPM.

•

The VSI Rotate software performs computed order tracking and exports Measurement Sets of order tracked operating data to ME'scopeVES.

2.

Import the order tracked Measurement Sets into ME'scopeVES from VSI Rotate.

3. Set].

Ensure that the DOFs of each Trace include its Roving DOF, Reference DOF, and [Measurement 2. See Editing Trace DOFs for Multiple Measurement Sets below for details.

4. Execute Transform | Calculate | ODS Order Track to create a new Data Block of ODS Order Tracks from the Order Tracks. •

See Transforming Order Tracks to ODS Order Tracks below for details.

5. Build a structure model and number its Roving response Points to match the Point numbers of the ODS Order Tracked Traces. 6. Execute Tools | Create Animation Equations (Assign M#s) in the ODS Order Track Data Block. 7. Execute Tools | Animation Shapes in the ODS Order Track Data Block to display Order Tracked ODS's in animation. Editing Trace DOFs for Multiple Measurement Sets

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•

Each Roving response Trace should have Output chosen in the Input Output column on the Traces spreadsheet.

•

Each Reference response Trace should have Input chosen in the Input Output column on the Traces spreadsheet.

•

Each response Trace that is both a Roving & Reference Trace should have Both chosen in the Input Output column on the Traces spreadsheet.

Signal Processing Commands Data Block Showing Order Tracks from Two Measurement Sets. The Transform | Calculate | ODS Order Track command carries out the following steps; 1.

Phase Correction 2. In each Measurement Set, the phase of the Reference response is subtracted from the phase of each Roving response. 3. The phase correction step insures that all of the Roving responses have a phase relative to the Reference response phase in each Measurement Set . 4. Since Roving response phases are corrected in all of the Measurement Sets by subtracting the phase of the same Reference response DOF, the Roving responses from all Measurement Sets will have correct phases relative to one another. 2. Magnitude Correction

3. In each Measurement Set, the magnitude of each Roving response is corrected using an average magnitude of the Reference responses for all Measurement Sets. 4. The magnitude correction step insures that if there are differences between the average magnitudes of the same Reference response among Measurement Sets, then all of the Roving responses are re-scaled using an average of the Reference response magnitudes. 5. The following formula is used to calculate a scale factor for correcting the Roving responses in each Measurement Set. Each Roving response in Measurement Set [ i ] is multiplied by the Scale Factor ( i ),

where: N = Number of Measurement Sets ARM(i) = Average Magnitude of the Reference response for Measurement Set [ i ]. •

If the Line cursor is displayed, average magnitudes are calculated from the reference responses at the Line cursor position.

•

If the Band or Peak cursor is displayed, average magnitudes are calculated using all the reference response samples in the band.

•

If no cursors are displayed, average magnitudes are calculated using all samples of the reference response Traces.

Shape Table Signal Processing Commands NOTE: If the VES-3000 Signal Processing option is authorized, the following Shape Table commands and spreadsheet columns are enabled in your software. Check Help | About to verify authorization of this option. Edit Menu •

Edit | Add Shapes

•

Edit | Delete Selected Shapes

•

Edit | Copy Shapes to File

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Edit | Paste Shapes from File

•

Edit | Add DOFs

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Edit | Delete Selected DOFs

Display Menu •

Display | Shapes | Acc, Vel, Disp

Tools Menu •

Tools | Integrate

•

Tools | Differentiate

•

Tools | Shape Product

DOFs Spreadsheet Columns •

Linear Power

•

Input Output

•

Peak RMS Pk-Pk

•

Z-Axis

Shape Table Edit Menu Edit | Add Shapes Adds new shapes to the Shape Table. Shape data can be added in several ways, 1. Click on a spreadsheet cell and type in data. 2. Or use the keyboard Ctrl C & Ctrl V commands to copy data between spreadsheet cells. 3. Or choose items from the drop down list in a cell when available. 4. Or double click on a column heading and enter data into the dialog box for all (or selected) Shapes. Edit | Delete Selected Shapes Deletes selected Shapes from the Shape Table. Edit | Copy Shapes to File Copies all (or selected) shapes and all (or selected) DOFs of each shape into a new Shape Table file. Edit | Paste Shapes from File Pastes shapes from another Shape Table file into the current Shape Table. When it is executed, the Shape Table Selection dialog box is opened. •

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Choose a Shape Table to paste and click on OK.

Signal Processing Commands

The shapes of the chosen Shape Table are pasted with those in the Shape Table window by comparing shape DOFs. If a matching DOF is found, the data for the new shapes is added to the same row in the DOFs spreadsheet where the matching DOF is found. If no matching DOF is found, a new row of the DOFs spreadsheet is created, and the new shape data is added to the new row. Edit | Add DOFs Adds DOFs (rows or M#s) to the end of the DOFs spreadsheet. When it is executed, a dialog box is opened; â€˘

Enter the number of DOFs to add, and click on OK.

Edit | Delete Selected DOFs Deletes the selected DOFs (rows or M#s) from the DOFs spreadsheet.

Display | Shape DOFs | Accel, Vel, Disp These commands display the shape columns in the Shape DOFs spreadsheet in Acceleration, Velocity or Displacement units. These values are calculated based on the output units of the shapes.

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If the output units are acceleration units, •

Shapes with velocity units are calculated by dividing the shape values by the shape frequency.

•

Shapes with displacement units are calculated by dividing the shape values by the shape frequency squared.

If the output units are velocity units, •

Shapes with acceleration units are calculated by multiplying the shape values by the shape frequency.

•

Shapes with displacement shapes are calculated by dividing the shape values by the shape frequency.

If the output units are displacement units, •

Shapes with velocity units are calculated by multiplying the shape values by the shape frequency.

•

Shapes with acceleration units are calculated by multiplying the shape values by the shape frequency squared.

Shape Table Tools Menu Tools | Multiply Shapes By Multiplies all (or selected) shapes by a user defined Scale Factor. When this command is executed, a dialog box will open. •

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Enter the scale factor to multiple by the shape magnitudes, and click on OK.

Signal Processing Commands Tools | Integrate Integrates all shape DOFs from acceleration to velocity output units, of from velocity to displacement units. •

Integration is performed by dividing each shape by its shape frequency.

•

If the shapes are Residue mode shapes, each shape is divided by its complex pole (frequency & damping).

NOTE: UMM mode shapes must be re-scaled to Residue mode shapes before using this command. Tools | Differentiate Differentiates all shape DOFs from displacement to velocity units or from velocity to acceleration units. •

Differentiation is performed by multiplying each shape by its shape frequency.

•

If the shapes are Residue mode shapes, each shape is multiplied by its complex pole (frequency & damping).

NOTE: UMM mode shapes must be re-scaled to Residue mode shapes before using this command. Tools | Shape Product Multiplies all (or selected) shapes together. A Shape Product shows where all shapes have node lines (zero values), and hence where poor reference DOFs are located. A Shape Product shows where all shapes have anti-nodes (large magnitudes), and hence where the good reference DOFs are located. A Shape Product can be displayed in animation on a connected Structure model to locate node lines and anti-nodes.

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Basic Modal Analysis Commands Data Block Basic Modal Analysis Commands NOTE: If the VES-4000 Basic Modal Analysis option is authorized, the following Data Block commands, and mouse and keyboard operations are enabled in your software. Check Help | About to verify authorization of this option. Modes Menu •

Modes | Modal Parameters

•

Modes | Display Traces menu

•

Modes | Copy Traces menu

•

Modes | Synthesize FRFs

Curve Fitting Menu •

Curve Fit | Quick Fit

•

Curve Fit | Sort Modes by Frequency

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Curve Fit | Select Modes menu

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Curve Fit | Delete Selected Modes

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Curve Fit | Clear All Fit Data

•

Curve Fit | Clear Fit Functions

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Curve Fit | Fit Function Synthesis

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Curve Fit | Mode Indicator menu

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Curve Fit | Shapes menu

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Curve Fit | Close

Special Mouse & Keyboard Commands The following commands operate on the Mode Indicator graph during curve fitting, •

Hold down the Alt key and place the mouse pointer near a frequency estimate (vertical line) to display its Frequency & Damping box.

•

Hold down the Alt key and click to toggle on & off the display of the nearest Frequency & Damping box.

•

Click & drag to move the nearest Frequency & Damping box on the Mode Indicator graph.

•

Enclose one or more frequency estimates (vertical lines) with the band cursor to select modes in the modal parameters spreadsheet.

Single Reference Modal Test The most common type of Experimental Modal Analysis (EMA) is done using a single reference. A single reference EMA can be performed in two ways; •

Using a fixed (reference) exciter and a one roving response transducers.

•

Using a fixed (reference) response transducer and a roving exciter.

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Reference Volume IIB - Options MIMO Model A MIMO model of a structure completely represents the dynamic properties of the structure between all pairs of Input (excitation) and Output (response) DOFs for which it is defined. A FRF matrix of a MIMO model contains rows & columns of FRFs. Each FRF defines the Output (response) of the structure at a DOF due to the force Input (excitation) at another DOF. Roving Response Test In a roving response test, a single fixed (reference) exciter is used to excite the structure, and a roving response transducer is used to measure its response. Each FRF measurement is calculated between the excitation force signal applied to the structure and the response signal from a response transducer. The FRFs correspond to measuring elements from a single column of the MIMO model for the structure. (See the Multi-Input Multi-Output Modeling & Simulation chapter for details.) The excitation force can be provided in two ways, 1. Attaching a shaker to the structure and driving it with a broad band signal. 2. Impacting the structure at the same DOF (point & direction) for each measurement. Roving Impact Test In a roving impact test, a single fixed (reference) response transducer is used, and the structure is excited using a roving impacter. Each FRF is calculated between the response signal from the same DOF and the excitation signal from a different roving DOF. The FRFs correspond to measuring elements from a single row of the MIMO matrix for the structure. The impact hammer applies a broad band impulsive force to the structure, which excites many resonances at a time. The excitation force is measured with a load cell attached to the head of the hammer. Maxwell's Reciprocity In modal testing, Maxwell’s Reciprocity is usually assumed. When Maxwell’s Reciprocity is assumed to be valid, •

An FRF calculated when excitation is provided at DOF A and response s measured at DOF B is the same as the FRF calculated when excitation is provided at DOF B and response is measured at DOF A. The structure is dynamically symmetrical.

•

Measuring elements from a column of the MIMO model of the structure is the same as measuring elements from its corresponding row. This also means that the MIMO model contains a symmetric matrix of FRFs.

•

Curve fitting FRF from any row or any column of the MIMO model will yield the same modal parameters for the structure.

Single Reference Modal Test When Maxwell’s Reciprocity is assumed to be valid, •

Any (fixed) Reference DOF (any row or any column of the MIMO model) can be used in a modal test.

•

Only one Reference DOF is required to obtain all of the modal parameters of the structure.

What is FRF Curve Fitting? •

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Curve fitting is a process of matching a parametric model of an FRF (in a least squared error sense) to a set of experimental FRF data.

Basic Modal Analysis Commands •

The unknown parameters of the parametric model are modal frequency, damping & mode shape components.

•

The outcome of curve fitting is a set of modal parameters (frequency, damping & mode shape) for each mode that is identified in the frequency span of the experimental FRFs.

After curve fitting is completed, mode shapes are stored into a Shape Table from which they can be displayed in animation on a 3D model of the test article. Curve Fitting Steps 1. Determine the Number of Modes in a frequency band of FRF measurement data. 2. Estimate modal Frequency & Damping for all modes in the frequency band. 3. Estimate modal Residues (mode shape components) for each mode in the frequency band. 4. Save the modal parameters into a Shape Table file.

FRFs in Terms of Modal Parameters •

FRF-based curve fitting assumes that any FRF calculated between two DOFs of a vibrating structure can be completely represented in terms of modal parameters.

Partial Fraction Expansion of the FRF Matrix The following parametric model is used to estimate experimental modal parameters by curve fitting FRF data. •

The FRF matrix is a summation of matrix pairs, each pair containing the contribution of a single mode (k).

•

Each matrix pair for each mode (k) consists of a positive frequency term and a negative frequency (or complex conjugate) term.

•

The unknown parameters of the parametric model are the modal frequency, damping & residue (mode shape component) for each mode of interest in the frequency band of the FRFs.

•

The residues from a row or column of the FRF matrix are then saved as the mode shape for each mode.

•

[H(ω)] - (n by n) FRF matrix.

•

ω -frequency variable

•

p(k) - pole location for mode(k): (p(k) = -σ(k) + jω(k) )

•

σ(k) - damping decay constant for mode (k) (in Hz or radians / second )

•

ω(k) - damped natural frequency for mode (k)

•

[R(k)] - (n by n) Residue matrix for mode (k).

•

n - number of DOFs of the MIMO model.

•

modes - number of modes of interest on the structure.

( Hz or radians / second )

(in Hz or radians / second )

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Reference Volume IIB - Options •

* - denotes the complex conjugate.

•

j - denotes the imaginary axis in the complex plane.

Local versus Global Curve Fitting •

The denominators of each term in the FRF matrix contain the same modal frequency & damping.

•

Since all of the denominators are the same, frequency & damping can be estimated by curve fitting a single FRF, or all FRFs taken from the test article.

Generally speaking, modes are global properties of a structure. Therefore, each mode has only one frequency & damping value, and one mode shape. •

During Local curve fitting, each FRF is curve fit and local frequency & damping estimates are obtained for each mode and each FRF.

•

During Global curve fitting, multiple FRFs are curve fit and only one global frequency & damping estimate is obtained for each mode.

Local curve fitting is necessary when physical changes such as mass loading, temperature changes, or other effects cause the resonant frequencies & damping to change during the course of a modal test. Residue Matrix •

In the partial fraction expansion equation, each mode (k) has a residue matrix [R(k)] associated with it.

•

Each residue matrix has the same dimensions as the (n by n) MIMO model.

Residues represent the "strength" of a resonance. That is, the stronger a resonance is relative to other resonances, the larger its residue will be. In general, residues are complex numbers with magnitude & phase. •

Residue units = ( FRF units ) x ( radians / second )

•

When one row or column of FRFs in the MIMO model is curve fit, the residues from the same row or column of the Residue matrix are estimated.

Parameter Estimation The partial fraction expansion form of the MIMO model is used for curve fitting. During curve fitting, four modal parameters are estimated for each mode (k), •

Frequency & damping, or the pole location p(k) = -σ(k)

•

Magnitude & phase of the complex Residue R(k).

+ jω(k).

Damped Natural Frequency •

Modal frequency is listed as the damped natural frequency in the Modal Parameters spreadsheet

•

ω(k) = damped natural frequency of mode (k) (in Hz)

Undamped Natural Frequency •

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The undamped natural frequency for mode (k) is defined as,

Basic Modal Analysis Commands

Damping Ratio or Percent of Critical Damping •

Modal damping can also be listed as the damping ratio or percent of critical damping.

•

The damping ratio for mode (k) is defined as,

Damping Decay Constant •

The damping decay constant for mode (k) can also be defined as,

Half Power Point (3 dB bandwidth) Damping •

The half power point damping for mode (k) is defined as,

•

This damping value is related to the width of a resonance peak.

This result is derived from a single pole approximation of an FRF

Evaluating the single pole approximation at the frequency of a single mode (k) gives,

Power is obtained by squaring the FRF value at the resonance,

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Equating half of this value to the square of the single pole form of the FRF gives,

Solving the above equation gives two frequencies at which the FRF squared equals half of the value at the resonance. These two frequencies are called the half power points,

Hence, the width of the resonance peak between the two half power points is equal to twice the modal damping decay constant,

Since 3 dB is also equal to one half of the value at the resonance peak, this bandwidth estimate of modal damping is also called the 3 dB bandwidth damping. Conclusions: •

The width of the resonance peak in an FRF at 70.7% of its magnitude at the peak is equal to twice the damping decay constant.

•

If the resonance peak of a mode is wider than the resonance peak of another mode, its damping is greater.

Quality Factor and Loss Factor The Loss factor η(k) is equal to twice the percent of critical damping.

The Quality factor Q(k) is the inverse of the Loss factor.

Frequency & Damping Plot The four definitions of modal frequency & damping are plotted on the top view of the S-plane, or complex frequency plane below.

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Basic Modal Analysis Commands

S-plane Showing Modal Frequency & Damping Terms.

Frequency & Damping Terminology The following definitions are used to define modal frequency & damping,

p(k) = -σ(k) + jω(k) = pole location of mode(k) (Hz) ω(k) = damped natural frequency of mode(k) (Hz) σ(k) = decay constant of mode(k) (Hz) Ω(k) = undamped natural frequency of mode(k) (Hz)

Half Power Point Bandwidth (3 dB Bandwidth) Damping Ratio (Percent of Critical) Decay Constant

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Loss Factor Quality Factor

Mode Shapes From Residues The FRF matrix can be represented in terms of mode shapes instead of residues. This relationship has very strong implications for modal testing. The FRF matrix can be further expressed in terms of modal poles & mode shapes as,

•

A(k) scaling constant for mode (k).

•

{u(k)} (n - vector).mode shape for the mode (k).

•

t - denotes the transposed vector.

Each numerator is written in terms of a mode shape vector instead of a Residue matrix. Comparing this equation with the previous partial fraction expansion of the MIMO model yields the relationship between mode shapes and Residues .

•

Each mode shape (a column vector), is multiplied by itself transposed (a row vector).

•

This vector product, (a column vector times a row vector), is called an outer product, and it yields a matrix.

•

The resultant matrix multiplied by the scaling constant A(k) equals the Residue matrix.

A mode shape, (also called an eigenvector), is unique in shape but not in value. A mode shape has no engineering units. The scaling constant A(k) is required to make the right-hand side of the above equation equal to the Residue matrix which contains unique values with engineering units. Since scaling of mode shapes is arbitrary, the scaling constant A(k) can always be chosen so that A(k) = 1. This simplifies the Residue equation,

Fundamental Modal Testing Criterion The above relationship leads to the following conclusions;

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Basic Modal Analysis Commands •

Every row and every column of the Residue matrix contains the mode shape multiplied by a different mode shape component.

•

Any row or any column of the FRF matrix contains the same mode shape, for each mode (k).

•

Any row or any column of the FRF matrix can be measured and curve fit to obtain the mode shape for each mode (k).

Mode Shape Node Points The Residue equation indicates that if a row or column of the Residue matrix corresponds to a node point (zero value) of the mode shape, the entire row or column of residues is zero. •

If a row or column of the Residue matrix corresponds to a node point of a mode shape, the numerators of all FRFs in the row & column are also zero.

•

If a row or column of the Residue matrix corresponds to a node point of a mode shape, then none of the FRF measurements will contain a resonance peak as evidence of the mode.

When all modes of interest cannot be identified using a single row or column of the FRF matrix, multiple rows or columns are required. Global Versus Local Modes Many structures exhibit resonant vibration in a localized region of the structure. Energy becomes "trapped" between stiff boundaries in a local region, and cannot readily escape, causing a standing wave of vibration, or local mode shape. •

Global modes have mode shapes that are mostly non-zero, except at node points.

•

Local modes have mode shapes that are non-zero in a local region of the structure, and are zero elsewhere.

Curve Fitting Guidelines 1. Overlay the FRFs A resonance peak should appear at the same frequency in every Trace, except where node points (zero residue) of the mode shape occur. •

Execute Format | Overlay to overlay the FRFs and look for resonance peaks at the same frequency in all FRFs.

2. Inspect the Impulse Response Functions (IRFs) •

Execute Transform | Inverse FFT to transform the FRFs into IRFs.

•

All of the IRFs should exhibit a damped sinusoidal decay to almost zero at the end of each Trace, as shown below.

NOTE: Wrap around error is not harmful to frequency domain curve fitting.

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Impulse Response Functions. 3. Use the Mode Indicator •

Press the Count Peaks button on the Mode Indicator tab to count the number of modes (resonance peaks) in a cursor band.

4. Use the Band cursor •

Curve fit only those portions of the data that contain valid resonance peaks.

If the Band cursor is displayed, only data in the cursor band is used for curve fitting. Otherwise, all of the data in each Trace is used for curve fitting. 5. Verify Fundamental Mode Shapes Low frequency modes have simple bending and torsional mode shapes. Points that animate substantially different from neighboring Points on the structure model are indications of poor measurements, poor curve fits, or both. •

Estimate modal parameters for a few of the lower frequency (fundamental) modes, save the results into a Shape Table and animate the mode shapes to verify their validity.

6. Compare Results from Different Curve Fitting Methods •

Curve fit the FRFs using more than one curve fitting method, and compare the mode shapes.

•

Execute Display | MAC (Modal Assurance Criterion) to numerically compare shapes between two different curve fitting methods.

•

Execute Animate | Compare Shapes to display shapes in animation from two Shape Tables.

Modes | Modal Parameters

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Basic Modal Analysis Commands Initiates modal parameter estimation, (or curve fitting). When curve fitting is enabled, the following changes take place in the Data Block window, •

Trace graphics is displayed on the upper left side of the window.

•

A Mode Indicator graph is displayed on the lower left side of the window.

•

A Curve Fitting panel is displayed on the right side of the window, separated from the graphics by a red splitter bar.

•

Mode Indicator, Frequency & Damping, and Residues & Save Shapes tabs are displayed at the top of the panel.

•

A Modal Parameters spreadsheet is displayed below the tabs, separated by a blue splitter bar.

•

The Curve Fit command menu is displayed.

Data Block Window at the Start of Curve Fitting.

Curve Fitting Splitter Bars During curve fitting, four splitter bars are displayed in the Data Block window. Vertical Splitter Bars •

The vertical blue splitter bar separates the Trace & Mode Indicator graphics on the left from the Trace properties spreadsheet on the right of the window.

•

The vertical red splitter bar separates the Trace and Mode Indicator graphics on the left from the Curve Fitting panel on the right of the window.

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Data Block Window Showing Curve Fitting Splitter Bars. •

Drag the vertical blue splitter bar horizontally to display the Traces spreadsheet.

•

Drag the vertical red splitter bar horizontally to change the size of the Curve Fitting panel or the graphics area.

Horizontal Splitter Bars •

The left horizontal blue splitter bar separates the curve fitting tabs and the Modal Parameters spreadsheet.

•

The right horizontal blue splitter bar on the left separates the Traces graph and the Mode Indicator graph.

•

Drag the left blue splitter bar vertically to change the size of the curve fitting tabs or the Modal Parameters spreadsheet.

•

Drag the right blue splitter bar vertically to change the size of the Traces graph or the Mode Indicator graph.

Modal Parameters Spreadsheet This spreadsheet is where all modal parameter estimates are displayed. Each row of the spreadsheet contains modal parameter estimates for one mode.

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Basic Modal Analysis Commands

Select Mode Column •

Click on the Select Mode button to toggle the mode selection.

•

Double click on the Select Mode column heading to toggle the selection of all modes.

•

Select a mode, hold down the Shift key, and select the second mode to select a range of modes.

Frequency & Damping Columns •

Modal frequency is always listed as the damped natural frequency.

•

The damped natural frequency is approximately equal to the peak frequency of the resonance peak in the FRF data.

•

Modal damping can be listed is two columns, either as the percent of critical damping (in %) or the half power point damping (in Hz).

Residue Magnitude & Phase Columns •

The residue for each mode is listed as magnitude & phase.

•

The magnitude units are the units of the FRF times (radians per second). For example, if the FRF units are (g/ N), the residue units are (g/ N-sec)

•

Phase units are in degrees.

Methods Column The curve fitting methods used to estimate the parameters of each mode are listed in the Frequency & Damping Method column, and the Residues Method column. The following abbreviations are used for the curve fitting methods in the Basic Modal Analysis option, •

"Local-Poly" Local Polynomial

•

"Global-Poly" Global Polynomial

•

"Peak" Peak method

•

"Poly" Polynomial

Cursor Columns

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Reference Volume IIB - Options These two columns contain the Band cursor positions that were used for Frequency & Damping curve fitting and for Residue curve fitting. Showing & Hiding Spreadsheet Columns All columns can be shown or hidden (except the Select column). •

Right click on the Modal Parameters spreadsheet, and select Show/Hide Columns from the menu.

The File | Data Block Options box will open displaying the Show/Hide tab. •

Un-check columns to hide them and check columns to show them.

Reset Spreadsheet Column Widths •

Right click on the Modal Parameters spreadsheet, and execute Reset Column Widths from the menu.

Editing Cells •

Select the text in one or more spreadsheet cells.

•

Hold down the Ctrl key and press the X key to cut the selected text to the Clipboard.

•

Hold down the Ctrl key and press the C key to copy the selected text to the Clipboard.

•

Hold down the Ctrl key and press the V key to paste text from the Clipboard into the selected cells.

Mode Indicator Tab The first step of modal parameter estimation is to determine how many modes are represented by resonance peaks in a set of FRF measurements. •

The number of modes is required by the curve fitting methods used on the Frequency & Damping tab.

The Mode Indicator tab is used to; •

Calculate a Mode Indicator function.

•

Count the peaks above a Noise Threshold Line on the Indicator graph, as shown below.

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Basic Modal Analysis Commands

Mode Indicator Tab Mode Indicator The Mode Indicator is used for two purposes, •

To provide a single curve for counting the number of resonance peaks in a frequency band.

•

To limit the Frequency & Damping curve fitting methods to using the data surrounding each resonance peak.

The Mode Indicator is calculated by processing either the Real part, Imaginary part, or Magnitude of all (or selected) Traces in a Data Block file. To calculate the Mode Indicator function and count its peaks, •

Choose an Indicator from the Method drop down list on the Mode Indicator tab.

•

Press the Count Peaks button. A dialog box will open allowing you to choose a part of the Trace data to use for calculating the Mode Indicator. 1. Choose the Imaginary part when it has a single resonance peak for each mode. (With FRFs, this occurs when the response units are Displacement or Acceleration.) 2. Or choose the Real part when it has a single resonance peak for each mode. (With FRFs, this occurs when the response units are Velocity.) 3. Or choose Magnitude when neither criterion for choosing the Real or Imaginary part is valid.

When the Count Peaks button is pressed, the following actions occur, 1. A graph of the Mode Indicator is displayed in the lower left corner of the window. 2. The peaks above the horizontal Noise Threshold line on the Mode Indicator graph are counted. Each modal peak is indicated with a red dot on the Mode Indicator curve. 3. The number of peaks counted is displayed in the Modes box on this tab and the Frequency & Damping tab. CAUTION: If you move either the Noise Threshold or the Band cursors, peaks on the Indicator graph will be counted again and the Modes box updated.

Frequency & Damping Methods

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Reference Volume IIB - Options Polynomial Method The Polynomial method is Multi-Degree-Of-Freedom (MDOF) method that simultaneously estimates the modal parameters of one or more modes. This method uses the complex (real & imaginary) FRF data in the cursor band for curve fitting. A least squared error curve fit is performed on the FRF data to obtain estimates of the coefficients of the FRF denominator polynomial, called the characteristic polynomial. Modal frequency & damping estimates are then extracted as the roots of the characteristic polynomial, or poles of the FRF. Curve Fitting Assumptions •

Modal frequency & damping are global properties of a structure.

•

Each resonance peak in an FRF is evidence of at least one mode.

•

All FRF measurements taken from the same structure should have a resonance peak at the same frequency for each resonance.

•

If multiple FRFs are overlaid on one another, each resonance peak should appear at the same frequency in all FRFs.

Non-Stationary Data If a set of FRFs is acquired under non-stationary conditions (such as different mass loading due to roving accelerometers, temperature changes, etc.), resonance peaks may not be at the same frequency for each resonance. Global Versus Local Curve Fitting •

Global curve fitting can be used when resonance peaks "line up" in a set of overlaid FRFs.

•

Local curve fitting should be used when resonance peaks "do not line up" in a set of overlaid FRFs.

Frequency & Damping Tab This tab contains Global and Local curve fitting methods for estimating modal frequency & damping. •

When the Frequency & Damping button is pressed, the current Method will find estimates for the number of modes in the Modes box

•

All modal parameter estimates are added to the Modal Parameters spreadsheet in the lower right corner of the window

•

The current Method is used to curve fit all (or selected) FRFs

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Frequency & Damping Tab Showing Frequency & Damping Estimates for Six Modes. Global Polynomial Method The Global Polynomial method estimates one global value of frequency & damping for each mode. Local Polynomial Method The Local Polynomial method estimates one local value of frequency & damping for each mode and for each FRF. Extra Numerator Polynomial Terms The residual effects of out-of-band modes are compensated for by using additional numerator polynomial terms with the Polynomial method. •

The number of extra numerator polynomial terms can be user-specified between 0 & 10.

•

Four (4) extra terms is usually sufficient in most cases.

Vertical Frequency Lines Each frequency estimate in the modal parameters spreadsheet is displayed as a blue vertical line on the Mode Indicator graph. •

If a mode is selected, a red vertical line is displayed at the modal frequency on the Mode Indicator graph.

•

In the Band cursor is displayed, the modes in the band are selected.

•

Hold down the Alt key and position the mouse pointer near a red vertical line to display its frequency & damping values.

Horizontal Damping Lines Each modal damping estimate is displayed as a horizontal line crossing the vertical frequency line at the top of the Mode Indicator graph.

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The length of the Horizontal Line is 2σ. σ is called the half power point damping (in Hz), the 3 dB point damping, or the damping decay constant.

•

2σ is approximately equal to the width of the resonance peak at 70.7 % of the FRF peak magnitude, or half of the peak magnitude squared.

•

2σ is the width at the half power point of a resonance peak.

•

Zoom the display to display the damping lines more clearly.

Zoomed Display Showing Half Power Point Damping Lines.

Residue Methods Lightly Coupled Modes NOTE: If the resonance peaks in a set of FRFs are widely separated, these modes are called lightly coupled modes. •

When modes are lightly coupled, a Single-Degree-Of-Freedom (SDOF) method can be used to estimate modal parameters one mode at a time without incurring significant errors.

•

SDOF methods are used to quickly obtain mode shape estimates with a minimum of user interaction.

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Light and Heavily Coupled Modes Peak Method The Peak method is an SDOF method that saves the Peak value of the displayed FRF data in a band surrounding each modal frequency as the residue. •

The Peak method is useful when resonance peaks shift slightly from one FRF to another, due to non-stationary effects.

•

If the Imaginary part of the FRF is displayed, the Peak value of the Imaginary part from each FRF is saved as the residue for each mode.

•

If the Real part of the FRF is displayed, the Peak value of the Real part from each FRF is saved as the residue for each mode.

•

If neither the Real nor the Imaginary part of the FRF is displayed, the Real & Imaginary parts from each FRF at the Peak value of the magnitude is saved as the residue for each mode.

Closely Coupled Modes NOTE: If the resonance peaks in a set of FRFs are closely spaced, these modes are called closely coupled modes. •

A Multi-Degree-Of-Freedom (MDOF) method should be used to simultaneously estimate the modal parameters of closely coupled modes.

Polynomial Method The Polynomial method is a Multi-Degree-Of-Freedom (MDOF) method that uses all of the complex (real & imaginary) FRF data, or the data in the cursor band if it is displayed. •

During residue curve fitting, the numerator polynomial of each FRF is estimated by a least squared error curve fitting process. The denominator polynomial is constructed using the frequency & damping of all (or selected) modes in the Modal Parameters spreadsheet.

•

The residue for each mode and each FRF is obtained by performing a partial fraction expansion of each rational fraction polynomial, following the curve fitting process.

Extra Numerator Polynomial Terms The residual effects of out-of-band modes are compensated for by the use of additional numerator polynomial terms during Polynomial curve fitting.

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The number of extra polynomial terms used is specified on the Frequency & Damping tab.

Residues & Save Shapes Tab Residues Button The Residues button is enabled when at least one mode has modal frequency & damping estimates listed in the Modal Parameters spreadsheet. •

When the Residues button is pressed, the curve fitting method chosen from the Methods list is used to a estimate a complex residue (magnitude & phase) for each mode and each FRF.

•

All (or selected) FRFs are curve fit, and the residue estimates are added to the Modal Parameters spreadsheet for each mode.

Fit Function After residues have been estimated, a red fit function is synthesized using the modal parameters, and is overlaid on each Trace in the upper left graphics area. •

Each red fit function should closely match its corresponding FRF over the curve fitting band.

•

Use the vertical scroll bar next to the Traces to display each FRF, its red fit function, and its modal parameters in the Modal Parameters spreadsheet.

•

Use several different display formats (Magnitude, Bode, Nyquist) to compare the FRF and its red fit function.

Curve Fitting After Residues Have Been Estimated. Save Shapes Button The Save Shapes button is enabled when at least one mode has a residue estimate listed in the Modal Parameters spreadsheet. •

When the Save Shapes button is pressed, modal parameters for all (or selected) modes and all (or selected) Traces are saved into a Shape Table.

Removing Exponential Window Damping

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Basic Modal Analysis Commands If an exponential window has been applied to any FRFs prior to curve fitting, each of the modal damping estimates will have a known amount of artificial damping added to them by the exponential window. •

The cumulative amount of damping (in Hz) due to exponential windowing is displayed in the Window Value column of the Traces spreadsheet.

•

When modal parameters are saved into a Shape Table, the amount of exponential window damping is subtracted from all modal damping estimates.

Residue Mode Shapes When the Save Shapes button is pressed, Residue mode shapes are saved into the Shape Table. •

If the FRFs were properly calibrated when they were acquired from the test structure, the Residue mode shapes will preserve the mass, stiffness, & damping properties of the structure.

NOTE: A set of Residue mode shapes estimated from calibrated FRFs is called a Modal Model of the structure.

Curve Fit | Delete All Fit Data NOTE: All curve fitting data is saved with the Data Block in which curve fitting was performed. When this command is executed, the following data is deleted, •

All Fit Functions

•

All Mode Indicators

•

All modal parameters (the Modal Parameters spreadsheet is cleared).

Before starting a new session of curve fitting, it is a good practice to delete all curve fitting data from the Data Block.

Curve Fit | Quick Fit Curve fits all (or the selected) Traces with a minimum of user interaction. Quick Fit Steps

When the Quick Fit command is executed, the following steps are carried out in succession; 1. If no Mode Indicator is displayed, a Mode Indicator is calculated using the current Method on the Mode Indicator tab. 2. Peaks are counted (above the current noise threshold level) on the Mode Indicator, and only in the cursor band if it is displayed. 3. Modal Frequency & Damping are estimated for the number of peaks counted, using the current Method on the Frequency & Damp tab. 4. Modal Residues are estimated for the modes estimated in the previous step, using the current Method on the Residues & Save Shapes tab. 5. A red Fit Function is synthesized for each FRF using the curve fitting parameters, and overlaid on the experimental data. When Quick Fit has finished you can, •

Scroll through the FRFs, and verify that the Fit Functions match the experimental data.

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Save mode shapes into a Shape Table, 1. Either by pressing the Save Shapes button on the Residues & Save Shapes tab 2. Or by executing Curve Fit | Shapes | Save Shapes.

Improving Quick Fit Results

After performing a Quick Fit, if the results are not satisfactory, the following steps can be followed; 1. Execute Curve Fit | Delete Selected Modes to remove all of the Quick Fit results from the Modal Parameters spreadsheet. 2. Display the Band cursor or change its position to surround fewer resonance peaks. 3. Execute Curve Fit | Mode Indicator | Smooth to remove noise peaks from the Mode Indicator. 4. Scroll the Noise Threshold on the Mode Indicator so that only resonance peaks are counted. 5. Execute Curve Fit | Quick Fit again.

Data Block Window Following a Quick Fit. Fixed Number of Modes Quick Fit estimates modal parameters for the number of modes in the Modes box on the Frequency & Damping tab. •

The Modes box is automatically updated whenever peaks are counted on the Mode Indicator curve.

Peaks are counted when; •

A new Mode Indicator is calculated.

•

Curve Fit | Mode Indicator | Smooth is executed to smooth the Mode Indicator.

•

The noise threshold is scrolled.

•

The band cursor is moved.

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Basic Modal Analysis Commands To use a fixed number of modes for curve fitting, •

Enter the number into the Modes box and press the Enter key.

Curve Fit | Sort Modes by Frequency •

Sorts the modes in the Modal Parameters spreadsheet by ascending order of frequency.

Curve Fit | Delete Selected Modes •

Deletes the selected modes from the Modal Parameters spreadsheet.

Curve Fit | Clear Fit Functions •

Clears (zeros) the red Fit Functions of all (or selected) Traces.

•

If the band cursor is displayed, the Fit Functions are cleared in the band.

Curve Fit | Fit Function Synthesis •

Synthesizes a red Fit Function for all (or selected) Traces, using the modal parameters of all (or selected) modes in the Modal Parameters spreadsheet.

•

A red Fit Function is overlaid on each Trace.

•

If the band cursor is displayed, Fit Functions are only synthesized in the band.

•

Otherwise, Fit Functions are synthesized over the entire Trace frequency span.

Bode Plot of a Synthesized Fit Function Overlaid on an FRF.

Curve Fit | Mode Indicator Menu Clear (Clear In Band)

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Reference Volume IIB - Options Clears (zeroes) the Mode Indicator in the lower left graphics area. •

If the band cursor is displayed, the Indicator is cleared in the cursor band.

NOTE: The Mode Indicator is used by the Polynomial method on the Frequency & Damping tab for curve fitting FRF data at each resonance peak. Smooth Smooths the Mode Indicator to remove noise peaks. •

An exponential window is applied to the Mode Indicator to smooth it. (See Transform | Window Data | Exponential command for details).

•

Each time the Mode Indicator is smoothed, the resonance peaks will become wider and the modes more closely coupled.

Curve Fit | Shapes Menu Animate Shapes Animates a selected shape from the Modal Parameters spreadsheet, on the structure model in the connected Structure window. MAC Opens the Modal Assurance Criterion (MAC) window for comparing shapes in the Modal Parameters spreadsheet with shapes in a chosen Shape Table. Save Shapes Saves all (or selected) modes from the Modal Parameters spreadsheet into a Shape Table. NOTE: This command is the same as pressing the Save Shapes button on the Residues & Save Shapes tab.

Curve Fit | Close Terminates curve fitting and returns the Data Block display to Traces only. •

Curve fitting can also be terminated by executing Modes | Modal Parameters while curve fitting.

Modes | Display Traces Menu Measurements Displays the FRF measurements in the upper graphics area of the Data Block window. Fit Functions Displays a red Fit Function overlaid on each FRF Trace.

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CMIFs Displays Complex Mode Indicator Functions (CMIFs) in the lower graphics area of the Data Block window. MMIFs Displays Multivariate Mode Indicator Functions (MMIFs) in the lower graphics area of the Data Block window.

Modes | Copy Traces Menu Fit Functions Copies all (or selected) Fit Function Traces into another Data Block file. CMIFs Copies the CMIF Traces (including their associated Modal Participation curves) into another Data Block file. MMIFs Copies the MMIF Traces (including their associated Modal Participation curves) into another Data Block file.

Modes | Synthesize FRFs Synthesizes FRFs using all (or selected) modes in a Shape Table.

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An FRF is a cross-channel function that can be synthesized between any pair of mode shape DOFs.

•

The synthesized FRFs can then be overlaid on FRF measurements to verify the validity of the modal parameters.

Residue Mode Shapes Residues obtained from curve fitting a set of FRFs are saved into a Shape Table as Residue mode shapes. •

Each component of a Residue mode shape is defined between a pair of DOFs (Roving DOF : Reference DOF)

NOTE: FRFs can be synthesized for any DOF pair (shape component) in a set of Residue mode shapes. UMM Mode Shapes If a set of Residue mode shapes contains Driving Point Residues, (where the Roving DOF = Reference DOF), the Residue mode shapes can be scaled into UMM mode shapes. •

See Tools | Scaling Menu commands in the Modal Analysis Shape Table Commands section for details.

NOTE: FRFs can be synthesized for any two DOFs (shape components) in a set of UMM mode shapes. Type of Shapes in Shape Table

FRFs Synthesized

Residue Mode Shapes

Only for the Shape DOF pairs

UMM Mode Shapes

Between any two Shape DOFs

When this command is executed, a dialog box will open allowing you to choose a Shape Table with modal parameters in it. •

Choose a Shape Table with modal parameters in it, and click on OK.

In the dialog box that opens, the Block Size and Frequency Axis parameters are defaulted to the Data Block values, but they can be edited if desired. •

If using Residue mode shapes, choose all of the DOF pairs for synthesizing FRFs.

•

If using UMM mode shapes, choose all of the desired Roving & Reference DOFs for synthesizing FRFs.

•

Click on OK.

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Comparing Synthesized & Measured FRFs •

Select the measured FRFs in their Data Block.

•

Execute Edit | Paste Trace from File in the Data Block window containing the synthesized FRFs, and paste the measured into the synthesized FRFs Data Block.

•

Use the Color column in the Traces spreadsheet to color the synthesized and measured FRFs differently.

•

Execute Format | Overlay by DOF to overlay the synthesized and measured FRFs.

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Synthesized and Measured FRFs Overlaid.

Shape Table Basic Modal Analysis Commands NOTE: If the VES-4000 Basic Modal Analysis option is authorized, the following Shape Table commands are enabled in your software. Check Help | About to verify authorization of this option. Display Menu •

Display | MAC

•

Display | MAC

Tools Menu •

Tools | Scaling menu

•

Tools | Synthesize FRFs

Display | MAC Opens the Modal Assurance Criterion (MAC) window. •

MAC values, CoMAC (Coordinate MAC) values, and Shape Difference Indicator (SDI) values between pairs of shapes in two Shape Tables are displayed in this window.

WARNING: MAC & SDI values are calculated using the shape components for matching shape DOFs on the two Shape Tables. Clear all shape DOFs from both Shape Tables that are not required for calculating MAC & SDI values between shape pairs.

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MAC 3D Bar Chart. What is MAC? A MAC value is a quantitative method for comparing two complex shape vectors, {X} and {Y}. MAC values range between 0 & 1; •

MAC = 1.00 - means the two shapes are co-linear.

•

MAC > 0.90 - means the two shapes are partially co-linear.

•

MAC < 0.90 - means the two shapes are not co-linear.

MAC is calculated between two shapes {X} and {Y} using the formula;

where: H - denotes the transposed complex conjugate vector. || || - denotes the magnitude squared of the vector. What is CoMAC? A CoMAC value is a quantitative method for comparing two complex valued shape components (or shape DOFs). CoMAC compares shape components from two rows of the DOFs spreadsheets of two Shape Tables. CoMAC uses the MAC formula, where {X} and {Y} are vectors of the data from two rows of the DOFs spreadsheets. CoMAC values also range between 0 & 1; •

CoMAC = 1.00 - means the shape components of the selected shapes for the DOF pair are identical.

•

CoMAC > 0.90 - means the shape components of the selected shapes for the DOF pair are similar.

•

CoMAC < 0.90 - means the shape components of the selected shapes for the DOF pair are different.

What is a Shape Difference Indicator (SDI)?

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Reference Volume IIB - Options A Shape Difference Indicator value is a quantitative measure of the difference between two complex shape vectors, {X} and {Y}. SDI values range between 0 & 1; •

SDI = 1.00 - means the two shapes are identical.

•

SDI > 0.90 - means the two shapes are similar.

•

SDI < 0.90 - means the two shapes are different.

SDI is calculated between two shapes {X} and {Y} using the formula;

where: H - denotes the transposed complex conjugate vector. || || - denotes the magnitude squared of the vector.

Shape Difference Indicator 3D Bar Chart. MAC Window Commands File | Copy Graphics to Clipboard Copies the MAC window Graphics to the Windows Clipboard. File | Print Prints the graphics on the system graphics printer. File | Close Closes the MAC window. Display | Spreadsheet Displays the MAC, CoMAC, or SDI values in a spreadsheet. Display | 3D Bar Chart

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Basic Modal Analysis Commands Displays the MAC, CoMAC, or SDI values in a 3D bar chart. â€˘

Click & drag to rotate the 3D Bar Chart.

Display | Values When checked, the MAC, CoMAC, or SDI value for one shape pair is displayed on the 3D Bar Chart. â€˘

Hover the mouse pointer over a bar to display its value.

Display | MAC, CoMAC, SDI When checked, displays MAC, CoMAC, or SDI values in either a 3D Bar Chart or a spreadsheet. Display | Real Scale Factor, Imaginary Scale Factor, Scale Factor Magnitude The complex scale factor matrix is calculated as the solution to the following equation

Each column of the two shape matrices [U] & [V] is either a mode shape, ODS, or engineering data shape. Each column of the complex scale factor matrix [W] is the contribution of each shape in [U] to a shape in [V]. NOTE: If [W] is a diagonal matrix, then each shape in [V] is dominated by a corresponding shape in [U].

Bar Chart of Imaginary Scale Factors. Structure Options Animation Tab

Additional controls are added to the Animation Tab in the File | Structure Options box when the Display | MAC is enabled in the Shape Table.

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Show MAC •

If checked, the Modal Assurance Criterion (MAC ) value between the two animated shapes is displayed with the Comparison display.

•

Click & drag to move this box in a View.

WARNING: MAC values are calculated using the shape components for matching Point numbers (Point Labels) on the two Structure models. Clear all Point Labels from both models that are not required for calculating MAC values between shape pairs. Show SDI •

If checked, the Shape Difference Indicator (SDI) between the two shapes is displayed with the Comparison display.

•

Click & drag to move this box in a View.

WARNING: SDI values are calculated using the shape components for matching Point numbers (Point Labels) on the two Structure models. Clear all Point Labels from both models that are not required for calculating SDI values between shape pairs. Animate | Compare Shapes | Synchronize MAC This command is is also enabled in the Structure window. It displays two shapes with the highest MAC value together. •

When the shape from one Animation Source is selected, the shape with the highest MAC value in the other Animation Source is displayed.

WARNING: MAC values are calculated using the shape components for matching Point numbers (Point Labels) on the two Structure models. Clear all Point Labels from both models that are not required for calculating MAC values between shape pairs.

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Basic Modal Analysis Commands What is a Modal Model? DEFINITION: A Modal Model is a set of mode shapes that has been scaled to preserve the mass, stiffness & damping properties of a structure. In ME'scope, Residue mode shapes are obtained by curve fitting a set of FRFs. •

A Modal Model of Residue mode shapes is obtained by curve fitting a set of calibrated FRFs.

•

A Modal Model of UMM mode shapes is obtained by re-scaled a set of Residue mode shapes.

Uses of a Modal Model A Modal Model is required by several commands in ME'scope, •

Modes | Synthesize FRFs in a Data Block, or Tools | Synthesize FRFs in a Shape Table

•

Transform | MIMO | Outputs in a Data Block

•

Transform | MIMO | Inputs in a Data Block

•

Transform | MIMO | Sinusoidal ODS in a Data Block, or Tools | Sinusoidal ODS in a Shape Table

•

SDM | Calculate New Modes in a Structure window

•

SDM | Modal Sensitivity in a Structure window

•

SDM | Add Tuned Absorber in a Structure window

•

FEA | FEA Model Updating in a Structure window

•

FEA | Calculate Updated FEA Modes in a Structure window

Tools | Scaling Menu Residue to UMM Shapes Converts a set of Residue mode shapes to UMM mode shapes. NOTE: Each Residue mode shape must have at least one non-zero Driving Point residue in order to convert it to a UMM mode shape. Multiple Reference Shapes If the Residue mode shapes contain multiple reference DOFs, the following dialog box will open,

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Multiple Reference Selection Box. The selected Reference DOF in the dialog box is the reference with the highest participation factor for each mode. NOTE: The highest participation factor is the highest driving point residue for each mode among its driving point residues. MAC Column If two Reference DOFs are selected for a mode, the Modal Assurance Criterion (MAC) value for the two shapes is displayed. MAC values should be used as follows; •

MAC > 0.9 indicates that the two shapes from the two selected References are essentially the same.

•

MAC < 0.9 indicates that the two shapes from the two selected References are different.

If two Residue mode shapes have a MAC > 0.9, then either one can be converted to a UMM shape. NOTE: When the Save button is pressed, a UMM mode shape will be saved for each selected reference DOF. UMM to Residue Shapes Converts a set of UMM mode shapes to Residue mode shapes. When executed, a dialog box will open, •

Select a Reference DOF

•

Or hold down the Ctrl key and select two or more DOFs

•

Click on OK.

NOTE: Any DOF of the UMM mode shapes can be chosen as a Reference DOF.

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Residue Mode Shapes •

A set of calibrated FRFs acquired from a structure will have engineering units of (displacement, velocity, or acceleration / excitation force).

•

A set of calibrated FRFs preserves the dynamic (mass, stiffness & damping) properties of the structure.

•

A set of Residue mode shapes obtained by curve fitting calibrated FRFs also preserves the dynamic (mass, stiffness & damping) properties of the structure.

Residue Mode Shape Units Residues are the numerator terms in an FRF. (See the FRFs in Terms of Modal Parameters section for details.) The FRF denominators have units of Hz, or (radians / second). Therefore, •

Residue mode shapes have units of (displacement, velocity, or acceleration) / force-sec).

•

Typical SI Residue mode shape units are; g / (N-sec)

•

Typical English Residue mode shape units are; g / (Lbf-sec)

Editing Residue Units To edit the Residue mode shape units, •

Double click on the Units column header in the DOFs spreadsheet.

•

Choose the proper response units (displacement, velocity or acceleration) in the dialog box that opens

•

Type in a "/", followed by the force units, followed by "-sec".

•

Click on OK.

UMM Mode Shapes A mode shape is an eigenvector, meaning that its "shape" is unique, but it values are not unique. Because they are eigenvectors, mode shapes don't normally have engineering units. On the other hand, Residue mode shapes do have engineering units because residues are the numerators of the parametric model used for curve fitting an FRF. When a set of Residue mode shapes (with units) is converted into a set of UMM mode shapes, the UMM mode shapes will also have units, and also preserve the dynamic properties of a structure.

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Reference Volume IIB - Options NOTE: If Residue mode shapes with engineering units are converted to UMM mode shapes with engineering units, the UMM mode shapes are called a Modal Model. UMM Displacement Response Units UMM mode shapes are always have (displacement / force-sec) units. Therefore, Residue mode shapes with (velocity / force-sec) or (acceleration / force-sec) units are integrated to (displacement / force-sec) units during the creation of UMM mode shapes. •

If Residue mode shapes with g / (N-sec) units are converted to UMM mode shapes, the UMM mode shapes will have m / (N-sec) units.

•

If Residue mode shapes with g / (lbf-sec) units are converted to UMM mode shapes, the UMM mode shapes will have in / (lbf-sec) units.

Compatibility Between UMM and Structure Units for SDM To use UMM mode shapes with the Structural Dynamics Modification (SDM) commands, the Structure length & force units must match the UMM mode shape length & force units. NOTE: Mass modifications in SDM are re-scaled to make them compatible with the UMM mode shape length & force units.

Tools | Synthesize FRFs Synthesizes FRFs from modal parameters in a Shape Table. •

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See Modes | Synthesize FRFs command description in this chapter for details.

Multi-Reference Modal Analysis Commands Data Block Multi-Reference Modal Commands NOTE: If the VES-4550 Multi-Reference Modal Analysis option is authorized, the following Data Block commands, and mouse and keyboard operations are enabled in your software. Check Help | About to verify authorization of this option. Multi-Reference Methods Multi-Reference curve fitting methods are enabled on the Mode Indicator, Frequency & Damping, and Residues tabs. Stability Tab The Stability tab is enabled during curve fitting, containing several Multi-Reference curve fitting methods and the Stability and Poles diagrams. Animate Menu •

Animate | Normalize Shapes

Display Menu •

Display | Complexity Plot

•

Display | Magnitude Ranking

Modes Menu •

Modes | Modal Decomposition

Special Mouse & Keyboard Operations •

Hold down the Alt key, and place the mouse pointer near a frequency estimate (vertical line) on the Mode Indicator graph to display its Frequency & Damping box.

•

Hold down the Alt key, and click the left mouse button to display its Frequency & Damping box permanently on the Mode Indicator graph.

•

Click & drag to move the nearest Frequency & Damping box on the Mode Indicator graph.

•

Hold down the Alt key, and click the right mouse button to erase all Frequency & Damping boxes on the Mode Indicator graph.

•

Right click near a frequency estimate (vertical line) to select the mode in the modal parameters spreadsheet.

•

Hold down the Ctrl key, click & drag to draw a selection box enclosing a group of stable poles on the Stability or Poles diagram.

When Is Multi-Reference Modal Analysis Necessary? Multi-Reference Modal Analysis is required when the resonances of a structure occur under one of the following conditions; •

Closely Coupled modes: One FRF resonance peak in FRFs represents two or more modes.

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Repeated roots: Two or more modes have the same natural frequency but different mode shapes.

•

Local modes: Different resonance peaks occur in FRFs from different references.

In each of the above cases, multiple reference curve fitting is required in order to properly extract all modal parameters from a set of FRFs. Multiple reference FRFs correspond to multiple rows or columns of the FRF matrix in the MIMO model. (See the Tutorial - MIMO Modeling & Simulation chapter for details.) Single Reference versus Multi-Reference FRFs A single reference set of FRFs is, •

The minimum requirement for extracting experimental modal parameters by FRF-based curve fitting.

•

Obtained by exciting the structure with a single (fixed) exciter, or a single (fixed) response transducer.

•

A single row or column of elements in the FRF matrix of a MIMO model of the structure.

•

Not sufficient for extracting closely coupled modes, repeated roots, or local modes of a structure.

A multi-reference set of FRFs is, •

Required for extracting closely coupled modes, repeated roots, or local modes of a structure.

•

Obtained by exciting the structure with multiple (fixed) exciters or using multiple (fixed) response transducers.

•

Multiple rows or columns of elements in the FRF matrix of a MIMO model of the structure.

•

Useful for extracting modes when a structure has high modal density.

Mult-Reference Modal Test A multiple reference modal test is done using either multiple (fixed) exciters or multiple (fixed) response transducers. NOTE: Each fixed transducer is called a Reference. Multiple Shaker Test In a multiple shaker test, two or more (fixed) shakers are used to simultaneously excite the structure. •

The multiple shakers must be driven with un-correlated broad band signals.

•

An FRF between each response and each (reference) force, plus Multiple & Partial Coherences are calculated in this multiple reference test.

•

The FRFs are elements from two or more columns of the FRF matrix in a MIMO model of the structure.

Large structures with non-linear dynamic behavior are tested using multiple shakers, driven by pure or burst random excitation signals. NOTE: Random excitation together with spectrum averaging is used to "average out" the non-linear dynamic behavior of the structure from the FRFs.

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Multi-Reference Modal Analysis Commands Multiple Reference Roving Impact Test In a multiple reference roving impact test, two or more (fixed) response transducers are used, and the structure is excited with a roving impactor. â€˘

This test is the same as performing two or more single Reference modal tests, but is much faster.

â€˘

The FRFs are elements from two or more rows of the FRF matrix in a MIMO model of the structure.

Multi-Reference Mode Indicators As part of the Multi-Reference Modal Analysis option, both Multi-Reference CMIFs (Complex Mode Indicator Functions) and Multi-Reference MMIFs (Multivariate Mode Indicator Functions) are added to the Mode Indicator methods list on the Mode Indicator tab. NOTE: A peak at or near the same frequency in two or more Multi-Reference Indicator curves indicates closely coupled modes or repeated roots.

CMIFs Indicating Two Closely Coupled Modes Near 200 Hz. Multi-Reference CMIF The Multi-Reference CMIF curves are calculated by performing a singular value decomposition of multi-reference FRF data, resulting in a separate CMIF curve for each reference. NOTE: Each peak on each CMIF curve is an indication of a resonance. Multi-Reference MMIF The Multi-Reference MMIF curves are calculated by performing an eigensolution of multi-reference FRF data, resulting in a separate MMIF curve for each reference. NOTE: Each peak (or valley) on each MMIF curve is an indication of a resonance. Modal Participation Factors

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Reference Volume IIB - Options The Multi-Reference CMIF & MMIF calculations also provide Modal Participation Factor curves for each reference of FRF data. NOTE: Modal participation factors are used to weight each reference of data during Multi-Reference curve fitting.

Multi-Reference Parameter Estimation Multi-Reference Polynomial Uses a multi-reference version of the Rational Fraction Orthogonal Polynomial method for estimating Frequency & Damping and Residues. Uses the curve fitting model size in the Modes box on the Frequency & Damping tab. Stability Diagram Methods When the Multi-Reference Modal Analysis is enabled, a Stability tab is added to the curve fitting tabs in a Data Block window. The Stability tab contains curve fitting methods for estimating modal frequency & damping using very large curve fitting model sizes. Alias Free Polynomial •

An extension of the Rational Fraction Orthogonal Polynomial method.

•

The term "alias free" refers to its characteristic of placing computational modes toward the edges of the curve fitting band, instead of aliasing them throughout the band.

Complex Exponential •

A time domain method that estimates poles by curve fitting Impulse Response Functions (IRFs).

•

During curve fitting, the Inverse FFT is applied to each FRF to obtain its corresponding IRF.

Z Polynomial •

An extension of the Rational Fraction Orthogonal Polynomial method.

•

Uses the Z transform to transform frequency to a unit circle, resulting in numerically stable solution equations.

Methods Column The curve fitting methods used to estimate the parameters of each mode are listed in the Frequency & Damping Method column, and the Residues Method column. The following abbreviations are used for the curve fitting methods in the Multi-Reference Modal Analysis option, •

"AF Poly" Alias Free Polynomial

•

"Comp Exp" Complex Exponential

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"Z Poly" Z Polynomial

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"M-Poly" Multi-Reference Polynomial

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"M-AF Poly" Multi-Reference Alias Free Polynomial

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"M-Comp Exp" Multi-Reference Complex Exponential

•

"M-Z Poly" Multi-Reference Z Polynomial

Stability Diagram

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Multi-Reference Modal Analysis Commands When the Multi-Reference Modal Analysis is enabled, a Stability tab is added to the curve fitting tabs in a Data Block window. •

The curve fitting methods on the Stability tab are used to obtain modal frequency & damping (pole) estimates without counting resonance peaks.

The Stability tab contains curve fitting methods for estimating modal frequency & damping using very large curve fitting model sizes. Why Use a Stability Diagram? A Stability diagram is a plot of frequency & damping (pole) estimates from multiple curve fitting model sizes. Stability curve fitting starts with a model for one (1) Poles and ends with a model for the number of poles in the Max Model Size box on the Stability Method tab. •

Each modal frequency estimate is displayed as a vertical line on the Stability diagram.

•

Each modal damping estimate is displayed as a horizontal line on the Stability diagram.

•

A Poles is said to be"stable" if its estimates do not change significantly from one curve fitting model size to the next (one row of the Stability diagram to the next).

Stability Diagram Showing Stable Poles and Computational Poles at Edges. Stable Group of Poles The Stability diagram is displayed on top of a Mode Indicator graph. A Stable Group of poles must meet all of the following criteria; •

A Poles must have a damping estimate less than or equal to the Maximum Damping to be a candidate for a Stable Group.

•

All poles with frequency estimates within the Frequency Tolerance are candidates for a Stable Group.

•

All poles with damping estimates within the Damping Tolerance are candidates for a Stable Group.

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If the number of poles satisfying the three criteria above is greater than or equal to the Min. Number of Stable Poles, the poles are displayed as a Stable Group on the Stability diagram using the same color.

NOTE: Stable Group Colors alternate between the top two Contour Colors in the File | Data Block Options box. •

Hold down the Alt key and position the mouse pointer near a Poles on the Stability diagram to display its frequency & damping values.

Stability Diagram Showing Stable Pole Groups. Poles Diagram The poles can also be displayed on a Poles diagram, as shown below. On the Poles diagram modal frequency estimates are plotted along the horizontal axis, and modal damping estimates along the vertical axis. •

Check the Poles box on the Stable Groups tab to display the Poles diagram,

•

Hold down the Alt key and position the mouse pointer near a Poles to display its frequency & damping values.

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Poles Diagram. Changing the Stable Group Tolerances The Stability diagram is updated whenever any of the Stability Tolerances on the Stable Groups tab is changed. •

To change a Stability Tolerance, click on its radio button, and scroll the slider bar on the right side of the Stable Groups tab.

•

Press the Reset button to reset all of the Stability Tolerances to default values.

Percentage of Critical Damping or 3 dB Bandwidth Damping Damping can be chosen either as a percentage of critical damping (%) or as the 3 dB or half power point damping (in Hz). •

The current type of damping is displayed next to its selected radio button.

•

See the FRFs in Terms of Modal Parameters section for definitions of these two damping terms.

Displaying Pole Values •

Hold down the Alt key and place the mouse pointer near a Poles to display its values.

•

Hold down the Alt key and click near a Poles to permanently display its values.

•

Hold down the Alt key and right click to clear all displayed Poles values.

Save Groups Button When the Save Groups button is pressed, •

The average value of the poles in each visible Stable Group is added to the Modal Parameters spreadsheet.

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If the Band cursor is displayed, the average value of the poles in each Stable Group within the band is added to the Modal Parameters spreadsheet.

Stability | Pole Selection Box Enables the drawing of a selection box to select Poles from the Stability or the Poles diagram. •

When the selection box is enabled, the mouse pointer on the Stability or Poles diagram will change to a "cross".

•

Click & drag to draw a selection box to enclose one or more desired poles.

•

All poles within the selection box are averaged together and added to the Modal Parameters spreadsheet.

•

Hold down the Ctrl to enable this command.

Stability | Clear Stability Diagram •

Clears the Stability Diagram from the Mode Indicator graph area.

Display | Complexity Plot (Data Block) Opens the Complexity Plot window, as shown below. •

A Complexity Plot displays the magnitudes & phases of all (or selected) Trace values, at the current Cursor position.

•

See the Display | Complexity Plot in the Shape Table commands section for more details.

Data Block Complexity Plot.

Animate | Normalize Shapes (Data Block) Displays shapes as either complex of normalized. When enabled, normalized shapes are displayed during shape animation from a Data Block. NOTE: See Display | Complexity Plot (Data Block) for more details. This command is also enabled in an Acquisition Window.

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Multi-Reference Modal Analysis Commands Display | Magnitude Ranking (Data Block) Displays a Magnitude Ranking bar chart from a Data Block window. •

This bar chart displays the magnitudes of the Trace values at the current cursor location.

•

Trace magnitudes are plotted on the vertical axis versus and Trace DOFs on the horizontal axis.

•

The magnitudes are ranked from the largest on the left to the smallest on the right.

•

The Magnitude Ranking chart is updated whenever the cursor is moved, or different Traces are selected.

Trace Magnitude Ranking Chart. Which Magnitudes Are Ranked? •

If the Real part of the Traces is displayed, the Real parts are ranked.

•

If the Imaginary part of the Traces is displayed, the Imaginary parts are ranked.

•

Otherwise, the magnitudes of the Traces are ranked.

Magnitude Values •

Hover the mouse pointer over a magnitude bar to display its value and DOFs on the bottom of the window.

Modes Modal Decomposition Decomposes time or frequency Data Block Traces into "resonance curves" that represent the contribution of each shape in a Shape Table to the overall Trace data. Solves the following equation for each Trace, at each sample of Trace data in a Data Block,

where:

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Reference Volume IIB - Options [ Shape Table ] = matrix of mode shapes or operating deflection shapes (ODS's). Each matrix column is a mode shape or ODS. { Weights } = vector of weights (one for each shape), for each sample of Trace data. { ODS } = the operating deflection shape (ODS) for each Trace sample. Each weight curve is saved as a new Trace in a new Data Block. For example, if there are 10 shapes in a Shape Table, then 10 Traces of weights are created for each Trace sample.

Data Block Showing Modal Decomposition Traces Overlaid.

Shape Table Multi-Reference Modal Commands NOTE: If the VES-4550 Multi-Reference Modal Analysis option is authorized, the following Shape Table commands, and spreadsheet columns are enabled in your software. Check Help | About to verify authorization of this option. Animate Menu •

Animate | Normalize Shapes

Display Menu •

Display | Shape DOFs | M,C,K

•

Display | Poles

•

Display | Complexity Plot

•

Display | Magnitude Ranking

Tools menu •

Tools | Shape Expansion

MPC (Modal Phase Colinearity) Column

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Multi-Reference Modal Analysis Commands The MPC is a measure of whether or not all of the components of a complex shape lie on a straight line in a Complexity Plot. •

MPC values range between 0 and 1.

•

If MPC = 1, all mode shape components lie on a straight line.

•

If MPC < 1, all mode shape components do not lie on a straight line.

•

If MPC is "close to 1", this indicates that the structure is lightly damped, or that the mode shape is a normal mode shape.

NOTE: An FEA model of a structure (with no damping) yields normal mode shapes. All phases of a normal mode shape are 0 & 180 degrees.

Display | Shape DOFs | M,C,K Displays the effective mass, damping & stiffness (also called the generalized mass, damping & stiffness) of each mode shape in the DOFs spreadsheet. •

Effective mass, damping & stiffness are the values each mode would have if it were a single Mass-Spring-Damper system located at each DOF of the mode shape.

The effective mass, damping & stiffness are calculated for each mode with the formulas, Effective Mass = 1 / (Freq x Real part (DP Residue) + Damp x Imaginary part (DP Residue) Effective Damping = 2 x Damp x Effective Mass 2

2

Effective Stiffness = (Freq + Damp ) x Effective Mass where: Freq - damped natural frequency of the mode. Damp - half power point damping of the mode. DP Residue - driving point Residue for each DOF of the mode shape. NOTE: This command can only be used with UMM mode shapes. The Effective Mass requires the driving point residue, which is calculated from each mode and each shape DOF of the UMM mode shapes.

Animate | Normalize Shapes (Shape Table) Displays shapes as either complex of normalized. When enabled, normalized shapes are displayed during shape animation from a Shape Table. NOTE: See Display | Complexity Plot (Shape Table) for more details.

Display | Poles Displays shape poles in a separate Poles Plot window. A Poles Plot displays shape frequency on the horizontal axis and damping on the vertical axis of each shape in a Shape Table. •

Damping can be displayed either as the percent of critical damping (%), or as the half power point damping (in Hz).

•

See the FRFs in Terms of Modal Parameters section in the Basic Modal Analysis Commands chapter for details.

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Poles Plot.

Display | Complexity Plot (Shape Table) Opens the Complexity Plot window, as shown below. •

A Complexity Plot displays the magnitudes & phases of all (or selected) shape DOFs for all (or selected) shapes.

Shape Table Complexity Plot. Normal Shape •

A normal shape has shape components with phases of 0 or 180 degrees.

•

A normal shape will look like a standing wave during shape animation, and its Node Lines will not move.

•

The shape components of a normal shape lie on a straight line in a Complexity Plot.

Complex Shape

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Multi-Reference Modal Analysis Commands •

A complex shape can have an arbitrary phase in each of its shape components.

•

A complex shape will look like a traveling wave during shape animation, and its Node Lines can move .

•

The shape components of a complex shape do not lie on a straight line in a Complexity Plot.

Experimental mode shapes can be complex valued for a number of reasons; •

Real structures with damping in them can have complex mode shapes.

•

Measurement errors introduce arbitrary phase in the shape component estimates.

•

Curve fitting errors introduce arbitrary phase in the shape component estimates.

Normalized Shapes Normal shapes are created by "normalizing" complex shapes. •

The normalization line (dashed line) on a Complexity Plot is used to normalize a complex shape.

•

When a shape is normalized, the magnitude of each shape component is retained but the phase is changed to either 0 or 180 degrees.

•

When a shape is normalized, the red (+) shape components are given 0 degrees phase, and the blue (-) shape components are given 180 degrees phase.

•

When Display | Shapes Normalized is checked, complex shape DOFs are displayed on the left, and normalized shape DOFs are displayed on the right of the Complexity Plot,

To rotate the normalization line to a different position, •

Click & drag near the normalization line.

•

Or execute Display | Set Normalization Angle, and enter an angle in the dialog box.

Complexity Plot with Shape Normalization Turned ON. MPC (Modal Phase Colinearity) If only one shape is displayed in the Complexity Plot, its MPC (Modal Phase Colinearity) value is also displayed. •

MPC values range between 0 &1.

•

If MPC = 1, all components the shape lie on a straight line.

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Reference Volume IIB - Options •

If MPC < 1, some shape components do not lie on a straight line.

Flipping the Sign of a Shape During Comparison Animation, if two similar shapes appear to be animating 180 degrees out of phase with one another, the phases of right hand shape can be changed by 180 degrees so that the two shapes animate more closely together. To flip the sign of the right hand shape; •

Execute Animate | Compare Shapes | Flip Sign in the Structure window to multiply the right hand shape by "-1".

•

Or rotate the normalization line on the Complexity Plot by dragging it to flip the phase.

Display | Magnitude Ranking (Shape Table) Displays a shape Magnitude Ranking bar chart from a Shape Table window. This bar chart displays the magnitude of all shape components, ordered from the largest to the smallest. •

Shape component magnitudes are plotted on the vertical axis versus shape DOFs on the horizontal axis.

•

The magnitudes are ranked from the largest on the left to the smallest on the right.

Shape Magnitude Ranking Chart. Which Magnitudes Are Ranked? •

If the Real parts of the shape DOFs are displayed, the Real parts are ranked.

•

If the Imaginary parts of the shape DOFs are displayed, the Imaginary parts are ranked.

•

Otherwise, the magnitudes of the shape DOFs are ranked.

Magnitude Values •

Hover the mouse pointer over a magnitude bar to display the magnitude value on the status bar at the bottom of the window.

Tools | Shape Expansion Expands the DOFs in a set of shapes using another set of shapes with many DOFs in them. This command is very useful for;

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Multi-Reference Modal Analysis Commands •

Expanding a set of experimental mode shapes using a set of FEA mode shapes with many DOFs in them.

•

Expanding an ODS using a set of mode shapes with many DOFs in them.

The algorithm performs a least-squared-error fit of the shapes with many DOFs in them to one or more shapes with a few DOFs. The frequency & damping of each shape with a few DOFs are also applied to each expanded shape.

•

Execute this command in the Shape Table containing the shape (or shapes) to be expanded.

•

A file dialog box will open from which the Shape Table containing shapes with many DOFs in them can be selected.

•

After the calculation is completed, another file dialog box will open for choosing a Shape Table for saving the expanded shapes.

NOTE: Shape expansion can be controlled by selecting shapes and/or DOFs in either Shape Table before executing this command.

Draw or Animate | Normalize Shapes Displays shapes as either complex of normalized. When enabled, normalized shapes are displayed during shape animation. NOTE: See Display | Complexity Plot (Shape Table) for more details.

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Operational Modal Analysis (OMA) Commands Data Block OMA Commands NOTE: If the VES-4750 Operational Modal Analysis option is authorized, the following Data Block commands are enabled in your software. Check Help | About to verify authorization of this option. Transform Menu •

Transform | Increase Resolution

•

Transform | Window Traces (DeConvolution window)

Curve Fitting OMA Measurements Experimental modal parameters are normally estimated by curve fitting a set of FRFs. To calculate an FRF, all excitation forces must be simultaneously acquired together with structural responses. However, structural responses can always be acquired, even when the excitation forces are not acquired. •

The Fourier spectra, Cross spectra or ODS FRFs can be calculated from Output only (or operating) data.

•

Operating mode shapes can be extracted from a set of Fourier spectra by using FRF-based curve fitting methods, but the Fourier spectra, but all of the responses must be simultaneously acquired.

•

Cross spectra and ODS FRFs are cross channel measurements, which can be measured a few at a time, if one of the channels is a (fixed) reference channel.

•

Operating mode shapes can be extracted from a set of Cross spectra or ODS FRFs using FRF-based curve fitting methods, but a DeConvolution window must be applied to these measurements before curve fitting them.

Fourier Spectra A Fourier spectrum is the Fourier transform of single channel time domain data using the FFT. In order to curve fit them and extract operating mode shapes, •

All response signals must be simultaneously acquired.

•

Operating mode shapes can be extracted from Fourier spectra using FRF-based curve fitting.

Cross Spectra A Cross spectrum is a cross channel measurement which is calculated using two channels of response data. The correct relative magnitude & phase between all Roving responses is preserved if all Cross spectra are calculated between a Roving response and the same (fixed) Reference response. •

Multiple Measurement Sets of Cross spectra are calculated from simultaneously acquired Roving responses and the same (fixed) Reference response.

•

After a DeConvolution window has been applied, operating mode shapes can be extracted from Cross spectra using FRF-based curve fitting.

ODS FRFs An ODS FRF is a "hybrid" cross channel measurement which is also calculated using two channels of response data. An ODS FRF combines the Auto spectrum of a Roving response (magnitude) with the phase of the Cross spectrum between the Roving and a (fixed) Reference response channel. The

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Reference Volume IIB - Options correct relative magnitude & phase between all Roving responses is preserved if all ODS FRFs are calculated between a Roving response and a (fixed) Reference response. •

Multiple Measurement Sets of ODS FRFs are calculated from simultaneously acquired Roving responses and the same (fixed) Reference response.

•

After a DeConvolution window has been applied, operating mode shapes can be extracted from ODS FRFs using FRF-based curve fitting.

Flat Force Spectrum FRF-based curve fitting is applied mainly around peaks in a Fourier spectrum, or in a windowed Cross spectrum or ODS FRF. If the following assumption is met, then peaks in these output-only measurements are due to modes of vibration ASSUMPTION: If the frequency spectrum of the un-measured excitation forces is assumed to be "relatively flat", then operating mode shapes can be extracted from output-only measurements using FRF-based curve fitting.

Transform | Increase Resolution Increases the resolution (reduces the spacing) between samples of data in either time or frequency domain data. Increasing the frequency resolution can help improve FRF-based curve fitting, by increasing the number of samples surrounding the resonance peaks. •

Each time this command is executed, the Block Size (number of samples) in a Data Block is doubled.

•

Linear interpolation is used between samples to increase the resolution.

After the resolution is increased, the File | Data Block Properties dialog box is opened showing the new Block Size and new Data Block resolution.

File Properties Before Increasing Resolution.

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File Properties After Increasing Resolution.

Transform | Window Traces | (DeConvolution window) Applies the DeConvolution window to all (or selected) Traces in a Data Block. The DeConvolution window smoothly zeroes (removes) the second half of each time domain Trace. When transformed to the frequency domain, these windowed Traces can be curve fit using FRF-based curve fitting methods. NOTE: The DeConvolution window must be applied to non-FRF measurements before FRF-based curve fitting methods can be used. When this command is executed in a Data Block containing frequency domain Traces, the following steps are carried out, 1. Transform all Traces to the time domain using the Inverse FFT. 2. Apply the DeConvolution window to all (or selected) Traces. 3. Transform all Traces back to the frequency domain using the FFT. The figures below show some Cross spectra before and after the DeConvolution window has been applied to them. Notice that noise is also removed from the measurements by the DeConvolution window.

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Cross Spectra Before Devolution Windowing.

Cross Spectra After Devolution Windowing.

Shape Table OMA Commands NOTE: If the VES-4750 Operational Modal Analysis option is authorized, the following Shape Table command is enabled in your software. Check Help | About to verify authorization of this option. Three Types of Mode Shapes UMM Mode Shapes UMM mode shapes preserve the dynamic properties of a structure. â€˘

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See Tools | Scaling in the Multi-Reference Modal Analysis Commands chapter and Uses of a Modal Model for details regarding UMM mode shapes.

Operational Modal Analysis (OMA) Commands FEA Mode Shapes FEA mode shapes are obtained from an FEA model of a test article and are typically scaled as UMM mode shapes. •

See the Tutorial - Experimental FEA chapter for details on FEA mode shapes.

Residue Mode Shapes Residue mode shapes are extracted by curve fitting a set of FRFs. •

Residue mode shapes with a little as one component can be extracted by curve fitting a Driving Point FRF taken from a test article.

•

A driving point Residue can be re-scaled to a UMM mode shape component.

Scaling Operational Mode Shapes or ODS's

Operational mode shapes and Operating Deflection Shapes (ODS's) can be rescaled so that they can be used as a modal model by using the Tools | Scaling | Unscaled to Scaled Shapes command. A set of UMM mode shapes, FEA mode shapes or Residue mode shapes can be used with this command to re-scale Operational mode shapes or ODS's. Tools | Scaling | Unscaled to Scaled Shapes Re-scales a set of shapes using another set of shapes. When this command is executed from the Shape Table with unscaled shapes in it, a dialog box will open for selecting a Shape Table with scaled shapes in it. The following dialog box will open next.

Unscaled Mode Shapes Dialog Box. •

Press Calculate Scale Factors.

A set of complex scale factors is determined by calculating a least squared error fit between each unscaled shape and each scaled shape. •

Notice that although the MAC values of the shapes are close to "1.0", indicating that the shapes are co-linear, the scale factors indicate that the shapes have different values.

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Reference Volume IIB - Options

Mode Shape Scale Factors. â€˘

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Press Save Scaled Shapes to save the re-scaled shapes into a new Shape Table.

Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands Data Block MIMO Commands NOTE: If the VES-3550 MIMO Modeling & Simulation option is authorized, the following Data Block commands are enabled in your software. Check Help | About to verify authorization of this option. Transform | MIMO Menu •

Transform | MIMO | Transfer Functions

•

Transform | MIMO | Outputs

•

Transform | MIMO | Inputs

•

Transform | MIMO | Sinusoidal ODS

What is a MIMO (Multi-Input Multi-Output) Model? Calculation of Outputs, Inputs, and Transfer Functions is based upon a MIMO (Multi-Input MultiOutput) model of the dynamics of a structure. A MIMO model is a frequency domain equation where the Fourier spectra of multiple Inputs are multiplied by elements of a Transfer Function matrix to yield the Fourier spectra of multiple Outputs. The MIMO model is written as,

{X(ω)} = [H(ω)] {F(ω)} where:

{F(ω)} - Input Fourier spectra (m - vector) [H(ω)] - Transfer Function matrix (n by m) {X(ω)} - Output Fourier spectra (n - vector) m - number of Inputs n - number of Outputs ω - frequency variable (radians per second) •

Rows of the Transfer Function matrix correspond to Outputs, and columns correspond to Inputs.

•

Each Input and each Output corresponds to a DOF (point & direction) on a structure.

•

Each Transfer Function is a cross-channel measurement between two DOFs, an Input DOF and an Output DOF.

MIMO Calculations NOTE: Any part of the MIMO model, (Inputs, Outputs, or Transfer Functions) can be calculated from the other two parts. •

Inputs & Outputs can be either time or frequency domain Traces, including Auto & Cross spectra and PSD's.

•

Transfer Functions can be either measured or synthesized from modal parameters.

Transfer Function

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Reference Volume IIB - Options •

A Transfer Function is the Fourier spectrum of an Output divided by the Fourier spectrum of an Input.

Frequency Response Function (FRF) •

An FRF is a special kind of Transfer Function.

•

An FRF is the Fourier spectrum of a displacement, velocity, or acceleration response divided by the Fourier spectrum of the excitation force that caused the response.

Transmissibility •

A Transmissibility is a special kind of Transfer Function.

•

A Transmissibility is the Fourier spectrum of an Output divided by the Fourier spectrum of an Input with the same units.

Trace DOFs and Input Output Before using one of the Transform | MIMO commands, the following steps must be carried out. 1. All Input Traces must be designated as Input or Both in the Input Output column of the Traces spreadsheet. 2. All Output Traces must be designated as Output or Both in the Input Output column of the Traces spreadsheet. 3. All Transfer Function Traces must be designated as Cross in the Input Output column of the Traces spreadsheet. 4. All Trace DOFs must be defined in the DOFs column of the Traces spreadsheet. •

Each Input & Output Trace must have a DOF.

•

Each Transfer Function Trace must have both Roving & Reference DOFs.

•

Input DOFs must match Transfer Function Reference DOFs.

•

Output DOFs must match Transfer Function Roving DOFs.

DOF Format Each Trace DOF has the following format, •

Trace DOF = Roving DOF : Reference DOF [Measurement Set Number]

•

The Roving DOF always precedes the colon ":" and the Reference DOF always follows the colon ":". The Measurement Set Number is placed inside brackets [ ].

A DOF consists of a Point number followed by a direction letter. •

DOF 1Z means that a measurement was made at Point 1 in the positive Z direction.

•

DOF -1Z means that a measurement was made at a Point 1 in the negative Z direction.

The following DOF directions are recognized in ME'scope;

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Measurement Axes

Direction Symbols

Rectangular

X, Y, Z

Cylindrical

R (radial), T (tangential), Z (axial)

Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands

Spherical

R (radial), T (tangential), P (elevation)

Machine

H (horizontal), V (vertical), A (axial)

MIMO DOFs The Transform | MIMO commands interpret Trace DOFs in the following way, •

Transfer Function DOFs (Output DOF : Input DOF)

•

All Transfer Functions are assembled into a Transfer Function matrix based on their Output & Input DOFs.

•

The Output DOF designates the row position, and the Input DOF designates the column position of each Transfer Function in the matrix.

•

Each Input Trace DOF is matched with an Input DOF (column) of the Transfer Function matrix.

•

Each Output Trace DOF is matched with an Output DOF (row) of a Transfer Function matrix.

Measurement Set Number The use of Measurement Set numbers is optional. All Traces having the same Measurement Set number means that the data was simultaneously acquired. NOTE: During MIMO calculations, all Traces with the same Measurement Set number are processed together. All Traces with no Measurement Set are also processed together. Editing Trace DOFs •

Double click on the DOFs column heading and open the DOF Generator. See Using the DOF Generator in the Data Block commands chapter for details.

•

Or manually edit the cells in the DOFs column of the Traces spreadsheet by clicking on each cell and typing in a new DOF.

Transform | MIMO | Transfer Functions Calculates Transfer Functions from time or frequency Traces. Transfer functions can be calculated from, •

Input & Output time domain Traces.

•

Input Auto spectra and Cross spectra between Inputs & Outputs.

Before executing this command, •

All Input Traces must be designated as an (Input or Both) in the Input Output column of the Traces spreadsheet.

•

All Output Traces must be designated as an (Output or Both) in the Input Output column of the Traces spreadsheet.

•

All Input & Output Traces must have DOFs.

•

All Input & Output Traces should have engineering units.

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Reference Volume IIB - Options When this command is executed, the MIMO dialog box will open for selecting Data Blocks with Input & Output traces in them.

•

If time domain Data Blocks are open in the Work Area, they will be listed in the Inputs & Outputs lists, and Time Waveforms will be enabled in the Data Source section.

•

If Data Blocks containing Auto & Cross spectra are open in the Work Area, they will be listed in the Inputs & Outputs lists, and Auto & Cross Spectra will be enabled in the Data Source section.

Using Auto & Cross Spectra Transfer Functions are calculated from Auto & Cross spectra using the following formula;

[H(ω)] = [{X(ω)} {F(ω)}t] [{F(ω)} {F(ω)}t]-1 where:

[{X(ω)} {F(ω)}t] = Cross spectrum matrix between Outputs & Inputs (n by m) [{F(ω)} {F(ω)}t] = Input Auto spectrum matrix (m by m) [H(ω)] - Transfer Function matrix (n by m) {F(ω)} - Fourier spectra of Inputs (m-vector) {X(ω)} - Fourier spectra of Outputs (n-vector) m - number of Inputs n - number of Outputs ω - frequency variable t - denotes conjugate transposed -1 - denotes the matrix inverse Using Time Waveforms If time domain Traces are used, time domain windowing, overlap processing,and spectrum averaging can be used to calculate the Auto & Cross spectra. •

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(See Transform | Calculate | Spectra for details on spectrum averaging.)

Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands •

Auto & Cross Spectra can also be saved with the Transfer Functions by checking them in the Include section of the dialog box.

•

Coherences can also be saved by checking them in the Include section of the dialog box.

Triggering If time domain Traces are used, triggering can be used to define the sampling windows used for Spectrum averaging. For example, triggering would be used if an Input Trace contained multiple impact signals, as shown below. •

If Triggered is checked in the Triggering section of the dialog box, the Trigger dialog box will open instead of the Spectrum Averaging dialog box.

•

The Waveform Processing section of this dialog is used in the same way as in the Spectrum Averaging dialog.

•

(See Spectrum Averaging in the Signal Processing chapter for details.)

Time Domain Traces Containing Multiple Impacts.

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Trigger Level & Pre-Trigger Delay •

The Trigger Level is entered as a percentage of the maximum magnitude of the data in Trace (M#1).

•

Trigger Level & Pre-Trigger Delay are applied only to the waveform in the first Trace (M#1).

•

The sampling window is started before the trigger event by the number of samples specified in the Pre-Trigger delay.

•

The number of samples in a sampling window is equal to twice the Spectrum Block Size.

Time Domain Windowing Time domain Traces can have different windows applied to them before the FFT is applied. Each window is most effective when used on a specific type of data, as described below. •

Rectangular (for periodic-in-the-window signals)

•

Hanning (for broad band signals)

•

Flat Top (for narrow band signals)

•

Force (for impact force signals)

•

Exponential (for impulse response signals)

•

See the Time Domain Windows section in the Signal Processing commands chapter for details.)

Calculating Outputs From Inputs Outputs can be calculated from Inputs & Transfer Functions in three different ways; 1. Time domain Outputs or Output Fourier spectra. 2. Cross spectra between Inputs & Outputs. 3. Output Auto spectra or PSDs Time Domain Outputs or Fourier Spectra

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Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands Output Fourier spectra are calculated from Transfer Functions and Input Fourier spectra using the formula;

{X(ω)} = [H(ω)] {F(ω)} where:

{F(ω)} - Fourier spectra of Inputs (m - vector) [H(ω)] - Transfer Function matrix (n by m) {X(ω)} - Fourier spectra of Outputs (n - vector) m - number of Inputs n - number of Outputs ω - frequency variable NOTE: If time domain Input Traces are provided, they are transformed to Fourier spectra before using the above equation. The calculated Output Fourier spectra are then transformed to time domain Output Traces. The following block diagram depicts Output calculation when Inputs are provided as time domain Traces, and either a Modal Model or Experimental FRFs are also provided..

MIMO Output Calculation. Cross Spectra Cross spectra between Inputs & Outputs are calculated from Input Auto spectra & Transfer Functions using the formula;

[{X(ω)}{F(ω)}t] = [H(ω)] [{F(ω)}{F(ω)}t] where:

[{F(ω)}{F(ω)}t] - Input Auto spectrum matrix (m by m) [H(ω)] - Transfer Function matrix (n by m)

[{X(ω)}{F(ω)}t] - Cross spectrum matrix between Inputs & Outputs (n by m) m - number of Inputs n - number of Outputs

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Reference Volume IIB - Options ω - frequency variable (radians per second) t - denotes transposed conjugate Output Auto Spectra Output Auto spectra (or PDS's) are calculated from Input Auto spectra & Transfer Functions using the formula;

[{X(ω)}{X(ω)}t] = [H(ω)] [{F(ω)}{F(ω)}t] [H(ω)]t where:

[{F(ω)}{F(ω)}t] - Input Auto spectrum matrix (m by m) [H(ω)] - Transfer Function matrix (n by m) [{X(ω)}{X(ω)}t] - Output Auto spectrum matrix (n by n) m - number of Inputs n - number of Outputs ω - frequency variable (radians per second) t - denotes transposed conjugate NOTE: Only the diagonal elements of the Output Auto spectrum matrix are calculated.

Transform | MIMO | Outputs Calculates multiple Outputs from Transfer Functions & Inputs. Different types of Input Traces can be used for this calculation, •

Input time domain Traces.

•

Input Auto spectra or Fourier spectra.

Before using this command, •

All Input Traces must be designated as (Input or Both) in the Input Output column of the Traces spreadsheet.

•

All Transfer Function Traces must be designated as Cross in the Input Output column of the Traces spreadsheet

•

Residue mode shapes or UMM mode shapes can also be used to synthesize the required FRFs.

When this command is executed, the following dialog box is opened,

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Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands

•

All open Data Blocks containing Input Traces are listed in the Inputs list box.

•

All open Data Blocks contain Cross Traces are listed in the Transfer Functions list box.

Time Domain Inputs Time domain Input Traces can be imported or synthesized using File | New | Data Block in the ME'scope window. NOTE: Time domain Input Traces are transformed to Fourier spectra before being multiplied by the Transfer Functions to yield Output Fourier spectra. The Output Fourier spectra are then transformed to time domain Traces. FRFs from Modal Parameters FRFs can be imported, acquired with an Acquisition window, or synthesized from modal parameters. •

If a Shape Table with modal parameters in it is chosen, the required FRFs are synthesized from the modal parameters.

•

The frequency axis parameters of the Input Fourier spectra are used for the FRF synthesis.

NOTES: If Residue mode shapes are used to synthesize FRFs, FRFs can only be synthesized with the same DOFs as the Residue mode shapes. If UMM mode shapes are used to synthesize FRFs, FRFs are synthesized with Reference DOFs to match the DOFs of the Input Traces. Transfer Function Matrix All Transfer Functions are assembled into a Transfer Function matrix based on their DOFs (Output DOF : Input DOF). •

The Output DOF designates the row position, and the Input DOF designates the column position of each Transfer Function in the Transfer Function matrix.

•

Each Input Trace DOF must match with an Input DOF (column) of the Transfer Function matrix.

•

Each calculated Output Trace DOF is given an Output DOF (row) of the Transfer Function matrix.

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Reference Volume IIB - Options Calculating Inputs From Outputs Inputs are calculated from Outputs & Transfer Functions in three different ways, 1. Time domain Inputs or Fourier spectra. 2. Input Auto spectra (or PSD's) from Output & Input Cross spectra 3. Input Auto spectra (or PSD's) from Output Auto spectra. Time Domain Inputs or Fourier spectra Input Fourier spectra are calculated from Output Fourier spectra & Transfer Functions using the formula;

{F(ω)} = [T(ω)] {X(ω)} where:

[T(ω)] = [[H(ω)]t [H(ω)]]-1[H(ω)]t matrix (m by n) [H(ω)] - Transfer Function matrix (n by m) {F(ω)} - Input Fourier spectra (m - vector) {X(ω)} - Output Fourier spectra (n - vector) m - number of Inputs n - number of Outputs ω - frequency variable (radians per second) t - denotes transposed conjugate -1- denotes matrix inverse NOTE: If time domain Output Traces are provided, they are transformed to Fourier spectra before using the above equation. The calculated Input Fourier spectra are then transformed to time domain Input Traces. Input Auto spectra From Cross spectra Input Auto spectra are calculated from Cross spectra & Transfer Functions using the formula;

[{F(ω)}{F(ω)}t ] = [T(ω)] {X(ω)}{F(ω)}t where:

[{F(ω)}{F(ω)}t ] = Input Auto spectrum matrix (m by m) [T(ω)] = [[H(ω)]t [H(ω)]]-1[H(ω)]t matrix (m by n) [H(ω)] = Transfer Function matrix (n by m) [{X(ω)}{F(ω)}t ] = Cross spectrum matrix (n by m) m - number of Inputs n - number of Outputs ω - frequency variable (radians per second) t - denotes transposed conjugate -1- denotes matrix inverse Input Auto spectra from Output Auto spectra

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Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands Input Auto spectra (or PSD's) are calculated from Output Auto spectra & Transfer Functions using the formula;

[{F(ω)}{F(ω)}t ] = [T(ω)] [{X(ω)}{X(ω)}t ] [T(ω)]t where:

[{F(ω)}{F(ω)}t ] = Input Auto spectrum matrix (m by m) [T(ω)] = [[H(ω)]t [H(ω)]]-1[H(ω)]t matrix (m by n) [H(ω)] = Transfer Function matrix (n by m) [{X(ω)}{X(ω)}t ] = Output Auto spectrum matrix (n by n) m - number of Inputs n - number of Outputs ω - frequency variable (radians per second) t - denotes transposed conjugate -1- denotes matrix inverse NOTE: Only the diagonal elements of the Output Auto spectrum matrix are used for this calculation.

Transform | MIMO | Inputs Calculates multiple Inputs from Transfer Functions & Outputs. Different types of Output Traces can be used for this calculation, •

Output Time domain Traces.

•

Output Auto spectra, Fourier spectra, or Cross spectra between Inputs & Outputs.

Before using this command, •

All Output Traces must be designated as (Output or Both) in the Input Output column of the Traces spreadsheet.

•

All Transfer Function Traces must be designated as Cross in the Input Output column of the Traces spreadsheet

•

Residue mode shapes or UMM mode shapes can also be used to synthesize FRFs.

When this command is executed, the following dialog box is opened,

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Reference Volume IIB - Options •

All open Data Blocks containing Output Traces are listed in the Outputs list box.

•

See Transform | MIMO | Outputs for more details concerning Time Domain Traces, Modal Parameters and FRFs, and Matching DOFs.

Transform | MIMO | Sinusoidal ODS Calculates a single frequency ODS due to multiple sinusoidal excitation forces. •

The Sinusoidal ODS can be saved in a Shape Table or displayed in animation in a connected Structure window.

The ODS is calculated by multiplying FRFs by the Fourier spectra of excitation forces at a single frequency. •

Forces can be applied at any Reference DOF of the FRFs.

•

Each force is defined by its magnitude, phase, and the FRF Reference DOF at which it is applied.

The DOFs of the Sinusoidal ODS are determined from the Roving DOFs of the FRFs. •

(See the Sinusoidal ODS using FRFs section in the Tutorial - MIMO Modeling & Simulation chapter for details.)

•

When this command is executed, the following dialog box is opened.

Sinusoidal ODS From a Data Block. Animating the ODS •

Press the Animate Shape button to display the Sinusoidal ODS in animation on the structure model in a connected Structure window,

In order to animate the ODS correctly, the Animation Equations in the connected Structure must be compatible with the DOFs (M#s) of the ODS. To insure that the ODS will animate correctly, •

Press Save Shape to save the ODS into a Shape Table.

•

Execute Tools | Create Animation Equations (Assign M#s) from the Shape Table to create new Animation Equations in the connected Structure window.

Shape Table MIMO Command

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Multi-Input Multi-Output (MIMO) Modeling & Simulation Commands NOTE: If the VES-3550 MIMO Modeling & Simulation option is authorized, the following Shape Table command is enabled in your software. Check Help | About to verify authorization of this option. Tools | Sinusoidal ODS Calculates a single frequency ODS due to multiple sinusoidal excitation forces. •

The Sinusoidal ODS can be saved in a Shape Table or displayed in animation in a connected Structure window.

The ODS is calculated by multiplying synthesized FRFs by the Fourier spectra of excitation forces at a single frequency. Forces can be applied at, •

Any Reference DOF of Residue mode shapes.

•

Any DOF of UMM mode shape.

Each force is defined by its magnitude, phase, and the FRF Reference DOF at which it is applied. The DOFs of the Sinusoidal ODS are determined from, •

The Roving DOFs of the Residue mode shapes.

•

All DOFs of the UMM mode shapes.

•

(See the Sinusoidal ODS using Mode Shapes section in the Tutorial - MIMO Modeling & Simulation chapter for details.)

When this command is executed, the following dialog box is opened.

Sinusoidal ODS From a Shape Table.

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Acoustics Commands Data Block Acoustics Commands NOTE: If the VES-6000 Acoustics option is authorized, the following Data Block commands and spreadsheet columns are enabled in your software. Check Help | About to verify authorization of this option. Display Menu •

Display | Real

•

Display | Magnitude

Tools | Animate Using | Sources Acoustics Menu •

Acoustics | ABC Weighting

•

Acoustics | Narrow to Octave Band

Acoustics | Calculate Menu •

Acoustics | Calculate | SPL

•

Acoustics | Calculate | Intensity

•

Acoustics | Calculate | P-I Index

Acoustics | Intensity to Power Acoustics | Source Ranking menu •

Acoustics | Source Ranking | Chart

•

Acoustics | Source Ranking | Save Shape by Source

Acoustics | Tone Calibration menu •

Acoustics | Tone Calibration | Calculate

•

Acoustics | Tone Calibration | Apply

Trace Spreadsheet Columns dB Reference Value Column Allows you to enter dB reference values that are used when dB is chosen for the Vertical Axis Scaling box. For Linearquantities (such as SPL), dB units are defined as; Linear dB Units = 20 log 10 (magnitude / dB Reference value) For Power quantities (such as Sound Power & Intensity), dB units are defined as; Power dB Units = 10 log 10 (magnitude / dB Reference Value) Weight Column Indicates the type of acoustic weighting (A, B, C) applied to each Trace (M#). Source Column

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Reference Volume IIB - Options Used to enter a text name for each Trace (M#) belonging to an Acoustic source.

Acoustic Surfaces An Acoustic Surface is a special type of SubStructure that is used to display acoustic data in a Structure window. Acoustic data is typically taken on a grid of spatial Points in the vicinity of one or more noise sources. SPL, Sound Power & Acoustic Intensity data is typically displayed on an Acoustic Surface. Acoustic surfaces are easily created by using the Drawing Assistant in the Structure window. •

Each measurement Point on an acoustic surface is surrounded by an area that is determined when the surface is created. This value is displayed in the Acoustic Area column of the Points spreadsheet.

•

A normal vector to the surface (in the Global X, Y, or Z direction) is also defined for each measurement Point. This axis is displayed in the Acoustic Normal column in the Points spreadsheet.

•

The Acoustic Area and Acoustic Normal of a Point are used to calculate Sound Power through the surface from Intensity data.

Acoustic Surface Showing Areas & Normals. Each of the bold measurement Points is surrounded by 4 Points which define its acoustic area. Acoustic areas & normals are calculated when an acoustic surface is created in the Drawing Assistant. •

Acoustic areas & normals are listed in the Points spreadsheet, and must be edited if the Point coordinates are changed.

Display | Display Objects | Points | Acoustic Normals Displays the acoustic normal at each Point.

Display Menu Display | Real Displays either real Trace data, or the Real part of complex Trace data in Octave band or dB Reference units.

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Acoustics Commands

Data Block Window Showing Real Part of Octave Data. Octave Band Data Log or dB formats can be chosen for displaying the Real part of Octave band data. Linear, Log, dB & decades choices are made in the Format | Y-Axis dialog box. â€˘

Right click in the Trace graphics area, and execute Format | Y-Axis from the menu to open the Y-Axis dialog box.

Real Part in dB Reference Units The Real part can also be displayed in dB (decibel) units relative to a reference level. (See Display | Magnitude for details.) For Linear (RMS) data, the Real part is displayed as, Real part (dB Reference) = Sign (Real part) [ 20 Log 10 ( Abs (Real part) / Linear Reference) ] For Power (MS) data, the Real part is displayed as, Real part (dB Reference) = Sign (Real part) [ 10 Log 10 ( Abs (Real part) / Power Reference) ] Display | Magnitude Displays the magnitude of the Trace data.

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Reference Volume IIB - Options

Data Block Window Showing Log Magnitude of Octave Data. Linear, Log or dB Magnitudes can be displayed in Linear, Log or dB format. When Log or dB is chosen, you can also choose 1 to 14 decades (powers of 10) to display. •

Linear, Log, dB & decades choices are made in the Format | Y-Axis dialog box.

•

Right click in the Trace graphics area, and execute Format | Y-Axis from the menu to open the Y-Axis dialog box.

dB Units for Linear Versus Power Quantities Magnitudes can be displayed in dB (decibel) units. For Linear (RMS) quantities, (such as FRFs, Linear Spectra, etc.) the Magnitude is displayed as, Magnitude (dB) = 20 Log

10 (

Magnitude )

For Power (MS) quantities, (such as Auto Power Spectra, PSD’s, etc.), the Magnitude is displayed as, Magnitude (dB) = 10 Log

10 (

Magnitude )

Magnitude in dB Reference Units Magnitudes can also be displayed in dB (decibel) units relative to a reference level. For Linear (RMS) quantities, (such as SPL) the Magnitude is displayed as, Magnitude (dB Reference) = 20 Log

10 (

Magnitude / Linear Reference)

For Power (MS) quantities, (such as Sound Power & Intensity), the Magnitude is displayed as, Magnitude (dB Reference) = 10 Log

10 (

Magnitude / Power Reference)

To display magnitudes in dB Reference units, the Linear (RMS) Reference or Power (MS) Reference values must be entered in the dB References column in the Traces spreadsheet. •

The Linear (RMS) Reference value is required for Linear (RMS) Trace data

•

The Power (MS) Reference value is required for Power (MS) Trace data.

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Acoustics Commands Tools | Animate Using | Sources (Data Block) Animates shape data from a Data Block by Source name. During shape animation, •

Source names are entered into the Acoustic Source column in the Traces spreadsheet.

•

Shape data for all M#s having the same source name is replaced with the sum of the data for those M#s.

Summing data from the same Source during shape animation shows the relative strength of shapes from different acoustic Sources. NOTE: Trace data for M#s with no Source name is not summed. •

See the Acoustics | Source Ranking | Chart command reference for details.

Acoustics | ABC Weighting Applies A, B or C weighting to all (or selected) frequency domain Traces in a Data Block. When it is executed a dialog box is opened. •

Choose the type of weighting to be applied, and click on OK to apply the weighting.

Acoustics | Narrow to Octave Band Creates a new Data Block of octave band Traces from a Data Block of narrow band frequency domain Traces. When it is executed, a dialog box is opened. •

Choose the octave band in the dialog box, and click on OK.

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Reference Volume IIB - Options

NOTE: If less than 5 samples of narrow band data were used to create an octave band, the octave band frequency is enclosed in brackets [ ]. Several Octave bands in the figure below were created with less than 5 samples.

Octave Band Trace Showing Bands Created With Less Than 5 Samples.

Acoustics | Calculate | SPL Creates a new Data Block of Sound Pressure Level (SPL) Traces from microphone Time domain, Fourier spectrum or Auto spectrum Traces. When this command is executed, the following dialog box will open.

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Acoustics Commands

Time Responses If Time Responses is chosen as the Data Source, all of the currently open time domain Data Blocks are listed in the dialog box. SPL’s are calculated from time responses using spectrum averaging. •

See Spectrum Averaging in the Signal Processing Commands chapter for details.

Fourier Spectra or Auto Spectra If Fourier, Auto Spectra is chosen as the Data Source, all of the currently open Data Blocks with Fourier spectrum or Auto spectrum Traces in them are listed in the dialog box. •

If a Trace is a Fourier spectrum, SPL Trace = magnitude (Fourier Spectrum)

•

If a Trace is an Auto spectrum with power units, SPL Trace = Square Root (Auto Spectrum)

•

If a Trace is an Auto spectrum with linear units, SPL Trace = Auto Spectrum

Acoustics | Calculate | Intensity Creates a new Data Block of Acoustic Intensity Traces from 2-microphone Acoustic Probe Time Responses or Cross spectrum Traces. •

Four-microphone data (taken with 3 Responses & 1 Reference) can also be used with this command.

When this command is executed, a dialog box is opened.

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Reference Volume IIB - Options

Time Responses If Time Responses is chosen as the Data Source, all of the currently open Time domain Data Blocks are listed in the dialog box. Intensity is calculated from time responses using spectrum averaging. •

Roving channels must be identified as (Outputs or Both) in the Input Output column of the Traces spreadsheet.

•

Reference (fixed) channels must be identified as (Inputs or Both) in the Input Output column of the Traces spreadsheet.

•

See Spectrum Averaging in the Signal Processing Commands chapter for details.

Cross Spectra If Cross Spectra is chosen as the Data Source, all of the currently open Data Blocks with Cross Spectrum Traces are listed in the dialog box. Intensity is calculated from a Cross spectrum of a pair of microphone responses.

where:

Air density is calculated from the air pressure and temperature values. SPL and P-I Index Both SPL and P-I Index Traces can also be calculated at the same time as Intensity by checking these selections in the Calculate Intensity dialog box.

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Acoustics Commands •

See the Acoustics | Calculate | SPL or P-I Index commands for details.

Acoustics | Calculate | P-I Index Calculates the Pressure-Intensity (P-I) Index from SPL and Intensity Traces. The P-I Index is defined as, P-I Index (dB) = (SPL (dB Reference 20 µ PA) - Intensity (dB Reference 1e-12 watts/m ) ) 2

When this command is executed, a dialog box is opened.

When Calculate is pressed, a new Data Block file with P-I Index Traces in it will be created.

Acoustics | Intensity to Power Calculates Sound Power Traces from a Data Block containing Intensity Traces. Sound Power is calculated by multiplying Intensity by the surface area surrounding its corresponding measurement Point on an Acoustic Surface in a connected Structure file. •

The connected Structure file must have an Acoustic Surface with uniquely numbered Points that match the Point numbers in the Roving DOFs of the Intensity Traces.

•

Each matching Point must also have a non-zero surface area associated with it. The calculated Sound Power Traces will be added to the Intensity Data Block Traces.

Animating Sound Power & Intensity Sound Power and Intensity shapes must be scaled differently in order to display them together in animation. This is done by defining two SubShapes. •

Execute Edit | Select Traces | Select By, choose Measurement Type from the drop down list, and choose Sound Power from the Measurement Type list.

•

Press the Select button to select the Sound Power Traces, and press Close.

•

Double click on the SubShape column heading in the Traces spreadsheet, and type "Sound Power" into the dialog box.

•

Execute Edit | Select Traces | Select By, choose Measurement Type from the drop down list, and choose Intensity from the Measurement Type list.

•

Press the Select button to select the Intensity Traces, and press Close.

•

Double click on the SubShape column heading in the Traces spreadsheet, and type "Intensity" into the dialog box.

To animate the Sound Power and Intensity data together, •

Execute Tools | Animate Using | SubShapes in the Data Block.

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Reference Volume IIB - Options Acoustics | Source Ranking | Chart Opens the Acoustic Source Ranking bar chart window. This window displays a bar chart ranking the relative strengths of the acoustic Sources at the cursor position of all (or selected) Traces. •

In this bar chart, Source percentages are plotted on the vertical axis and Source names on the horizontal axis.

NOTE: The first bar is the Sum of all sources, and is always 100%.

Source Ranking Chart Values at Cursor Position The Source Ranking bar chart is updated whenever the Data Block cursor is moved. •

If the Line or Peak cursor is turned ON, the Trace values at the cursor position are Source ranked.

•

If the Band cursor is turned ON, the sum of the Trace values in the band are Source ranked.

Which Magnitudes Are Ranked? •

If the Real part of the Traces is displayed, the absolute values of the Real parts are ranked.

•

If the Imaginary part of the Traces is displayed, the absolute values of the Imaginary parts are ranked.

•

Otherwise, the magnitudes of the Trace data are ranked.

Status Bar •

Hover the mouse pointer over the Source Rank bar of a source to display information for that source on the Status Bar at the bottom of the window.

Source Ranking Groups of Traces in a Data Block can be associated with an acoustic source by giving them a common Source name. An acoustic source would typically be a physical source which is nearest to the Points associated with a group of measurements, or Traces. •

178

Source names are entered as ASCII text in the Source column of the Traces spreadsheet.

Acoustics Commands Source ranking sums the Trace data from all of the Points associated with each Source. After each Source value is calculated, it is normalized by the total of the magnitudes of all of the Sources, yielding a percentage value for each Source. Source ranked data can be, •

Displayed in a bar chart using this command.

•

Animated on an acoustic surface using Tools | Animate Using | Source.

•

Saved in a Shape Table using Acoustics | Source Ranking | Save Shape by Source.

Naming Acoustic Sources To give the same Source name to a group of Traces assigned to Points on an acoustic surface, •

Execute Tools | Create Animation Equations (Assign M#s) in the Data Block window to create Animation equations in a connected Structure window containing the structure model and acoustic surface.

•

Select a SubStructure that defines a single acoustic Source on the model in the Structure window.

•

Execute Draw | Animation Equations | Select M#s to select the M#s in the Data Block that are assigned to the Source.

•

Double click on the Acoustic Source column in the Traces spreadsheet.

•

Enter a name for the Source, and click on OK.

•

Repeat the above steps to name the other Sources on the acoustic surface.

Source Ranking | Save Shape By Source Saves Source ranked shape data into a Shape Table. •

See Acoustics | Animate Using | Sources for details.

Acoustics | Tone Calibration Menu Tone Calibration | Calculate Creates a Shape Table of scale factors that can be used to calibrate Traces. When this command is executed, a dialog box is opened. •

Enter the Tone Frequency, Desired Magnitude, and Desired Phase into the dialog box, and click on OK.

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Reference Volume IIB - Options Tone Calibration | Apply Applies the tone calibration scale factors stored in a Shape Table to the Traces in a Data Block. •

The Shape Table containing the tone calibration scale factors can be created using Acoustics | Tone Calibration | Calculate, or they can be entered by hand.

The scale factor for each M# in the DOFs spreadsheet is applied to each matching M# in the Data Block so that each Trace (M#) has the tone calibration value at the frequency of the shape in the Shape Table.

Shape Table Acoustics Commands NOTE: If the VES-6000 Acoustics option is authorized, the following Shape Table commands and spreadsheet columns are enabled in your software. Check Help | About to verify authorization of this option. Display | Source Ranking Tools | Animate Using | Sources DOFs Spreadsheet Columns Weight Column Indicates the type of acoustic weighting applied to each DOF (M#). Source Column Used to enter a text name for each DOF (M#) belonging to an acoustic source. •

Execute Tools | Animate Using | Sources to display in animation acoustic shapes showing the relative strength of each Source.

Display | Source Ranking Opens the Source Ranking bar chart window. This window displays a bar chart ranking the relative strengths of the acoustic Sources for the selected shape of all (or selected) DOFs. •

In this bar chart, Source percentages are plotted on the vertical axis and Source names on the horizontal axis.

NOTE: The first bar is the Sum of all sources, and is always 100%.

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Acoustics Commands

Shape Table Source Ranking Chart Which Magnitudes Are Ranked? •

If the Real part of the DOFs is displayed, the absolute values of the Real parts are ranked.

•

If the Imaginary part of the DOFs is displayed, the absolute values of the Imaginary parts are ranked.

•

Otherwise, the magnitudes of the DOFs are ranked.

Status Bar •

Hover the mouse pointer over the Source Rank bar of the source to display information for that source on the Status Bar at the bottom of the window.

Source Ranking Groups of DOFs in a Shape Table can be associated with an acoustic source by giving them a common Source name. •

Source names are entered as text into the Source column of the DOFs spreadsheet.

An acoustic source would typically be a physical source which is nearest to the Points associated with a group of shape DOFs or M#s. Source ranking sums the shape data from all of the Points associated with each Source. After each Source value is calculated, it is normalized by the total of the magnitudes of all of the Sources, yielding a percentage value for each Source. Source ranked data can be, •

Displayed in a bar chart using this command.

•

Animated on an acoustic surface using Tools | Animate Using | Source.

Naming Acoustic Sources To give the same Source name to a group of M#s assigned to Points on an acoustic surface, •

Execute either Tools | Create Animation Equations (Assign M#s) in the Shape Table window to create Animation equations in the Structure window with the structure model and acoustic surface in it.

•

Select a SubStructure that defines a single Source in the Structure window

•

Execute Display | Points | Select Measurements to select the M#s in the Shape Table that are assigned to the Source.

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Reference Volume IIB - Options •

Double click on the Animation Source column in the DOFs spreadsheet.

•

Enter a name for the Source, and click on OK.

•

Repeat the above steps to name the other Sources on the acoustic surface.

Tools | Animate Using | Sources (Shape Table) Animates shape data from a Shape Table by Source name. During shape animation, •

Source names are entered into the Acoustic Source column in the DOFs spreadsheet.

•

Shape data for all M#s having the same source name is replaced with the sum of the data for those M#s.

Summing data from the same Source shows the relative strength of shapes from multiple acoustic Sources during shape animation. NOTE: Shape data for M#s with no Source name is not summed together.

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Structural Dynamics Modification (SDM) Commands Structure Window SDM Commands NOTE: If the VES-5000 Structural Dynamics Modification option is authorized, the following Data Block commands and spreadsheet Objects are enabled in your software. Check Help | About to verify authorization of this option. SDM Menu •

SDM | Modal Sensitivity

•

SDM | Calculate New Modes

•

SDM | Add Tuned Absorber

•

SDM | Interpolate Source

FEA Menu •

FEA | Materials List

•

FEA | Properties List

•

FEA | FEA Objects List

•

FEA | Calculate FEA Modes

FEA Objects •

FEA Objects are added to the Edit | Objects List.

What is SDM? The Structural Dynamics Modifications (SDM) method allows you to model the addition (or subtraction) of physical elements to a structure, and observe their effects on its modes of vibration. •

All structural modifications are converted to changes in the mass, stiffness & damping properties of the structure.

•

These changes in mass, stiffness & damping properties are then used together with the modes of the unmodified structure to calculate the modes of the modified structure.

NOTE: The modes of the unmodified structure must be UMM mode shapes.

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Reference Volume IIB - Options

Structural Dynamics Modification (SDM)

FEA Objects The following FEA elements are used by the VES-5000 SDM, VES-8000 Experimental FEA, & VES9000 FEA Model Updating options to ME'scope. FEA Mass Adds a Mass (or Inertial effects) to a Point on a structure model. •

Applies translational or rotational inertial effects in up to three directions at a Point.

•

Inertia can be constrained to specific directions by making the appropriate selections in the Orientation column of the Mass Objects spreadsheet.

•

The FEA Mass is defined in the FEA Properties List.

•

A Mass from the FEA Properties List must be chosen in the Property cell of each FEA Mass in the Objects spreadsheet.

FEA Spring & FEA Damper Add linear stiffness (or damping) between 2 Points on a structure model. •

Apply forces either axially (along their axis) or as translational or rotational stiffness or damping between two Points.

•

Can be constrained to specific directions by making selections from the Orientation columns of their end Points in their respective Object spreadsheets.

•

The stiffness for an FEA Spring is defined on the Springs tab in the FEA Properties List.

•

The damping for an FEA Damper is defined on the Dampers tab in the FEA Properties List.

•

A Spring (or Damper) from the FEA Properties List must be chosen in the Property cell of each FEA Spring (or FEA Damper) in the Objects spreadsheet.

FEA Rod A linear element added between 2 Points on a structure model. •

Applies translational force axially (along its axis) between its two end Points.

•

The cross sectional area of an FEA Rod is defined on the Rods tab in the FEA Properties list.

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Structural Dynamics Modification (SDM) Commands •

The elasticity & density of an FEA Rod are defined first in the FEA Materials list, and then chosen in the Material column on the Rods tab in the FEA Properties list.

•

A Rod from the FEA Properties List must be chosen in the Property cell of each FEA Rod in the Objects spreadsheet.

FEA Bar A linear element added between 2 Points on a structure model. •

A long slender element that applies translational force axially (along its axis), and bending forces at its end Points.

•

Same as a beam element but with a fixed cross section.

•

The cross sectional area & cross sectional inertias (X Inertia, Y Inertia, XY Inertia) are defined on the Bars tab in the FEA Properties list. •

The cross section is oriented by pointing the X-Axis of the cross section to an Orientation Point in the structure window.

•

The Orientation Point (row number in the Points spreadsheet) must be entered into the Orientation cell in the FEA Bar spreadsheet.

•

The material properties of an FEA Bar are defined first in the FEA Materials list, and then chosen in the Material column on the Bars tab in the FEA Properties list.

•

A Bar from the FEA Properties List must be chosen in the Property cell of each FEA Bar in the Objects spreadsheet.

FEA Triangle & FEA Quad Plate Two types of linear plate elements, also called membrane elements. •

An FEA Triangle is defined between 3 Points

•

An FEA Quad is defined between 4 Points

NOTE: Plate elements should be used to model parts of a structure that are relatively thin compared to their width & height dimensions. •

The thickness is defined on the Plates tab in the FEA Properties list.

•

The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Plates tab in the FEA Properties list.

•

A Plate from the FEA Properties List must be chosen in the Property cell of each FEA Triangle (or FEA Quad) in the Objects spreadsheet.

Plate Stiffness Multiplier The Stiffness Multiplier is used to increase or decrease the bending stiffness of an Plate element. The bending stiffness of a Plate element is calculated as a function of its thickness and material properties. •

The Plate stiffness calculation assumes that the plate cross section consists of a uniform distribution of the plate material.

In cases where a plate cross section consists of two or more dissimilar materials, its bending stiffness could be greater or less than the stiffness calculated with a single material cross section. •

Stiffness Multiplier = 1 calculates the bending stiffness from the Plate thickness & material properties.

•

Stiffness Multiplier > 1 increases the bending stiffness of the Plate element.

•

Stiffness Multiplier < 1 decreases the bending stiffness of the Plate element.

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Reference Volume IIB - Options

Correct Point Selection for Adding Plates & Solid Elements. FEA Tetra, FEA Prism & FEA Brick These elements are called solid elements because they are 3-dimensional. NOTE: Solid elements should be used to model parts of a structure that have approximately the same width, height, & length dimensions. •

An FEA Tetra is defined between four Points.

•

An FEA Prism is defined between six Points.

•

An FEA Brick is defined between eight Points.

•

The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Solids tab in the FEA Properties list.

•

A Solid from the FEA Properties List must be chosen in the Property cell of each FEA Tetra, FEA Prism, & FEA Brick in the Objects spreadsheet.

Adding FEA Objects to a Structure Model •

Choose the FEA Object type from the Edit | Object Type list.

•

Execute Edit | Add Objects

•

Click near the required number of end Points for the FEA Object to select them. (See examples below).

•

If you select the wrong Point, click on it again to un-select it.

•

After the required number of Points has been selected, a new FEA Object is displayed on the model and a new row is added to its Objects spreadsheet.

•

The new FEA Object is given a default Label, which is also displayed on the model.

•

Execute Edit | Add Objects

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to enable the Add Objects operation.

again to disable the Add Objects operation.

Structural Dynamics Modification (SDM) Commands

Correct Point Selection for Adding Plate & Solid Elements.

Validating UMM Mode Shapes There are two ways to validate the UMM mode shapes of the unmodified structure. 1. Synthesize FRFs using the UMM mode shapes and overlay the synthesized & experimental FRFs. 2. Perform a ”round trip check” of the SDM calculations. Round Trip Check •

Add a point Mass to the structure model, execute SDM | Calculated New Modes, and save the new mode shapes in a Shape Table.

•

Change the Mass value to "minus" the same value, execute SDM | Calculated New Modes again, but use the new mode shapes from the previous step.

•

Execute Display | MAC to compare the original UMM mode shapes with the mode shapes obtained from the previous step.

SDM | Calculate New Modes Calculates new modes for a structure using the Structural Dynamics Modification (SDM) method. The following items are required before using this command, •

A Shape Table containing UMM mode shapes for the unmodified structure.

•

A structure model with FEA Objects attached to it that model the structural modification.

•

Engineering units in the Structure window that match the units of the UMM mode shapes. (see below)

When the SDM calculation is completed, •

The UMM mode shapes of the modified structure can be displayed in animation or used for FRF Synthesis, MIMO Modeling & Simulation, or FEA Model Updating studies.

UMM Mode Shape and Structure Units •

The Structure window Force & Length units (chosen on the Units tab in the File | Structure Options box), must match the Force & Length units of the UMM mode shapes.

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Reference Volume IIB - Options •

SDM Mass modifications are scaled to make their units compatible with the Force & Length units of the UMM mode shapes.

FEA Objects Valid FEA Object properties for use with the SDM commands are listed in the Table below. •

Object properties must also be entered into the FEA | Materials List and FEA | Properties List for each modification FEA Object.

•

See the Adding FEA Objects to a Model section in this chapter for details of adding FEA Objects to a model. FEA Object

Object Properties

Spring

Stiffness

Damper

Damping

Mass

Mass

Rod

cross sectional Area Elasticity, Density

Bar

cross sectional Area X inertia, Y inertia, XY inertia Elasticity, Density

Triangular Plate

Thickness, Elasticity Poisson's Ratio, Density

Quad Plate

Thickness, Elasticity Poisson's Ratio, Density

Tetrahedron

Elasticity, Poisson's Ratio, Density

Prism

Elasticity, Poisson's Ratio, Density

Brick

Elasticity, Poisson's Ratio, Density

SDM | Modal Sensitivity Modal Sensitivity provides a family of SDM solutions that allows you to determine how much modification is necessary to change the modal properties of a structure to match target values. •

This command uses SDM to solve for new mode shapes over a solution space of FEA properties.

•

The solution space is defined by the Minimum, Maximum & Number of Steps of each FEA property.

•

Solutions are ordered from best to worst.

•

The best solution is the one that minimizes the percent difference between calculated & target modal frequencies & damping.

The following Table lists the FEA Object properties that can be changed using this command. NOTE: Material properties are Density, Poisson's ratio, and Young's Modulus of Elasticity.

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Structural Dynamics Modification (SDM) Commands

FEA Object

Property to Change

Target Modal Parameter

Spring

stiffness

frequency

Damper

damping

damping

Mass

mass

frequency, damping

Rod

cross sectional area, material properties

frequency, damping

Bar

cross sectional area & inertias, material properties

frequency, damping

Plate

thickness, material properties

frequency, damping

Solid

material properties

frequency, damping

FEA Object Properties and Target Modal Parameters. When this command is executed, the Shape Table selection dialog box will open. â€˘

Choose a Shape Table file containing the UMM mode shapes of the unmodified structure, and click on OK.

â€˘

The Modal Sensitivity window will open next.

Modal Sensitivity Window Showing No Target Modes. Upper Spreadsheet

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Reference Volume IIB - Options •

The Current Frequency & Damping listed in the upper spreadsheet are the modal parameters for the unmodified structure.

•

The Target Frequency & Damping listed in the upper spreadsheet are the modal parameter values that you must enter.

NOTE: If no target modal parameters are entered, the solutions will not be ordered from best to worst, but simply in the order calculated. Lower Spreadsheet The lower spreadsheet lists the properties of all visible FEA Objects on the structure model. •

The Properties in the lower spreadsheet will be changed during the sensitivity calculations.

•

The Minimum, Maximum & Steps of all (or selected) Properties define the solution space.

Error Function An error function is calculated, and used to order the solutions from best to worst. •

The error is a summation of terms, one for each non-zero Target Frequency & Damping value in the upper spreadsheet.

where: Fs = solution frequency, Ft = target frequency Ds = solution damping, Dt = target damping •

Each frequency term is the absolute difference between the Solution & Target frequency divided by the Target frequency.

•

Each damping term is the absolute difference between the Solution & Target damping divided by the Target damping.

•

The minimum error for all calculated solutions is listed in the Error box at the top of the window.

Solution Space Each property on the lower spreadsheet has a Minimum, Maximum & Steps column. These three columns together define the solution space for the property in that row of the spreadsheet. •

The Property Minimum & Maximum define the lower & upper bounds of a property in the solution space.

•

The Property Steps is the number of steps to be evaluated between the Minimum & Maximum in the solution space.

•

The solution spaces of all (or selected) Properties multiplied together defines the entire solution space.

Solution Space Example •

If Property Minimum = 1, Property Maximum = 10 and Property Steps = 10, then 10 Property values (1,2,3,4,5,6,7,8,9,10) would be used during the solution process.

•

If three properties each have 10 Steps, then the solution space consists of a total of 1000 solutions.

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Structural Dynamics Modification (SDM) Commands NOTE: The Minimum, Maximum, and Steps of all (or selected) Properties in the lower spreadsheet define the solution space over which solutions are calculated. Calculation Process •

When Solution | Start Calculation is executed, SDM solutions over the solution space of all (or selected) Properties in the lower spreadsheet are calculated.

•

The Error (listed at the top of the window), is the minimum error calculated during the calculation process.

•

Calculation over the entire solution space guarantees that the best solution will always be found.

Before Starting a Calculation •

Enter a Target frequency and/or damping value into the upper spreadsheet for each desired mode pair to be used for calculating the Error function. •

•

If no Target values are entered, no Error function will be calculated, and the solutions will be in the order in which they are calculated.

Depress the Select Mode buttons to select each mode pair to be used in evaluating the Error function. •

If no mode pairs are selected, all mode pairs with non-zero Target frequencies will be used to calculate the Error function.

•

Enter Property Minimum, Maximum & Steps into the lower spreadsheet to define the solution space for each Property.

•

Depress the Select Property button to select each property to be used in the calculations. •

If no properties are selected, the Minimum, Maximum & Step of all properties in the lower spreadsheet will be used.

Best Solution Shown in the Spreadsheets. STOP Calculation Solution | Stop Calculation is enabled after Solution | Start Calculation has been executed. •

Execute Solution | Stop Calculation to stop the calculation process and display the solutions that have already been calculated.

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Reference Volume IIB - Options Solution Scroll Bar After the calculation process is completed or is stopped, a Solution scroll bar is displayed on the right hand side of the window. The solutions are displayed in both the upper & lower spreadsheets by scrolling the scroll bar. •

The best solution is displayed when the scroll is at the top of the scroll bar.

•

The worst solution is displayed when the scroll is at the bottom of the scroll bar.

Bar Graphics •

Check the Graphics check box to display the solutions graphically, as shown below.

•

The upper right bar graph displays the MAC values between the Solution & Target mode shapes.

•

The lower bar graph displays the Current & Solution values of the Properties.

•

The upper left bar graph shows the percent difference between the Solution & Target frequency & damping of each mode.

•

Hover the mouse pointer over a bar graph to display its values.

Best Solution Shown Graphically. Calculating New Modes •

Scroll the scroll on the right hand side to display the desired Solution.

•

Execute Solution | Save Solution in FEA Properties to save the Current Property values into the FEA | Materials List and FEA | Properties List.

•

Execute SDM | Calculate New Modes to calculate new UMM mode shapes using the saved FEA Object Properties.

SDM | Add Tuned Absorber Adds a Mass, Spring, Damper Tuned Absorber to a structure.

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Structural Dynamics Modification (SDM) Commands A Tuned Absorber is used to suppress the amplitude of a particular mode of vibration. If the frequency of the Tuned Absorber is "close" to the frequency of a structural mode, the Absorber will "split" original resonance peak into two resonance peaks with lower amplitudes. •

The three components of a Tuned Absorber model are a point mass, and a spring & damper connecting the mass to the structure.

The SDM method is used to connect the Absorber mass to the structure using the spring & damper. A new set of modes is calculated using SDM which reflects the influence of the Tuned Absorber. To define a Tuned Absorber, the following is required, •

Absorber mass

•

Absorber frequency (should be "close" to the frequency of the mode to be suppressed)

•

Absorber damping (optional. An estimate of the percent of critical damping of the Absorber)

The Tuned Absorber is attached to a DOF of a structure model using the spring. The stiffness of the spring that connects the mass to the structure is calculated using the formula, stiffness = Absorber Mass x (Absorber Frequency)

2

The optional damper is also added between the mass and the same DOF as the spring. Before Adding The Absorber The following items are required before executing this command, 1. A Shape Table containing UMM mode shapes of the unmodified structure. (The mode shapes must contain the DOF where the Tuned Absorber will be attached.) 2. A structure model containing the Point & direction (DOF) where the Tuned Absorber will be attached. 3. Mass, Force & Length units chosen on the Units tab in the File | Structure Options box, that match the Force & Length units of the UMM mode shapes. When this command is executed, the following dialog box will open;

Tuned Absorber Dialog Box. •

Select the Shape Table containing the UMM mode shapes of the unmodified structure from the UMM Shapes to Modify list.

•

Select the Number of Absorbers to be attached to the structure.

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Reference Volume IIB - Options For each Absorber, •

Select a DOF for attaching the Absorber

•

Enter an Absorber Mass in the spreadsheet

•

Enter the Absorber Frequency into the spreadsheet

•

(optionally) Enter the Absorber Damping value (in %) into the spreadsheet

After all Absorber parameters have been entered, •

Press the Calculate New Modes button.

When the calculation is completed, all Tuned Absorbers defined in the dialog box will have been added to the structure model. •

The Shape Table selection box will open allowing you to save the new UMM mode shapes of the modified structure.

SDM | Interpolate Source Uses the M#s in the Animation equations of the structure model in the Structure window to interpolate the M#s in the current Animation source. •

A new Animation source file containing the interpolated measurements (M#s) is created.

The Animation equation for each DOF of the structure model is used to create each new M# (Trace or Shape DOF) in the new Animation source file. •

If a Point on the structure model has a numerical Label, each new interpolated M# is given the number & direction of the Point where an Animation equation was evaluated to create the interpolated M#.

•

Execute Tools | Create Animation Equations (Assign M#s) in the new Animation source window, to create new Animation equations using the new Source M#s.

FEA | Materials List Opens the FEA Materials List window. This window contains material properties that are referenced in the FEA Properties List. NOTE: The FEA Materials List is saved with the current Project file when it is saved to the disk.

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Structural Dynamics Modification (SDM) Commands

FEA Materials Window. Each FEA Material is defined by three properties, •

Young's Modulus of Elasticity (Pascals (Pa) in Metric units or Pounds per square inch (psi) in English units)

•

Poisson's Ratio (unit-less)

•

Density (N/cm^3 in Metric units or Lb/in^3 in English units)

File Menu File | Import Imports a Materials spreadsheet from another ME'scopeVES Project file. File | Print Spreadsheet Prints the Materials spreadsheet on the system printer or into a PDF file. Edit Menu Edit | Add Adds a new Material (new row) to the Materials spreadsheet. •

Select each cell in the new row, and enter the new Material value into the cell.

Edit | Delete Deletes the currently selected Material (row) from the Materials spreadsheet. Display Menu Display | Center window Centers the window in the Work Area of the ME'scopeVES window. •

Repeated execution centers the window and returns it to its former position.

Display | Toolbar If checked, the Toolbar is displayed in the window.

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Reference Volume IIB - Options FEA | Properties List Opens the Properties List window. This window contains the Properties that are referenced by FEA Objects on a structure model. •

Properties from the FEA Materials List are used as part of the definition of some Object Properties in this window.

•

Properties are assigned to FEA Objects using the FEA Assistant, or by choosing them from the FEA Properties column in an Objects spreadsheet.

NOTE: The FEA Properties List is saved in the current Project file when it is saved to the disk.

FEA Properties List Window. Masses require a mass value. Springs require a stiffness value. Dampers require a damping value. Rods require a material from the FEA Materials List, and a cross sectional area. Bars require a material from the FEA Materials List, and cross sectional area & inertia. Plates require a material from the FEA Materials List, and a thickness. Solids require a material from the FEA Materials List. •

Click on a tab at the top of the Properties window to enter the Properties of each type of FEA Object

•

Units (English or Metric) are determined by the Mass, Force & Length units chosen in the File | Structure Options box in the Structure window.

File Menu File | Import Imports a Property spreadsheet from another ME'scopeVES Project file. File | Print Spreadsheet

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Structural Dynamics Modification (SDM) Commands Prints the Property spreadsheet on the system printer or into a PDF file. Edit Menu Edit | Add Adds a new (empty) Property row to the currently displayed property spreadsheet. •

In the Material column, click on the cell in the new row.

•

Select a material from the FEA Materials List.

•

In all columns except the Material column, select each cell in the new row, and enter a property value.

Edit | Delete Deletes the currently selected Property (row) from the Properties spreadsheet. Display Menu Display | Center window Centers the window in the Work Area of the ME'scopeVES window. •

Repeated execution centers the window and returns it to its former position.

Display | Toolbar If checked, the Toolbar is displayed in the window.

FEA | FEA Objects List Opens the FEA Objects window which lists all of the FEA Objects currently attached to the structure model. •

To exclude an FEA Object from use by SDM, Experimental FEA, & FEA Model Updating commands, click the Visible button to change it to No.

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Reference Volume IIB - Options FEA Objects List Box.

FEA | Calculate FEA Modes Calculates the modes of the FEA model represented by all of the visible FEA Objects on the structure model in the Structure window. When this command is executed, a dialog box will open,

Calculate FEA Modes Dialog Box. Normal Modes If there are no FEA damper Objects on the model, Normal modes will be calculated. •

Normal modes have no modal damping and have real valued (or Normal) mode shapes.

Number of Modes •

Enter the number of modes desired, starting with the lowest frequency flexible body mode.

Rigid Body Offset (Hz) •

Enter a frequency greater than the expected lowest frequency flexible body mode, (20 is typical)

Maximum Iterations •

Enter the number of expected iterations required to converge on a solution (20 to 50 is typical).

Include Damping •

If checked, proportional damping is included in the equations for the FEA model.

•

Enter the percentage A of Mass; (A x [M]) and the percentage B of Stiffness; (B x [K]) to be used for the damping matrix.

Compute from Mode Shapes •

198

If a Shape Table with mode shapes in it is chosen from the list in the dialog box, A & B values will be calculated from the modal frequency & damping and placed into the A & B boxes.

Structural Dynamics Modification (SDM) Commands When the FEA modes have been calculated, the Shape Table selection dialog box will open allowing you to save the FEA mode shapes into a Shape Table file.

Shape Table Window Showing FEA Mode Shapes.

199

Experimental Finite Element Analysis (FEA) Commands Structure Window Experimental FEA Commands NOTE: If the VES-8000 Experimental FEA option is authorized, the following Structure window commands and spreadsheet Objects are enabled in your software. Check Help | About to verify authorization of this option. FEA Menu •

FEA | Materials List

•

FEA | Properties List

•

FEA | FEA Objects List

•

FEA | FEA Assistant

•

FEA | Calculate | FEA Modes

•

FEA | Point Matching

•

FEA | Export the FEA Model

FEA Objects •

FEA Objects are added to the Edit | Object Types list.

FEA Objects The following FEA elements are used by the VES-5000 SDM, VES-8000 Experimental FEA, & VES9000 FEA Model Updating options to ME'scope. FEA Mass Adds a Mass (or Inertial effects) to a Point on a structure model. •

Applies translational or rotational inertial effects in up to three directions at a Point.

•

Inertia can be constrained to specific directions by making the appropriate selections in the Orientation column of the Mass Objects spreadsheet.

•

The FEA Mass is defined in the FEA Properties List.

•

A Mass from the FEA Properties List must be chosen in the Property cell of each FEA Mass in the Objects spreadsheet.

FEA Spring & FEA Damper Add linear stiffness (or damping) between 2 Points on a structure model. •

Apply forces either axially (along their axis) or as translational or rotational stiffness or damping between two Points.

•

Can be constrained to specific directions by making selections from the Orientation columns of their end Points in their respective Object spreadsheets.

•

The stiffness for an FEA Spring is defined on the Springs tab in the FEA Properties List.

•

The damping for an FEA Damper is defined on the Dampers tab in the FEA Properties List.

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Reference Volume IIB - Options •

A Spring (or Damper) from the FEA Properties List must be chosen in the Property cell of each FEA Spring (or FEA Damper) in the Objects spreadsheet.

FEA Rod A linear element added between 2 Points on a structure model. •

Applies translational force axially (along its axis) between its two end Points.

•

The cross sectional area of an FEA Rod is defined on the Rods tab in the FEA Properties list.

•

The elasticity & density of an FEA Rod are defined first in the FEA Materials list, and then chosen in the Material column on the Rods tab in the FEA Properties list.

•

A Rod from the FEA Properties List must be chosen in the Property cell of each FEA Rod in the Objects spreadsheet.

FEA Bar A linear element added between 2 Points on a structure model. •

A long slender element that applies translational force axially (along its axis), and bending forces at its end Points.

•

Same as a beam element but with a fixed cross section.

•

The cross sectional area & cross sectional inertias (X Inertia, Y Inertia, XY Inertia) are defined on the Bars tab in the FEA Properties list. •

The cross section is oriented by pointing the X-Axis of the cross section to an Orientation Point in the structure window.

•

The Orientation Point (row number in the Points spreadsheet) must be entered into the Orientation cell in the FEA Bar spreadsheet.

•

The material properties of an FEA Bar are defined first in the FEA Materials list, and then chosen in the Material column on the Bars tab in the FEA Properties list.

•

A Bar from the FEA Properties List must be chosen in the Property cell of each FEA Bar in the Objects spreadsheet.

FEA Triangle & FEA Quad Plate Two types of linear plate elements, also called membrane elements. •

An FEA Triangle is defined between 3 Points

•

An FEA Quad is defined between 4 Points

NOTE: Plate elements should be used to model parts of a structure that are relatively thin compared to their width & height dimensions. •

The thickness is defined on the Plates tab in the FEA Properties list.

•

The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Plates tab in the FEA Properties list.

•

A Plate from the FEA Properties List must be chosen in the Property cell of each FEA Triangle (or FEA Quad) in the Objects spreadsheet.

Plate Stiffness Multiplier The Stiffness Multiplier is used to increase or decrease the bending stiffness of an Plate element. The bending stiffness of a Plate element is calculated as a function of its thickness and material properties.

202

Experimental Finite Element Analysis (FEA) Commands •

The Plate stiffness calculation assumes that the plate cross section consists of a uniform distribution of the plate material.

In cases where a plate cross section consists of two or more dissimilar materials, its bending stiffness could be greater or less than the stiffness calculated with a single material cross section. •

Stiffness Multiplier = 1 calculates the bending stiffness from the Plate thickness & material properties.

•

Stiffness Multiplier > 1 increases the bending stiffness of the Plate element.

•

Stiffness Multiplier < 1 decreases the bending stiffness of the Plate element.

Correct Point Selection for Adding Plates & Solid Elements. FEA Tetra, FEA Prism & FEA Brick These elements are called solid elements because they are 3-dimensional. NOTE: Solid elements should be used to model parts of a structure that have approximately the same width, height, & length dimensions. •

An FEA Tetra is defined between four Points.

•

An FEA Prism is defined between six Points.

•

An FEA Brick is defined between eight Points.

•

The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Solids tab in the FEA Properties list.

•

A Solid from the FEA Properties List must be chosen in the Property cell of each FEA Tetra, FEA Prism, & FEA Brick in the Objects spreadsheet.

FEA | Materials List Opens the FEA Materials List window. This window contains material properties that are referenced in the FEA Properties List. NOTE: The FEA Materials List is saved with the current Project file when it is saved to the disk.

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Reference Volume IIB - Options

FEA Materials Window. Each FEA Material is defined by three properties, •

Young's Modulus of Elasticity (Pascals (Pa) in Metric units or Pounds per square inch (psi) in English units)

•

Poisson's Ratio (unit-less)

•

Density (N/cm^3 in Metric units or Lb/in^3 in English units)

File Menu File | Import Imports a Materials spreadsheet from another ME'scopeVES Project file. File | Print Spreadsheet Prints the Materials spreadsheet on the system printer or into a PDF file. Edit Menu Edit | Add Adds a new Material (new row) to the Materials spreadsheet. •

Select each cell in the new row, and enter the new Material value into the cell.

Edit | Delete Deletes the currently selected Material (row) from the Materials spreadsheet. Display Menu Display | Center window Centers the window in the Work Area of the ME'scopeVES window. •

Repeated execution centers the window and returns it to its former position.

Display | Toolbar If checked, the Toolbar is displayed in the window.

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Experimental Finite Element Analysis (FEA) Commands FEA | Properties List Opens the Properties List window. This window contains the Properties that are referenced by FEA Objects on a structure model. •

Properties from the FEA Materials List are used as part of the definition of some Object Properties in this window.

•

Properties are assigned to FEA Objects using the FEA Assistant, or by choosing them from the FEA Properties column in an Objects spreadsheet.

NOTE: The FEA Properties List is saved in the current Project file when it is saved to the disk.

FEA Properties List Window. Masses require a mass value. Springs require a stiffness value. Dampers require a damping value. Rods require a material from the FEA Materials List, and a cross sectional area. Bars require a material from the FEA Materials List, and cross sectional area & inertia. Plates require a material from the FEA Materials List, and a thickness. Solids require a material from the FEA Materials List. •

Click on a tab at the top of the Properties window to enter the Properties of each type of FEA Object

•

Units (English or Metric) are determined by the Mass, Force & Length units chosen in the File | Structure Options box in the Structure window.

File Menu File | Import Imports a Property spreadsheet from another ME'scopeVES Project file. File | Print Spreadsheet

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Reference Volume IIB - Options Prints the Property spreadsheet on the system printer or into a PDF file. Edit Menu Edit | Add Adds a new (empty) Property row to the currently displayed property spreadsheet. •

In the Material column, click on the cell in the new row.

•

Select a material from the FEA Materials List.

•

In all columns except the Material column, select each cell in the new row, and enter a property value.

Edit | Delete Deletes the currently selected Property (row) from the Properties spreadsheet. Display Menu Display | Center window Centers the window in the Work Area of the ME'scopeVES window. •

Repeated execution centers the window and returns it to its former position.

Display | Toolbar If checked, the Toolbar is displayed in the window.

FEA | FEA Objects List Opens the FEA Objects window which lists all of the FEA Objects currently attached to the structure model. •

206

To exclude an FEA Object from use by SDM, Experimental FEA, & FEA Model Updating commands, click the Visible button to change it to No.

Experimental Finite Element Analysis (FEA) Commands FEA Objects List Box.

FEA | FEA Assistant Adds FEA Objects to a structure model. NOTE: The FEA Assistant includes all of the Drawing Assistant tabs plus the Add FEA Objects tab. •

See Draw | Drawing Assistant for details on using the Drawing Assistant tabs.

Structure Window Showing FEA Assistant Tabs. Add FEA Objects Tab •

Adds FEA Objects of the same type to the selected SubStructure.

NOTE: Before using the FEA Assistant, use Draw | Add Selected Objects to SubStructure to create as many SubStructures as necessary for adding FEA Objects to a model using the following rules. Rules for Adding FEA Objects •

FEA Mass •

•

FEA Spring, FEA Damper, FEA Rod or FEA Bar •

•

Will be added wherever there is a visible Surface Triangle on the selected Substructure.

FEA Quad •

•

Will be added between the same Point pairs as each visible Line on the selected Substructure.

FEA Triangle •

•

Will be added wherever there is a visible Point on the selected SubStructure.

Will be added wherever there is a visible Surface Quad on the selected Substructure.

FEA Tetra, FEA Prism & FEA Brick

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Reference Volume IIB - Options NOTE: Solid FEA Objects will only be added to a selected SubStructure that was created with the Extrude or Revolve command. To add FEA Objects to a selected SubStructure; •

Choose a property from the Properties list next to the M,C,K, Rods,Bars, Plates or Solids button.

•

If the FEA | Properties List is empty, press the New button to add a new property to the FEA Properties list.

•

Press the enabled M,C,K, Rods,Bars, Plates or Solids button to add the FEA Objects to the selected SubStructure.

FEA | Calculate FEA Modes Calculates the modes of the FEA model represented by all of the visible FEA Objects on the structure model in the Structure window. When this command is executed, a dialog box will open,

Calculate FEA Modes Dialog Box. Normal Modes If there are no FEA damper Objects on the model, Normal modes will be calculated. •

Normal modes have no modal damping and have real valued (or Normal) mode shapes.

Number of Modes •

Enter the number of modes desired, starting with the lowest frequency flexible body mode.

Rigid Body Offset (Hz) •

Enter a frequency greater than the expected lowest frequency flexible body mode, (20 is typical)

Maximum Iterations •

Enter the number of expected iterations required to converge on a solution (20 to 50 is typical).

Include Damping

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Experimental Finite Element Analysis (FEA) Commands •

If checked, proportional damping is included in the equations for the FEA model.

•

Enter the percentage A of Mass; (A x [M]) and the percentage B of Stiffness; (B x [K]) to be used for the damping matrix.

Compute from Mode Shapes •

If a Shape Table with mode shapes in it is chosen from the list in the dialog box, A & B values will be calculated from the modal frequency & damping and placed into the A & B boxes.

When the FEA modes have been calculated, the Shape Table selection dialog box will open allowing you to save the FEA mode shapes into a Shape Table file.

Shape Table Window Showing FEA Mode Shapes.

FEA | Point Matching There can be several differences between an FEA model and an EMA 3D model, 1. The Points on the FEA model are oriented differently than on the EMA model. 2. The FEA model has many more Points (nodes) than the EMA model. 3. The Points on the FEA model are numbered differently than on the EMA model.

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Reference Volume IIB - Options In order to compare FEA & EMA mode shapes using MAC values, each EMA mode shape DOF must match with the FEA mode shape DOF corresponding to the Point on the FEA model nearest to a Point on the EMA model. NOTE: The use of mode shape MAC values is optional during FEA Model Updating. Point Matching is not required if mode shape MAC values are not used during FEA Model Updating. Point Matching Steps •

Geometrically align the FEA & EMA models using the Drawing Assistant.

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Execute FEA | Point Matching

The FEA | Point Matching command carries out the following steps, •

Local each Point on the FEA model that is closest geometrically to each Point on the EMA model.

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Re-number each EMA Point using the Point number of its matching FEA Point.

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Re-number each EMA shape DOF using the re-numbered EMA Point.

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Copy the Measurement Axes of each EMA Point to its matching FEA Point.

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Transform the FEA mode shape components at each FEA Point into the Measurement Axis coordinates of the matching EMA Point.

Creating Two SubStructures NOTE: The FEA | Point Matching command operates on the Points referenced by an FEA SubStructure and an EMA Substructure. Both SubStructures must be contained in the same Structure window, and the FEA SubStructure must precede the EMA SubStructure in the SubStructure spreadsheet. To create an FEA SubStructure, •

Select all Points on the model In the FEA Model window, and execute Draw | Add SELECTED Objects to SubStructure. A dialog box will open.

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Press the New SubStructure File button, enter "FEA SubStructure" into the next dialog box, and click on OK.

To create an EMA SubStructure, •

Select all Points on the model in the EMA Structure window, and execute Draw | Add SELECTED Objects to SubStructure. A dialog box will open.

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Press the New SubStructure File button, enter "EMA SubStructure" into the next dialog box, and click on OK.

To place the two SubStructures together in the same window, •

Select the FEA SubStructure, and execute Edit | Copy Objects to File in its window.

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Press the New Structure File button in the dialog box that opens, and save the FEA SubStructure into a new Structure file.

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Select the EMA SubStructure, and execute Edit | Copy Objects to File in its window.

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Select the Structure file with the FEA SubStructure in it and click on the Add To button.

Aligning the SubStructures In the structure window containing both the FEA SubStructure and the EMA SubStructure;

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Experimental Finite Element Analysis (FEA) Commands •

Execute Draw | Drawing Assistant to open the Drawing Assistant tabs.

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Select only the EMA SubStructure or the FEA SubStructure.

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Use the controls on the Dimensions and Position tabs to align the Points of the two SubStructures as closely as possible.

When the two SubStructures are aligned, they are ready for point matching. •

Select both the FEA SubStructure and the EMA SubStructure.

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Make sure that the two Shape Tables with FEA modes and EMA modes are open.

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Execute FEA | Point Matching.

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Select the FEA modes in the left list, and the EMA modes in the right list in the Point Matching dialog box, and click on OK.

Point Matching Dialog Box. When Point Matching is completed, a series of dialog boxes will open, asking if you want to save each of SubStructures and Shape Tables into new files. The two saved SubStructure models and their corresponding Shape Tables can now be used for MAC calculations. NOTE: Point matching is required if mode shapes are used in the cost function during FEA Model Updating. If only modal frequencies are used in the cost function, Point Matching is not required.

FEA | Export the Model Exports an FEA model into a disk file using the NASTRAN bulk data deck format.

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FEA Model Updating Commands Structure Window FEA Model Updating Commands NOTE: If the VES-9000 FEA Model Updating option is authorized, the following Structure window commands are enabled in your software. Check Help | About to verify authorization of this option. •

FEA | Model Updating

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FEA | Calculate Updated Modes

Targeted FEA Model Updating FEA Model Updating involves changing the Properties of an FEA model so that its FEA modes more closely match a set of experimental (EMA) modes. This approach is called Targeted Model Updating because you can; 1. Select modal frequencies & mode shape pairs to be matched. 2. Select FEA properties to be updating. 3. Select portions of an FEA model to be updating. FEA model updating uses the SDM method to calculate new FEA modes due to changes in each FEA property. •

Only the mode shapes of the unmodified structure and the FEA elements to be modified are required in order to do model updating.

FEA Model Updating calculates all solutions over a user-defined solution space and orders the solutions from best to worst. The best solution is the one that minimizes the difference between the FEA & EMA modal parameters for all selected mode pairs. However, any solution can be used to calculate the new modes of the updated FEA model. NOTE: Point Matching is only required if mode shapes are used in the error function calculation during FEA Model Updating. Difference Between SDM and Model Updating •

The SDM commands model the effects of additions (or subtractions) of FEA Objects to a structure. The SDM | Calculate New Modes command calculates new mode shapes which reflect the addition (or subtraction) of FEA elements to the structure.

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The FEA Model Updating commands model the effects of changes in the Properties of FEA Objects already on a structure model. The FEA | Calculate Updated FEA Modes calculates new mode shapes which reflect updated Properties of FEA Objects on a structure.

FEA Objects The following FEA elements are used by the VES-5000 SDM, VES-8000 Experimental FEA, & VES9000 FEA Model Updating options to ME'scope. FEA Mass Adds a Mass (or Inertial effects) to a Point on a structure model. •

Applies translational or rotational inertial effects in up to three directions at a Point.

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Reference Volume IIB - Options •

Inertia can be constrained to specific directions by making the appropriate selections in the Orientation column of the Mass Objects spreadsheet.

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The FEA Mass is defined in the FEA Properties List.

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A Mass from the FEA Properties List must be chosen in the Property cell of each FEA Mass in the Objects spreadsheet.

FEA Spring & FEA Damper Add linear stiffness (or damping) between 2 Points on a structure model. •

Apply forces either axially (along their axis) or as translational or rotational stiffness or damping between two Points.

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Can be constrained to specific directions by making selections from the Orientation columns of their end Points in their respective Object spreadsheets.

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The stiffness for an FEA Spring is defined on the Springs tab in the FEA Properties List.

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The damping for an FEA Damper is defined on the Dampers tab in the FEA Properties List.

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A Spring (or Damper) from the FEA Properties List must be chosen in the Property cell of each FEA Spring (or FEA Damper) in the Objects spreadsheet.

FEA Rod A linear element added between 2 Points on a structure model. •

Applies translational force axially (along its axis) between its two end Points.

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The cross sectional area of an FEA Rod is defined on the Rods tab in the FEA Properties list.

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The elasticity & density of an FEA Rod are defined first in the FEA Materials list, and then chosen in the Material column on the Rods tab in the FEA Properties list.

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A Rod from the FEA Properties List must be chosen in the Property cell of each FEA Rod in the Objects spreadsheet.

FEA Bar A linear element added between 2 Points on a structure model. •

A long slender element that applies translational force axially (along its axis), and bending forces at its end Points.

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Same as a beam element but with a fixed cross section.

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The cross sectional area & cross sectional inertias (X Inertia, Y Inertia, XY Inertia) are defined on the Bars tab in the FEA Properties list. •

The cross section is oriented by pointing the X-Axis of the cross section to an Orientation Point in the structure window.

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The Orientation Point (row number in the Points spreadsheet) must be entered into the Orientation cell in the FEA Bar spreadsheet.

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The material properties of an FEA Bar are defined first in the FEA Materials list, and then chosen in the Material column on the Bars tab in the FEA Properties list.

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A Bar from the FEA Properties List must be chosen in the Property cell of each FEA Bar in the Objects spreadsheet.

FEA Triangle & FEA Quad Plate Two types of linear plate elements, also called membrane elements.

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FEA Model Updating Commands •

An FEA Triangle is defined between 3 Points

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An FEA Quad is defined between 4 Points

NOTE: Plate elements should be used to model parts of a structure that are relatively thin compared to their width & height dimensions. •

The thickness is defined on the Plates tab in the FEA Properties list.

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The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Plates tab in the FEA Properties list.

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A Plate from the FEA Properties List must be chosen in the Property cell of each FEA Triangle (or FEA Quad) in the Objects spreadsheet.

Plate Stiffness Multiplier The Stiffness Multiplier is used to increase or decrease the bending stiffness of an Plate element. The bending stiffness of a Plate element is calculated as a function of its thickness and material properties. •

The Plate stiffness calculation assumes that the plate cross section consists of a uniform distribution of the plate material.

In cases where a plate cross section consists of two or more dissimilar materials, its bending stiffness could be greater or less than the stiffness calculated with a single material cross section. •

Stiffness Multiplier = 1 calculates the bending stiffness from the Plate thickness & material properties.

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Stiffness Multiplier > 1 increases the bending stiffness of the Plate element.

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Stiffness Multiplier < 1 decreases the bending stiffness of the Plate element.

Correct Point Selection for Adding Plates & Solid Elements. FEA Tetra, FEA Prism & FEA Brick These elements are called solid elements because they are 3-dimensional. NOTE: Solid elements should be used to model parts of a structure that have approximately the same width, height, & length dimensions. •

An FEA Tetra is defined between four Points.

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An FEA Prism is defined between six Points.

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An FEA Brick is defined between eight Points.

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Reference Volume IIB - Options •

The material properties are defined first in the FEA Materials list, and then chosen in the Material column on the Solids tab in the FEA Properties list.

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A Solid from the FEA Properties List must be chosen in the Property cell of each FEA Tetra, FEA Prism, & FEA Brick in the Objects spreadsheet.

FEA | Model Updating FEA Model Updating changes the Properties of certain FEA Objects on an FEA model so that its modes more closely match a set of experimental (EMA) modal parameters. During FEA Model Updating you can, •

Select pairs of FEA & EMA modal frequencies & mode shapes to be matched.

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Select portions of the FEA model and certain FEA Properties to be updating.

The FEA Model Updating solutions are ordered from best to the worst based on the values of an Error function. •

The best solution yields FEA modes that are closest to the EMA modes.

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Solutions are calculated over a user-defined solution space and ordered from best to worst.

Command Requirements Before this command can be executed, several items are required, 1. A Structure window containing a structure model with FEA Objects added to it. 2. A Shape Table containing FEA mode shapes that have been displayed in animation of the model. 3. A Shape Table containing EMA mode shapes. Properties that can be updated (changed) using FEA Model Updating are listed in the Table below. Material properties include Elasticity, Poisson's ratio, and Density.

FEA Object

Property to Update

Spring

stiffness

Mass

mass

Rod

cross sectional area, material properties

Bar

cross sectional area & inertias material properties

Plate

thickness material properties

Solid

material properties

FEA Properties That Can Be Modified During Model Updating. When this command is executed in the Structure window containing the FEA model, the following dialog box will open.

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FEA Model Updating Commands

Shape Table Selection Dialog Box. â€˘

Choose a Shape Table containing the FEA mode shapes and a Shape Table containing the EMA mode shapes, and click on OK.

The FEA Model Updating window will open, as shown below.

FEA Model Updating Window Showing 5 Selected Modes and 1 Selected Property for Updating.

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Reference Volume IIB - Options Upper Spreadsheet •

The FEA frequencies are listed in the first column and the EMA frequencies are listed in the second column of the upper spreadsheet.

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The MAC values between each FEA & EMA mode shape pair are listed in the third column.

Error Function To order the solutions, an Error function containing a sum of the error between each selected FEA & EMA frequency pair is calculated. In addition, Include MAC is depressed for a mode shape pair, another term (1 - MAC) is added to the Error function. NOTE: The use of mode shape MAC values is optional for calculating the Error function. Point Matching is required if mode shape MAC values are used in the Error function. The formula for the Error function is:

where: Fup = Updated FEA frequency Fema = EMA frequency MACup = MAC value between each Updated FEA & EMA mode shape pair.

As the solution calculation progresses, the current minimum Error function is listed in the Error box at the top of the FEA Model Updating window. Lower Spreadsheet The lower spreadsheet lists the Properties of all visible FEA Objects on the structure model. •

The solution space for each Property is defined by its Property Minimum, Property Maximum, and Property Steps.

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Property Minimum & Maximum define the lower & upper bounds of the solution space.

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Property Steps is the number of steps to be evaluated between the Property Minimum & Maximum.

Solution Space Example •

If Property Minimum = 1, Property Maximum = 10 and Property Steps = 10, then 10 Property values (1,2,3,4,5,6,7,8,9,10) would be used during the solution process.

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If three properties each have 10 Steps, then the solution space consists of a total of 1000 solutions.

NOTE: The Minimum, Maximum, and Steps of all (or selected) Properties in the lower spreadsheet define the solution space over which solutions are calculated. Calculating Solutions •

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Depress the Select Mode button for each mode pair to be used in evaluating the Error function.

FEA Model Updating Commands If no modes are selected, then all modes with non-zero frequencies will be used. •

Depress the Include MAC button to include the mode shape pair MAC value in the Error function.

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Depress the Select Property button of a Property to include it in the solution space.

If no Properties are selected, then all properties in the lower spreadsheet will be used. •

Execute Solution | Start Calculation, and click on OK in the dialog box that opens to begin the calculations.

FEA Model Updating Window After Solutions are Calculated. Solution Scroll Bar When the solution process has been completed, a Solution scroll bar will be displayed on the right hand side of the window. •

Each solution is displayed by scrolling the scroll bar.

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The best solution is displayed when the scroll is at the top of the scroll bar.

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The worst solution is displayed when the scroll is at the bottom of the scroll bar.

Bar Graphics •

Execute Display | Graphics to display the solutions using bar graphics.

The upper left bar graph shows two bars for each mode pair.

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Reference Volume IIB - Options •

The left (blue) bar is the Percent Difference between the FEA & EMA frequencies.

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The right (green) bar is the Percent Difference between the Solution & EMA frequencies.

The upper right bar graph displays MAC values using two bars for each mode pair. •

The left (blue) bar is the MAC between the FEA & EMA mode shapes.

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The right (red) bar is the MAC between the Solution & EMA mode shapes.

The lower bar graph displays the Current & Solution values of the FEA Properties. •

Hover the mouse pointer over each bar graph to display its numerical values.

Graphical Solution Display. Saving a Solution •

Drag the scroll on the right hand scroll bar to display the desired Solution.

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Execute Solution | Save Solution in FEA Properties to save the Property values as Updated Properties in the FEA Properties & FEA Materials lists.

FEA | Calculate Updated FEA Modes Calculates the new modes of an Updated FEA model. NOTE: This command uses the mode shapes of the unmodified FEA model together with its current & updated FEA Properties to calculate the new modes of the updated FEA model. When this command is executed, the Shape Table selection dialog box is opened. •

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Choose a Shape Table with the FEA modes for the unmodified FEA model, and click on OK.

FEA Model Updating Commands When the calculation is completed, a dialog box will open, allowing you to save the mode shapes of the updated FEA model into a Shape Table.

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Glossary

A Acoustic Source: A group of Points on an Acoustic Surface containing measurements from an identified noise source. Sources are used for Source Ranking of acoustic data. Source names are entered in the Acoustic Source column in the Traces or Shapes spreadsheet. Acoustic Surface: A special type of SubStructure represented by a grid of measurement Points. Each measurement Point has a surrounding area and surface normal. Acoustic Surfaces are created with the Drawing Assistant. Active Graph: Either the upper or lower Traces in the graphics area on the left side of the Acquisition window. The upper or lower Traces are made active by clicking on them, or by executing Display | Active Graph in the Acquisition window. Active Traces: The Acquisition window displays upper & lower Traces in its graphics area. The upper Traces are time domain data acquired from the front end. The lower Traces are time or frequency domain measurements calculated from the upper Traces. The Display | Active Graph command toggles the active Traces between the upper & lower Traces. Active View: One of the four Views in the Structure window graphics area. Drawing operations like Move, Rotate and Resize are performed in the active View. A View is made active by clicking on it, or by executing on of the Display | View commands. Animation Equation: All animation is created in a Structure window by evaluating the Animation equations at each Point on a structure model. Each animation equation defines which measurements (M#s) are used to animate a Point in a direction. Animation equations are displayed on tabs above the Points spreadsheet by executing Edit | Animation Equations | Equation Editor in the Structure window. Animation Frame: Animation is created by displaying still pictures (frames) in rapid succession in a Structure window. The animation can be paused and stepped through the frames by using the Animate | Step commands. Animation Source: Any Data Block, Shape Table, or Acquisition window that is open in the Work Area. The current Animation Source is displayed in the Animation Source list on the Toolbar in the Structure window. During animation, M# data from the current Animation Source is animated using the Animation equations for each Point on the structure model. During a Comparison display, two Animation Sources are used. Auto spectrum: An Auto Spectrum is calculated by multiplying a Fourier spectrum by its complex conjugate. The Auto spectrum has magnitude only. Its phase is zero. An Auto spectrum can have either Linear (RMS) units or Power (MS) units.

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Reference Volume IIB - Options

B Band Cursor: One of the Data Block window cursors, represented by two vertical lines on each Trace. Click & drag inside the band to move it. Click & drag outside the band to move the nearest edge of the band. Bitmap: A copy of the pixels used to draw the graphics in a window. Bitmaps are used in all Copy to Clipboard and Print commands that operate on graphics. Block Size: The number of samples (time or frequency values) in the Traces of a Data Block or Acquisition window. The current Block Size can be viewed and edited in the File | Properties dialog box. Increasing the Block Size appends zero valued samples to each Trace. Decreasing the Block Size removes samples from the high frequencies or time values of each Trace.

C Center Point: Any Point that is referenced in the Center Point column of the Points spreadsheet. A Point that references a Center Point is called a Radial Point. If a Center Point has a Machine Rotation Animation equation, all Radial Points that reference the Center Point will exhibit rotational motion about the Center Point during animation. Closely Coupled Modes: Two or more modes that appear as a single peak in a frequency domain function. This occurs when two or more modes have resonance curves that sum together to form a single peak. CMIF: CMIF is an acronym for Complex Mode Indicator Function. Peaks in multiple CMIF curves will indicate closely coupled modes and repeated roots. Modal participation factors are calculated along with the CMIFs, and are used in succeeding multiple reference curve fitting steps. CoMAC: CoMAC is an Acronym for Coordinate Modal Assurance Criterion. CoMAC indicates whether or not two shape components are co-linear for all (or selected) shapes in a Shape Table. If CoMAC > 0.9, the two shape components are similar (co-linear). If CoMAC < 0.9 the two shape components are different for all shapes. Complex Shape: A shape with components that have phases other than 0 or 180 degrees. During animation, complex shapes will exhibit a "traveling wave" motion. Complex shape components can be normalized (to phases of 0 or 180 degrees) using the Normalize Shapes coomands in a Strucutre, Shape Table, Data Block or Acquisition window. Contour: A locus of equal magnitudes of a displayed shape during animation. Contours are displayed only on surfaces of a structure model. Data Block Traces can also be displayed in a contour format. Cross spectrum: A cross-channel function, calculated by multiplying the Fourier spectrum of a waveform by the complex conjugate of the Fourier spectrum of another waveform.

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Glossary Cross-channel Measurement: A measurement function that is calculated between two different simultaneously acquired signals. Examples are Transfer Functions, Impluse Response functions, Transmissibility's, Cross spectra, Cross Correlations, and ODS FRFs. Current Animation Source: The Data Block, Shape Table, or Acquisition window that is currently used for animating shapes in a Structure window. The current Source name is displayed in the Animation Source list on the Structure window Toolbar.

D Data Block file: One or more Traces of measurement data with a common time or frequency axis. Time domain measurements are real valued. Frequency domain measurements are complex valued. Each Trace has a unique measurement number M#. M#s are displayed in the Select Trace column of the Traces spreadsheet, and are used by the Animation equations in a Structure window for retrieving shape data at the cursor position in a Data Block. DFT: DFT is an acronym for Digital Fourier Transform. The forward FFT transforms a sampled time domain waveform into its equivalent DFT. The inverse FFT transforms a DFT back into its equivalent sampled time waveform. If the time domain signal has N real samples, the DFT will have (N/2) complex samples. Digital Movie: A Windows video file that documents the animation in the Structure window. Digital Movies are made using commands in the Movies menu. Each Movie file is played back in its own window. A Movie is not saved in a Project but is attached to it as an Added file. DOF: DOF is an acronym for degree-of-freedom. A DOF includes a Point number & direction. If each measurement (M#) in a Data Block, Shape Table or Acquisition window has a DOF defined for it, the DOF can be used to create Animation equations by assigning M#s to Points & directions on a 3D model of the test article. Each Point number should correspond to a numbered Point on the model . Each DOF direction should correspond to a Measurement Axis direction at the Point on the model. Scalar data has no direction associated with it. Drawing Assistant: A set of tabs in the Structure window that are used for drawing and modifying structure models. The Drawing Assistant tabs are displayed above the SubStructure spreadsheet by executing Draw | Drawing Assistant. Drawing Object: A Point, Line, Surface, or SubStructure on a structure model. Each Point is defined by its global X, Y, Z coordinates. Each Line is defined between two Points, each Surface Triangle between three Points, and each Surface Quad between four Points. Each SubStructure is a collection of Points, Lines, and Surfaces. Driving Point: The DOF (Point & direction) where excitation is applied to a test article. A driving point measurement has the same Roving and Reference DOFs.

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Reference Volume IIB - Options Driving Point Residue: A modal Residue is the numerator term or the "stength" of a mode in an FRF measurement function. A driving point Residue is obtained by curve fitting a driving point FRF measurement.

E EDS: EDS is an acronym for Engineering Data Shape, a general term used for any type of data measured from two or more points on a machine, structure, or acoustic surface. EMA: EMA is an acronym for Experimental Modal Analysis. During an EMA, the test article is artificially excited with either an impactor or a shaker. The excitation force and one or more responses caused by the force are simultaneously measured, and a set of FRF measurement functions is calculated The FRFs are then curve fit to obtain experimental modal parameters for the test article.

F FEA Assistant: A set of tabs in the Structure window that are used for drawing a structure model and adding FEA Objects to it. The FEA Assistant tabs are displayed above the SubStructure spreadsheet by executing FEA | FEA Assistant. FEA Object: FEA Objects are used by the SDM, Experimental FEA, and FEA Model Updating commands in ME'scope. FEA Objects are added between Points on a structure model. Their physical properties are defined in the FEA Properties window, and their material properties are defined in the FEA Materials window. FEA Rotations: FEA rotational data is used for SDM and FEA Model Updating calculations, and can be displayed in animation by executing Animate | Animate Using | FEA Rotations. FEA Rotational data is animated using FEA Rotation equations. Up to three FEA Rotation animation equations can be defined at each Point on a structure model. FFT: FFT is an acronym for Fast Fourier Transform. The FFT is an algorithm that transforms a uniformly sampled time domain signal into its equivalent Digital Fourier Transform (DFT). The Inverse FFT transforms the DFT back into its original sampled time domain signal. The FFT in ME'scope transfroms any number of samples, not just powers of 2 samples. Fixed DOF: A Fixed DOF on a structure model will not move during animation. Fixed DOFs are defined by executing Draw | Animation Equations | Fix DOFs. Fixed DOFs are removed by executing Draw | Animation Equations | Fixed to Interpolated. Fourier spectrum: A Fourier spectrum is the FFT of a uniformly sampled time waveform. The Fourier spectrum is also called the Discrete Fourier Transform, or DFT. FRF: FRF is an acronym for Frequency Response Function. An FRF is a cross-channel frequency domain function that defines the dynamic properties of a structure 226

Glossary between an excitation force DOF and a response DOF caused by the force. An FRF is defined as the ratio (response Fourier spectrum / force Fourier spectrum). The FRF is a special case of a Transfer Function, where the force is the denominator (Input) and the response is the numerator (Output) between to DOFs of a structure.

G Geometric Center: The average of the minimum & maximum coordinates in each direction (X,Y,Z) of all Points on a Drawing Object, FEA Object, or structure model. Global Curve Fitting: Global curve fitting processes multiple FRF Traces in a Data Block to obtain a global frequency & damping estimate for each mode in the measurement span or cursor band of interest. Group: Either Traces (M#s) in a Data Block or DOFs (M#s) in a Shape Table can be grouped together by giving them a common name in the Group column of the Traces or the DOFs spreadsheet. During shape animation, if the Animate | Animating Using | Groups command is enabled, then each Group is scaled separately so that data from two or more Groups can be displayed together.

I Input, Output, Both: These designations are used for MIMO modeling & simulation. When an FRF is calculated, the excitation force waveform is designated as the Input and the response waveform is designated as the Output. These choices are made in the Input Output column of the Traces spreadsheet. When Both is chosen, the waveform can be used as both an Input and an Output in MIMO calculations. Interpolated Equation: An Interpolated Animation equation is used to animate all unmeasured DOFs of a structure model. Interpolated Animation equations are created by executing Draw | Animation Equations | Create Interpolated. Interpolated equations are only used by animation when Animate | With Interpolation is enabled.

L Line Cursor: A Line cursor is one of the three toyes of Data Block or Acquisition window cursors. It is represented by a vertical line on each Trace. The Line cursor is moved by clicking & dragging on any Trace. Also, just clicking on a Trace will place the cursor at the mouse pointer position. Line Object: A Drawing Object, displayed as a straight line between two Points. Lines are displayed by executing Display Objects | Lines | Show Lines. All Line properties are displayed in the Objects spreadsheet by executing Edit | Object Type | Lines.

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Reference Volume IIB - Options Local Curve Fitting: Local curve fitting extracts a modal frequency & damping estimate from each FRF Trace in a Data Block, for each mode.

M M#: M# is an abbreviation for Measurement number. Each Trace in a Data Block or Acquisition window has a unique M#. Also, each shape component (or DOF) in a Shape Table window has a unique M#. M#s are used by the Animation equations at each Point on a structure model to animate the Point using data from the M#s in the Animation Source. MAC: MAC is an Acronym for Modal Assurance Criterion. MAC indicates whether or not two shapes are co-linear (they lie on the same straight line). If MAC =1 the shapes are co-linear. If MAC > 0.90, the shapes are simlar (close to co-linear). If MAC < 0.90 the shapes are different. Machine Rotation Data: One of the kinds of shape data that can be displayed in animation on a structure model. Machine rotation data must be assigned to a Center Point in the Z-direction. During animation, all of the Radial Points that reference a Center Point are animated with rotation about the Center Point. Measured Equation: A Measured animation equation is a weighted summation of M#s that specifies which Trace M# or Shape component M# will be used to animate a Point & direction on a structure model. Animation equations can be viewed on the Animation Equation tab by executing Draw | Animation Equations | Equation Editor. They are also displayed at selected Points by executing Draw | Animation Equations | Show Equations. Measurement: A Trace in a Data Block or Acquisition window, or a shape component in a Shape Table. Each Trace or Shape DOF has a unique M#. Shapes are displayed in animation by evaluating Animation equations at each Point on a structure model. Measured Animation equations are created by assigning each M# to a Point & direction on the model. Interpolated Animation equations are created by assigning M#s from nearby Points to un-measured Points & directions. Measurement Axes: Each Point on a structure model has 3 Measurement Axes. Measurement Axes define the directions in which measurements were made at the Point. Measurement Axes are displayed and edited using the Measurement Axes tab, which is displayed by executing Draw | Animation Equations | Equation Editor. Measurement Set: A Measurement Set is all of the data that is simultaneously acquired during acquisition. Simultaneous acquisition requires simultaneous amplification, anti-alias filtering, and analog to digital conversion by a multi-channel acquisition front end. Measurement Sets are defined in an Acquisition window. Crosschannel measurements are calculated using data from the same Measurement Set. The current Measurement Set number is appended to the DOFs of all measurement functions calculated using the current Measurement Set.

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Glossary Meshing: Meshing subdivides selected Lines, Surfaces, FEA Objects, and SubStructures into more Objects. If a SubStructure is meshed, all of its Lines, Surfaces, and FEA Objects are meshed. The commands in the Draw | Mesh menu are used for meshing. MIMO model: A MIMO model is a Multiple Input Multiple Output frequency domain matrix model, where Inputs are multiplied by Transfer functions to obtain Outputs. A Transfer function matrix is multiplied by Fourier spectra of multiple Inputs to obtain Fourier spectra of multiple Outputs. Inputs, Outputs and Transfer functions can be calculated using different forms of the MIMO model equation. MMIF: MMIF is an acronym for Multivariate Mode Indicator Function. Peaks in multiple MMIFs will indicate closely coupled modes and repeated roots. Modal participation factors are calculated along with the MMIF curves, and are used in succeeding multiple reference curve fitting steps. Modal Model: A set of mode shapes that have been scaled so that they preserve the dynamic properties of a structure. Unit modal mass (UMM) scaling is used in ME'scope to create a modal model. A modal model is required for SDM amd FEA Model Updating. A modal model can also be used for FRF synthesis and MIMO Input & Output calculations. Mode Indicator Function: A mode indicator function is used for counting resonance peaks (or modes) in a set of frequncy domain functions. The number of modes in the data is then used for estimating modal frequency & damping using the Polynomial method. Mode Shape: Modes are used to characterize resonant vibration in structures. Each mode has a natural frequency, damping value, and a mode shape. The mode shape is a standing wave deformation of the structure at its natural (resonant or modal) frequency. An ODS for any time or frequency value is a summation of contributions from all of the mode shapes of a structure. mooZ: mooZ is the reverse of a Zoom operation in a Structure, Data Block, or Acquisition window. It restores the full display of the structure model in a Structure window, or the display of all of the Trace data in a Data Block or Acquisition window. MPC: MPC is an Acronym for Modal Phase Colinearity. The MPC has values between 0 & 1. If MPC = 1, all of the components of a shape lie on a straight line in the complex plane. If MPC < 1, the components do not lie on a strraight line. Lightly damped structures normally have mode shapes with MPC's close to 1. Multiple Reference Test: A Multiple Reference Test uses two or more fixed exciters to excite a test article, or two or more fixed response sensors. This is equivalent to measuring two or more columns (fixed exciters or Inputs), or two or more rows (fixed responses or Outputs) of the Transfer function matrix in the MIMO model.

N

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Reference Volume IIB - Options Nodal Line: A Nodal Line is a line of the surface a structure where all shape components are zero. The Nodal Lines of a complex shape will move during shape animation, while the Nodal Lines of a normalized shape will not move. Normalized Shape: A Normalized Shape has shape components with phases of 0 or 180 degrees. During shape animation, a Normalized Shape will exhibit a "standing wave" motion, and its Nodal Lines will not move. Complex shapes can be normalized (have their phases rotated to 0 or 180 degrees) by executing Animate | Normalize Shapes in a Shape Table, Data Block, or Acquisition window.

O Octave: An Octave band is a frequency band where the highest frequency is twice the lowest frequency. Acoustic measurements are often displayed using 1/1, 1/3, or 1/12 octave bands. ODS: ODS is an acronym for Operating Deflection Shape. An ODS is the deformation of a structure at two or more DOFs due to its own operation and/or applied forces. A time domain ODS characterizes the structural deformation at a specific time. A frequency domain ODS characterizes the structural deformation at a specific frequency. An ODS for any time or frequency is a summation of contributions from all of the mode shapes of a structure. ODS FRF: An ODS FRF is a cross-channel frequency domain measurement that is obtained from operating data. It requires a Roving response and a (fixed) Reference response. An ODS FRF is created by attaching the phase of the Cross spectrum between the Roving & Reference responses to the Auto spectrum of the Roving response. ODS's can be displayed in animation directly from a set of ODS FRFs. Operating mode shapes can be extracted by curve fitting a set of ODS FRFs. OMA: OMA is an acronym for Operational Modal Analysis. An OMA is performed when the excitation forces are not or cannot be measured, and hence FRFs cannot be calculated. Cross spectra or ODS FRFs calculated instead of FRFs, and are curve fit to extract operating modal parameters. Operating Mode Shape: A mode shape obtained by curve fitting a set of output-only cross-channel measurements, either Cross spectra or ODS FRFs. Orthogonal Polynomial: Orthogonal Polynomial is an MDOF curve fitting method for estimating modal parameters from a set of FRFs. Modal frequency & damping estimates can be obtained by using either a Global or a Local version of this curve fitting method. Orthogonal Views: The Quad View in a Structure window displays four Views of the structure model, a 3D View and three orthogonal 2D Views (X View, Y View, and Z View). A single View is obtained by double-clicking on one of the four Views in the Quad View.

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Glossary

P Peak Cursor: A Peak cursor is one of the three Data Block or Acquisition window cursors. A Peak cursor is displayed on each Trace as a band with two vertical lines, and the Trace peak value in the band displayed with a red dot. Click & drag inside the band to move the peak cursor band. Click & drag outside the band to move the nearest edge of the band. Periodic Signal: The FFT assumes that the waveform to be transforming is periodic in its transform window (the samples used by the FFT). Traces that are completely contained within the transform window satisfy this criterion. Cyclical signals that complete an integer number of cycles within the transform window also satisfy this criterion. If a waveform is not periodic in its window, the transformed signal will have "leakage" (or distortion) in it. Photo Realistic Model: A Photo Realistic Model is a structure model that has digital photographs attached to its surfaces. Photo Realistic Models are created using third party software, and imported into ME'scope using the .OBJ file format. Point Matching: Point Matching is the process of matching and re-numbering Points and mode shape DOFs between an FEA model and an EMA model. Point matching is part of the FEA Model Updating option to ME'scope. Point Object: A Point Object is defined by its three global coordinates (X,Y,Z). Points are used as end points for defining all other Objects in the Structure window. Each Point has its own Animation equations that are used to animate the Point with shape data from an Animation Source (Data Block, Shape Table or Acquisition window). Point properties are displayed in the Objects spreadsheet by executing Edit | Object Type | Points. Pole: A pole is the frequency & damping pair for mode of vibration or structural resonance. Pole Plot: A graph of modal frequency versus modal damping estimates for several modes. Modal frequencies are plotted on the horizontal axis and modal damping values on the vertical axis. A pole plot can be displayed during Stability curve fitting, or from a Shape Table by executing Display | Poles. Project: All work in ME'scope is done with data in a Project file. A Project file can contain one or more Structure, Data Block, Shape Table, Acquisition, Program, Report, or Added files. Only one Project can be open in ME'scope at a time. All of the names of the data files in the currently open Project are displayed in the top (or left) pane of the Project Flyout panel. PSD: PSD is an acronym for Power Spectral Density. A PSD is calculated by dividing an Auto spectrum by its frequency resolution (the increment between frequency lines). PSD units are typically (g^2/Hz) or (g/(Hz^1/2))

Q

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Reference Volume IIB - Options Quad View: A Quad View of a structure model consists of four Views (X View, Y View, Z View & 3D View). The Quad View is obtained by double-clicking on a single View. Double-clicking on one of the Views in the Quad View will display only that View.

R Radial Point: A Radial Point is any Point that references another Point in the Center Point column of the Points spreadsheet. If a SubStructure has one or more Center Points defined for it, and Rotatation is set to Yes in the SubStructure Object spreadsheet, then during shape animation, all Radial Points will rotate about their Center Points. Also, if a Center Point has a Machine Rotation Animation equation defined for it, then during shape animation, all Radial Points will be animated with rigid body rotatation about the Center Point. Reference DOF: A Reference DOF is the fixed DOF in a set of cross-channel measurements. All cross-channel measurements should have both a Roving and a Reference DOF. The Reference DOF follows the colon in a measurement DOF = Roving DOF : Reference DOF. Repeated Roots: Two or more modes with the same modal frequency but different mode shapes is called a Repeated Root. Repeated Roots can occur in many types of geometrically symmetric structures such as disks, cylinders, square plates and cubes. Residue: A Residue is one of the three modal parameters (along with frequency & damping) obtained from FRF-based curve fitting. The model residue is the constant numerator term in the partial fraction form of an analytical FRF. It is also referred to as the "strength" of a resonance or mode. It carries the FRF engineering units multiplied by Hz (or radians per second). Each mode has a Residue matrix, which is associated with a corresponding MIMO model of the structure. The residues from one row or column of the Residue matrix define a Residue mode shape. Residue Mode Shapes: Residue mode shapes are created following curve fitting when the modal parameter estimates are saved into a Shape Table. Residue mode shapes can be scaled into UMM mode shapes if Driving Point Residues are present in the mode shapes. Residue mode shapes are also used to synthesize FRFs. Roving DOF: The Roving DOF is the DOF that changes in a set of cross-channel measurements. All cross-channel measurements have both a Roving DOF and a (fixed) Reference DOF. The Roving DOF preceeds the colon in a measurement DOF = Roving DOF : Reference DOF.

S Sampling Window: The Sampling Window is the time domain samples used by the FFT to calculate a DFT. The Sampling Window is also called the transform

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Glossary window. To create certain properties in its spectrum, a special time domain windowing function (Hanning, Flat Top, Exponential, etc.) may be applied to the samples in the Sampling Window prior to transforming them with the FFT. Scalar Data: Scalar data is one of the kinds of shape data that can be displayed in animation on a structure model. Scalar data has no direction associated with it. Examples of Scalar data include Sound Pressure Level (SPL), Sound Power, temperature, and pressure. Scalar data is animated on a structure model using color contours on surfaces. SDI: SDI is an Acronym for Shape Difference Indicator. SDI indicates whether two shapes have shape components with the same or different values in them. SDI values range between 0 & 1. If SDI =1.0 the shapes have identical shape components. If SDI < 1.0 the shapes have different shape components. Shape: A Shape consists of two or more measured or calculated values at DOFs on a structure or acoustic surface. Specific types of shapes are an Operating Deflection Shape (ODS ), mode shape, acoustic shape, and Engineering Data Shape (EDS). Shape components can be Translational, Rotational, or Scalar. For correct shape animation, all shape components must have correct magnitude & phase values relative to one another. Shape Interpolation: Shape components for each Point & direction on a structure can be Measured, Fixed or Interpolated. During animation, the shape components of Interpolated DOFs are calculated by evaluating Interpolated Animation equations. Interpolated Equations are created using neighboring Measured or Fixed DOFs. Interpolated Animation equations are created by executing Draw | Animation Equations | Create Interpolated. Shape Table file: A Shape Table is a file for storing shapes. An ME'scope Project file can contain multiple Shape Tables. A shape is a spatial description of data measured or calculated for two or more Points or DOFs on a structure or Acoustic surface. Shapes can be imported from an external source, saved from an Animation Source, saved from the Structure window during animation, or created by saving modal parameter estimates into a Shape Table. Sine Dwell: Sine Dwell in one of the three types of shape animation in ME'scope. During Sine Dwell animation, the displayed shape is animated by multiplying it by sine wave values. Single Reference Test: A Single Reference test uses a single fixed exciter or a single fixed response transducer during the test. If the exciter is fixed, the roving DOFs of response transducer define the components of the ODS's or mode shapes obtained from the measurements. If a fixed response transducer is used, the DOFs of the roving exciter define the components of the ODS's or mode shapes. A Single Reference test is equivalent to measuring one row or one column of the FRF matrix in the MIMO model of the structure. Single-channel Measurement: A Single Channel Measurement is calculated using data acquired from a single acquisition channel. Examples are a Fourier spectrum or an Auto spectrum. If multiple channels are simultaneously acquired,

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Reference Volume IIB - Options then their Fourier spectra can be curve fit, and valid mode shapes extracted from them. Auto spectra can also be curve fit, but the resulting mode shapes will not have correct phases since the Auto spectra have no phases. SPL: SPL is an acronym for Sound Pressure Level. An SPL is a measure of the RMS sound pressure relative to a reference value. It is measured in logarithmic units of decibels (dB) above a standard reference level. A common reference level used is 20 ÎźPa RMS, which is considered the threshold of human hearing. Stability Diagram: A Stabiliy Diagram is created by pressing the Stability button on the Stability curve fitting tab. It is a graph of modal frequency & damping estimates for multiple curve fitting model sizes, from 1 to a Max. Model Size. All estimates that lie within user-specified tolerance limits are grouped into Stable Pole Groups. When the Save Stable Groups button is pressed on the Stability tab, the average value of the poles in each Stable Group is added to the Modal Parameters spreadsheet. Stationary Dwell: Stationary Dwell is one of the three types of shape animation in a Structure window. During stationary dwell animation, each shape is displayed without any animation. Stationary Dwell is most often used together with color contours for displaying acoustic shapes. Structure file: A Structure file contains the drawing Objects used to define a 3D model of a machine, structure, or acoustic surface. The structure model is used for displaying structural shapes in animation. Points, Lines & Surfaces are used for drawing 3D structure models and Acoustic Surfaces. FEA Objects can also be added between Points on the model. FEA Objects are used by the SDM, Experimental FEA, and FEA Model Updating commands in ME'scope. Structure Model: A Structure Model is used for displaying operating deflection shapes (ODS's), mode shapes, acoustic shapes or engineering data shapes in animation. A "stick model" consists of multiple Points connected by Lines. A "surface model" has triangular or quad surfaces added between Points. A "texture model" has textures defined for its surfaces. A "photo realistic model" has digital photographs attached to its surfaces. SubStructure: A SubStructure is a collection of Points, Lines, Surfaces, and FE Objects. SubStructures can be selected, moved, cut, copied & pasted like any other Object. SubStructure properties are displayed in the SubStructures spreadsheet. The Drawing Assistant is used to add SubStructures from the SubStructure Library to a model drawing. The FEA Assistant is used to add FEA Objects to SubStructures. SubStructure Library: The SubStructure Library is a special Project file containing predefined structure models. The Drawing Assistant is used to add SubStructures from the Library to a structure drawing. Any structure model can be saving into the Library by executing File | Save In Library in its Structure window. Surface Quad: A Surface Quad is a Drawing Object that defines a surface between four Points on a structure model. Surfaces are used for hidden line display, surface fills, surface textures, photo realistic models, and contour displays.

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Glossary Surface Quad properties are displayed in the Objects spreadsheet by executing Edit | Object Type | Surface Quads. Surface Triangle: A Surface Triangle is a Drawing Object that defines a surface between three Points on a structure model. Surfaces are used for hidden line display, surface fills, surface textures, photo realistic models, and contour displays. Surface Triangle properties are displayed in the Objects spreadsheet by executing Edit | Object Type | Surface Triangles. Sweep Animation: Sweep Animation is one of the three types of shape animation in a Structure window. During Sweep animation from a Data Block or Acquisition window, the cursor is moved through the Traces from left to right, and the data at each cursor position is displayed as a shape on the model. During Sweep animation from a Shape Table, each shape is displayed in succession using Dwell Animation and the number of dwell cycles from the Animation tab in the File | Shape Table Options box.

T Tool Tip: A Tool Tip is a brief description of each button (or Tool) on a Toolbar. If Help | Show Tool Tips is enabled, a Tool Tip will be displayed when the mouse pointer is hovered on a button. Trace: A Trace is one of the measurement functions displayed in a Data Block or Acquisition window. Each Trace has a unique measurement number (M#) associated with it, which is listed in the first column of the Traces spreadsheet. These M#s are used in the Animation equations on a structure model to display shapes directly from the cursor position in the Trace data. Trace Matrix: A Trace Matrix is a Data Block where each Trace Roving DOF designates the row, and each Reference DOF designates the column of the Trace in a matrix of Traces. Trace matrices can be manipulated using matrix algebra commands in ME'scope.. Transfer Function: A Transfer function is a cross-channel frequency domain measurement between an Output waveform and an Input waveform. A Transfer function is defined as the ratio (Output Fourier spectrum / Input Fourier spectrum). An FRF is a special case of a Transfer Function where the Input is a force, and the Output is caused by the force. Translational Data: Translational data is one of the kinds of shape data that can be displayed in animation on a structure modal. Examples of Translational data are vibration and acoustic intensity. Each Translational measurement has a direction associated with it. Measurement directions are defined by the Measurement Axes at each Point on the structure model. Up to three Translational measurements can be defined at each Point on a model. Transmissibility: Transmissibility is a cross-channel frequency domain measurement typically made from operating or output-only data. Transmissibility is defined as the ratio (Output Fourier spectrum / Input Fourier spectrum). Operating mode

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Reference Volume IIB - Options shapes can be obtained by saving the cursor values at a resonant frequency in a set of Transmissibility's. A set of Cross spectra can be obtained by multiplying a set of Transmissibility's by a reference Auto spectrum.

U UFF: UFF is an acronym for Universal File Format. UFF is a disk file format used for exchanging data between different structural testing & analysis systems. Structure models (Points & Lines), mode shapes, ODS's, and time or frequency domain measurements can be imported & exported using UFF files. Typical UFF file name extensions are .UFF, .UNV and .ASC. UMM Mode Shapes: UMM Mode Shapes is a set of mode shapes that have been scaled to Unit Modal Masses. A set of UMM mode shapes is called a modal model, and it also preserves the dynamic properties of a structure. UMM mode shapes are used for SDM, FRF Synthesis, MIMO modeling & simulation, and FEA Modal Updating in ME'scope.

Z Zoom: Zooming enlarges the display of the model in a Structure window, or the Trace graphics in a Data Block or Acquisition window. A Zoom is initiated by executing Display | Zoom, or by clicking in the graphics area and spinning the mouse wheel.

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Index A

Modal Peaks Function ...................... 120

Acoustic Surface ...................... 177, 182

N

B

Notch Window .............................. 70, 77

Band Pass window ............................. 77

O

C

ODS FRF ........................................... 84

CMIF ........................................ 120, 121

ODS Order Track ............................... 88

Comparison ...................... 119, 121, 132

P

Complex Exponential ....................... 136

Paste .................................................. 64

Complexity Plot ........................ 140, 144

R

D

Residue .............................................. 98

Damping 98, 99, 106, 108, 117, 136, 187

S

DOF Generator ................................ 156

Shape

E

Mode Shape ........................... 98, 134

Exponential Window ........................... 77

Operating Deflection Shape ............ 84

F

Sound Power .................... 174, 177, 178

FEA Object ............... 184, 186, 201, 213

Source Ranking ........................ 178, 180

FFT............................................... 73, 75

SPL .................................................. 174

FRF .......................... 119, 121, 132, 155

Stability Diagram .............................. 136

I

Surface Area .................................... 177

Intensity .................................... 175, 177

T

M

Trace Matrix ....................................... 44

Magnitude Ranking .................. 141, 146

Traces spreadsheet.................. 156, 178

Mass-stiffness-damping ........... 108, 143

Transmissibility ................................. 155

MIMO ....................................... 155, 156

U

MMIF ........................................ 120, 121

UFF .................................................... 63

Modal Frequency ............... 98, 108, 117

Unit Modal Mass .............. 121, 129, 132

Modal Parameters Spreadsheet ....... 119

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