ME’scopeVES Tutorial Manual Volume IB – Options

(February 2014)

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Table of Contents Tutorial #6 - Signal Processing ....................................................................................... 1 The FFT and DFT............................................................................................................ 1 1. Sampled Time Domain Waveform ........................................................................... 1 2. Digital Fourier Transform (DFT) ............................................................................... 1 3. Shannon's (Nyquist) Sampling Criterion .................................................................. 1 Fundamental Sampling Rule ....................................................................................... 1 Sampling Rate and Frequency Resolution .................................................................. 1 Anti-Aliasing Filter ........................................................................................................ 2 Frequency Spectra .......................................................................................................... 2 Fourier spectrum.......................................................................................................... 2 Auto spectrum ............................................................................................................. 2 Cross spectrum............................................................................................................ 2 Power Spectral Density (PSD) ..................................................................................... 2 Energy Spectral Density (ESD) ................................................................................... 3 Time Domain Windows ................................................................................................... 3 Non-Periodic Signals ................................................................................................... 3 Time Domain Windowing to Reduce Leakage ............................................................. 3 Hanning Window for Broad Band Signals .................................................................... 3 Flat Top Window for Narrow Band Signals .................................................................. 4 Exponential Window for Transient Response Signals ................................................. 4 Rectangular Window for Periodic Signals .................................................................... 5 Spectrum Averaging ........................................................................................................ 5 Number of Averages .................................................................................................... 6 Overlap Processing ..................................................................................................... 6 Linear Averaging.......................................................................................................... 7 Peak Hold Averaging ................................................................................................... 7 Fourier Spectrum of a Sinusoidal Signal ......................................................................... 7 One Sided versus Two Sided FFT ............................................................................... 8 Calculating the Fourier Spectrum ................................................................................ 8 Spectrum Averaging .................................................................................................... 8 Overlap Processing ..................................................................................................... 9

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Tutorial Volume IB - Options Time Domain Window.................................................................................................. 9 Auto Spectrum of a Sinusoidal Signal ........................................................................... 10 Calculating the Auto Spectrum .................................................................................. 10 Spectrum Averaging .................................................................................................. 11 PSD of a Sinusoidal Signal ........................................................................................... 12 Calculating the PSD................................................................................................... 12 Periodic Signals ............................................................................................................ 14 What is an ODS FRF?................................................................................................... 16 Advantages of ODS FRFs ......................................................................................... 17 ODS FRFs from Auto & Cross Spectra ......................................................................... 17 Illustrative Example.................................................................................................... 17 Measurement Sets..................................................................................................... 17 Checking the DOFs ................................................................................................... 18 Calculate ODS FRFs ..................................................................................................... 19 Overlaying the Reference Auto Spectra ........................................................................ 20 Scaling ODS FRFs ........................................................................................................ 21 Scaling Method .......................................................................................................... 21 ODS Animation ............................................................................................................. 22 Deleting Duplicate ODS FRFs ................................................................................... 22 ODS Animation .......................................................................................................... 23 Displaying Operating Mode Shapes .......................................................................... 23 Tutorial #7 - Basic Modal Analysis ................................................................................ 25 Modal Analysis Options ................................................................................................. 25 ODS Analysis Versus Modal Analysis ....................................................................... 25 What is FRF Curve Fitting? ........................................................................................... 25 Curve Fitting Steps .................................................................................................... 25 Curve Fitting Guidelines ................................................................................................ 25 1. Overlay the FRFs................................................................................................... 25 2. Inspect the Impulse Response Functions (IRFs) ................................................... 26 3. Use the Mode Indicator.......................................................................................... 26 4. Use the Band cursor .............................................................................................. 26 5. Verify Fundamental Mode Shapes......................................................................... 26 6. Compare Results from Different Curve Fitting Methods ........................................ 27 iv

Table of Contents Illustrative Example ....................................................................................................... 27 Splitter Bars ............................................................................................................... 27 Deleting All Fit Data....................................................................................................... 28 1. Counting Modal Peaks .............................................................................................. 28 Count Peaks Button ................................................................................................... 28 2. Estimating Frequency & Damping ............................................................................. 29 Fitting One FRF ......................................................................................................... 29 Frequency Lines ........................................................................................................ 30 Half Power Point Damping......................................................................................... 30 Global Fitting All FRFs ............................................................................................... 31 Frequency & Damping Terminology .............................................................................. 32 3. Estimating Residues.................................................................................................. 33 Fit Function ................................................................................................................ 34 Using the Band Cursor .............................................................................................. 34 Quick Fit ........................................................................................................................ 35 Saving Shapes .............................................................................................................. 36 Terminating Curve Fitting .............................................................................................. 37 Animating the Mode Shapes ......................................................................................... 37 Tutorial #8 - Multi-Reference Modal Analysis ................................................................ 39 When Is Multi-Reference Modal Analysis Necessary? .................................................. 39 Single Reference versus Multi-Reference FRFs ........................................................ 39 Mult-Reference Modal Test ........................................................................................... 39 Multiple Shaker Test .................................................................................................. 39 Multiple Reference Roving Impact Test ..................................................................... 40 Illustrative Example ....................................................................................................... 40 Multi-Reference Curve Fitting ........................................................................................ 42 Multi-Reference Mode Indicator ................................................................................. 42 Quick Fit .................................................................................................................... 43 First Bending and First Torsional Mode......................................................................... 44 Using the Stability Diagram ........................................................................................... 45 Comparing Mode Shapes .......................................................................................... 46 Tutorial #9 - Operational Modal Analysis (OMA) ........................................................... 49 OMA Simulation ............................................................................................................ 49 v

Tutorial Volume IB - Options Acquiring Cross Spectra................................................................................................ 51 Acquiring Data ........................................................................................................... 51 Curve Fitting Cross Spectra .......................................................................................... 52 DeConvolution Window ............................................................................................. 53 Curve Fitting .............................................................................................................. 53 Fit Functions .............................................................................................................. 54 Saving The Mode Shapes ......................................................................................... 54 Comparing Mode Shapes.............................................................................................. 55 Summary of OMA Round Trip ....................................................................................... 55 Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation ......................... 57 What is a MIMO (Multi-Input Multi-Output) Model? ....................................................... 57 Definitions .................................................................................................................. 57 Transfer Function ................................................................................................... 57 Frequency Response Function (FRF) .................................................................... 57 Transmissibility....................................................................................................... 57 MIMO Calculations .................................................................................................... 57 Frequency Response Functions (FRFs)........................................................................ 58 Experimental Modal Analysis ..................................................................................... 58 Measuring Rows & Columns of the FRF Matrix ......................................................... 58 Mult-Reference Modal Test ........................................................................................... 58 Multiple Shaker Test .................................................................................................. 58 Multiple Reference Roving Impact Test ..................................................................... 59 Illustrative Example ....................................................................................................... 59 Using Time Waveforms ............................................................................................. 59 Editing the Force and Response Trace Properties .................................................... 60 Calculating MIMO FRFs ................................................................................................ 61 Hanning Window........................................................................................................ 62 Removing Measurement Sets ................................................................................... 63 Displaying FRFs and Coherences Together ................................................................. 64 Deleting Duplicate Traces .......................................................................................... 65 Multiple Coherence ................................................................................................ 65 FRFs ...................................................................................................................... 65 Partial Coherence .................................................................................................. 66 vi

Table of Contents 2 FRFs, 1 Multiple Coherence, 2 Partial Coherences ................................................ 66 Animating Shapes from Multiple Reference FRFs ........................................................ 67 Creating Measured Equations (Assigning M#'s) ........................................................ 67 Creating Interpolated Equations ................................................................................ 68 Displaying ODS's ....................................................................................................... 68 Selecting a Reference ............................................................................................... 68 Multiple Reference FRFs Verify Single Modes .......................................................... 69 MIMO Outputs (Forced Response) ............................................................................... 69 Sinusoidal ODS using Mode Shapes ............................................................................ 70 Simultaneous Excitation Forces ................................................................................ 70 In-Phase Forces ........................................................................................................ 70 Out-of-Phase Forces ................................................................................................. 71 Sinusoidal ODS using FRFs .......................................................................................... 72 Synthesizing FRFs..................................................................................................... 72 In-Phase Forces ........................................................................................................ 73 Out-of-Phase Forces ................................................................................................. 74 Forced Response using Time Waveforms .................................................................... 74 Synthesized Sinusoidal Forces .................................................................................. 75 Using a Modal Model ................................................................................................. 76 Animating the In-Phase Forced Response ................................................................ 76 Out-of-Phase Response ............................................................................................ 78 Tutorial #11 - Acoustics ................................................................................................. 79 Creating an Acoustic Surface ........................................................................................ 79 Rectangular Surface .................................................................................................. 79 Tutorial #12 - Direct Data Acquisition ............................................................................ 81 Using the Acquisition Window ....................................................................................... 81 Illustrative Example ....................................................................................................... 81 Creating a Plate Model .............................................................................................. 82 Acquiring Data from a Data Block ................................................................................. 83 Applying a Hanning Window ...................................................................................... 85 Calculating FRFs and Coherence ................................................................................. 86 Overlap Processing ................................................................................................... 86 Displaying the Results ............................................................................................... 87 vii

Tutorial Volume IB - Options Leakage Effects on Random Data ............................................................................. 87 Larger Block Size Reduces Leakage ......................................................................... 87 Saving Measurement Set [1] ......................................................................................... 88 Acquiring Measurement Set [2] ..................................................................................... 89 Saving Measurement Set [2] FRFs ............................................................................ 89 ODS Animation ............................................................................................................. 89 Tutorial #13 - Structural Dynamics Modification (SDM) ................................................. 91 Modeling Structural Changes ........................................................................................ 91 FEA Objects .................................................................................................................. 91 FEA Mass .................................................................................................................. 91 FEA Spring & FEA Damper ....................................................................................... 92 FEA Rod .................................................................................................................... 92 FEA Bar ..................................................................................................................... 92 FEA Triangle & FEA Quad Plate ............................................................................... 92 Plate Stiffness Multiplier ......................................................................................... 93 FEA Tetra, FEA Prism & FEA Brick ........................................................................... 93 Adding FEA Objects to a Structure Model ..................................................................... 94 Adding An FEA Object ............................................................................................... 94 Illustrative Example.................................................................................................... 94 Changing Engineering Units ...................................................................................... 95 Calculating New Modes................................................................................................. 96 Animating the New Mode Shapes ................................................................................. 97 Truncated Modal Model ............................................................................................. 98 Modal Sensitivity ........................................................................................................... 98 Illustrative Example.................................................................................................... 99 Target Frequency ...................................................................................................... 99 Solution Scroll Bar ................................................................................................... 100 Unrealistic Solutions ................................................................................................ 101 Saving a Solution ..................................................................................................... 101 Mode Shape Comparison ........................................................................................ 101 Adding a Tuned Absorber ........................................................................................... 102 Illustrative Example.................................................................................................. 102 Tutorial #14 - Experimental Finite Element Analysis (FEA) ......................................... 105 viii

Table of Contents Experimental FEA ....................................................................................................... 105 FEA Prior to a Modal Test ....................................................................................... 105 Spatial Aliasing ........................................................................................................ 105 Creating an FEA Model ............................................................................................... 106 Creating a 2D Profile ............................................................................................... 106 Creating a SubStructure for Extruding the Profile .................................................... 108 Changing Engineering Units .................................................................................... 109 Adding FEA Quads to the Surface Model.................................................................... 109 Meshing the FEA Quads.......................................................................................... 110 Solving for the FEA Modes.......................................................................................... 111 Comparing FEA & EMA Mode Shapes........................................................................ 113 Creating Animation Equations ................................................................................. 113 Out-of-Phase Animation .......................................................................................... 115 Shape Normalization ............................................................................................... 115 Mode Shape MAC Values ........................................................................................... 115 MAC Rules .............................................................................................................. 115 Matching DOFs ........................................................................................................ 115 MAC Bar Chart ........................................................................................................ 116 MAC Comparison in Z Direction Only ...................................................................... 116 Point Matching Example.............................................................................................. 117 Comparing Mode Shapes ........................................................................................ 118 Aligning the FEA & EMA Models ................................................................................. 119 Creating Two SubStructures.................................................................................... 120 Aligning the SubStructures ...................................................................................... 120 Using the Point Matching Command ........................................................................... 121 Creating Animation Equations ................................................................................. 122 Comparing Shapes .................................................................................................. 122 MAC Bar Chart ........................................................................................................ 123 Tutorial #15 - FEA Model Updating ............................................................................. 125 Targeted FEA Model Updating .................................................................................... 125 Illustrative Example ..................................................................................................... 125 Comparing Shapes .................................................................................................. 125 Preparing for FEA Model Updating ............................................................................. 126 ix

Tutorial Volume IB - Options 1. Delete the FEA Rigid Body Shapes ..................................................................... 126 2. Add an EMA Shape ............................................................................................. 127 3. Select FEA Quads on the Vertical Plate .............................................................. 127 4. Check the Engineering Units ............................................................................... 128 Calculating Solutions ................................................................................................... 129 Upper Spreadsheet.................................................................................................. 129 Error Function .......................................................................................................... 129 Lower Spreadsheet.................................................................................................. 130 Solution Space ........................................................................................................ 130 Calculate Model Updating Solutions ........................................................................ 130 Calculating Updated FEA Modes ................................................................................ 131 Solution Scroll Bar ................................................................................................... 131 Graphics Display...................................................................................................... 131 Frequency Bar Chart ............................................................................................... 132 MAC Bar Chart ........................................................................................................ 132 Lower Bar Charts ..................................................................................................... 132 Calculating Modes of the Updated Model ................................................................ 132 Glossary ...................................................................................................................... 135 Index ........................................................................................................................... 149

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Tutorial #6 - Signal Processing 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.

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

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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) •

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

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

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

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.

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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

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Tutorial Volume IB - Options 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.

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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.

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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.

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

Frequency Spectra Several types of frequency spectra can be calculated in ME'scope. Fourier spectrum •

Calculated by averaging together multiple DFT's of a time domain signal.

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The FFT algorithm is used to calculate the DFT of a time domain signal.

Auto spectrum •

Calculated by averaging together multiple Auto spectrum estimates.

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

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The DFT is complex valued, having Real & Imaginary parts, or Magnitude & Phase.

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An Auto spectrum is real valued, having Magnitude only.

Cross spectrum •

Calculated by averaging together multiple Cross spectrum estimates.

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

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The Cross spectrum is complex valued, having Real & Imaginary parts, or Magnitude & Phase.

Power Spectral Density (PSD) •

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A PSD is an Auto spectrum divided by the frequency resolution of the Auto Spectrum.

Tutorial #6 - Signal Processing •

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

Energy Spectral Density (ESD) •

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

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

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ESD's are used to characterize transient signals.

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.

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

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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.

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

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Tutorial Volume IB - Options

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.

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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.

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

Tutorial #6 - Signal Processing

Exponential Window. Rectangular Window for Periodic Signals •

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

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

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

Rectangular Window.

Spectrum Averaging Spectrum averaging is used to, •

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

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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. 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.

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Tutorial Volume IB - Options 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 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.

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Tutorial #6 - Signal Processing 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))

Fourier Spectrum of a Sinusoidal Signal To illustrate the calculation of a Fourier Spectrum, a new Data Block file with a single Trace containing a sinusoidal signal will be created as the time domain signal source. •

Execute File | Project | New in the ME'scopeVES window to start a new Project.

This clears all ME'scopeVES data from the computer memory and displays an empty Work Area. •

Execute File | New | Data Block in the ME'scopeVES window.

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Click on the Sinusoidal Tab in the dialog box, and enter the parameters as shown below.

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Click on OK.

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Tutorial Volume IB - Options Synthesize Time Traces Dialog Box. A new Data Block window will open showing one Trace with 20,000 samples of sinusoidal data over a time period of 50 seconds. This signal has a frequency span (0 to 200 Hz), and contains three sine waves (20, 30 & 50 Hz) with magnitude = 1 & phase = 0. •

Click on the Trace and spin the mouse wheel to display the signal more clearly.

New Data Block Showing Zoomed Display of Sinusoidal Signal. One Sided versus Two Sided FFT The One Sided FFT assigns all of the energy in the time domain signal to the positive frequencies of the spectrum (the part that is displayed). The Two Sided FFT assigns half of the energy to the positive frequencies and half to the negative frequencies in the spectrum. The One Sided FFT yields spectrum values that are twice as large as the values of the Two Sided FFT. •

Right click on the Traces spreadsheet, and select Show/Hide Columns from the menu.

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The File | Options box will open.

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Check the FFT column to display it, and click on OK.

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Choose One Sided in the FFT column on the Traces Spreadsheet.

Calculating the Fourier Spectrum •

Execute Transform | Spectra in its Data Block window.

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Choose Fourier Spectrum from the drop-down list in the dialog box that opens.

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Click on the Calculate button.

Spectrum Averaging Notice that the Spectrum Block Size = 10000 samples. This is half the number of samples of the time domain Trace. Since the FFT requires 20000 time domain samples to calculate a DFT with 10000 samples in it, no spectrum averaging can be done with the Spectrum Block Size = 10000.

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Tutorial #6 - Signal Processing •

Enter Spectrum Block Size = 1000 into the Spectrum Averaging dialog box.

Notice that the Number of Averages = 10, and that the Percent Overlap = 0%. This is the number of averages that can be calculated using 20000 samples of time domain data without any overlap processing. Overlap Processing •

Click on the Up Arrow one more time so that Number of Averages = 11.

Notice that Percent Overlap = 10%. This means that 10 percent of the time domain samples will be used over again in each successive sampling window to calculate 11 DFT's and average them together. Time Domain Window Normally, sinusoidal time domain data is not necessarily periodic in each sampling window. When it is not periodic, leakage will occur in the Fourier Spectrum. Therefore, to preserve the magnitudes of the three sine waves in the Fourier Spectrum, a Flat Top window should be applied to each sampling window before the FFT is applied. •

Choose the Flat Top Time Domain Window in the Spectrum Averaging dialog box as shown below.

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Click on OK.

Spectrum Averaging Dialog Box. A new Data Block window will open showing the calculated Fourier Spectrum. •

Execute Display | Cursors | Peak Cursor

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Execute Display | Cursors | Cursor Values to display the Peak cursor value.

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Click & drag the Peak cursor to enclose one of the peaks, as shown below.

to display the Peak cursor.

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Tutorial Volume IB - Options

Fourier Spectrum Showing Three Sinusoidal Peaks with Magnitude 1. Notice that the three sine wave peaks appear at their respective frequencies, and that their magnitudes are all "1". Notice also that the sine wave peaks have some "width" to them. This is caused by the Flat Top window, which preserves peak magnitudes, but increases the peak widths.

Auto Spectrum of a Sinusoidal Signal The same sinusoidal signal that was used to calculate the Fourier Spectrum will also be used to calculate an Auto Spectrum. •

The sinusoidal signal shown below contains 20000 samples of data over a time period of 50 seconds, with a frequency span (0 to 200 Hz).

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The signal contains three sine waves (20, 30 & 50 Hz), all of magnitude = 1 and phase = 0.

Data Block Showing Zoomed Display of Sinusoidal Signal. Calculating the Auto Spectrum •

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Execute Transform | Spectra in either Data Block window.

Tutorial #6 - Signal Processing •

Choose the Data Block with the Sinusoidal Waveform in it as the source file in the dialog box that opens.

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Choose Auto Spectrum from the drop-down list.

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Click on the Calculate button.

Spectrum Averaging •

Enter a Spectrum Block Size = 1000 into the Spectrum Averaging dialog box.

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Press the Up Arrow until Number of Averages = 11.

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Choose the Flat Top Time Domain Window, as shown below.

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Press the OK button.

A dialog box will open allowing you to select another frequency domain Data Block into which to save the Auto Spectrum. •

Select the Data Block with the Fourier Spectrum in it.

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Press the Add To button to add the Auto Spectrum to the Fourier Spectrum Data Block.

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Execute Format | Strip Chart and select "2" from the drop-down list.

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Tutorial Volume IB - Options Fourier spectrum and Auto spectrum in Strip Chart Format. Notice that the three sine wave peaks have magnitudes of "1". Notice also that the units of the Auto Spectrum are (g^2). This is a power (mean squared) quantity. Notice also that the units of the Fourier Spectrum are (g). This is a linear (RMS) quantity. •

Execute Format | Overlay Traces.

It is now clear that the Auto spectrum (power) is different from the Fourier Spectrum (linear).

Fourier & Auto spectra Overlaid.

PSD of a Sinusoidal Signal The same sinusoidal signal that was used to calculate the Fourier Spectrum and Auto Spectrum will also be used to calculate a PSD. •

The sinusoidal signal shown below contains 20000 samples of data over a time period of 50 seconds, with a frequency span (0 to 200 Hz).

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The signal contains three sine waves (20, 30 & 50 Hz), all of magnitude = 1 and phase = 0.

Data Block Showing Zoomed Display of Sinusoidal Signal. Calculating the PSD

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Tutorial #6 - Signal Processing •

Execute Transform | Spectra.

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Select the Sinusoidal Signal Data Block as the source file in the dialog box that opens.

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Choose Power Spectral Density from the drop-down list.

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Click on the Calculate button.

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Enter a Spectrum Block Size = 1000 into the Spectrum Averaging dialog box.

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Press the Up Arrow until Number of Averages = 11.

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Select Flat Top in the Time Domain Window list.

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Press the OK button.

A dialog box will open allowing you to select another frequency domain Data Block into which to save the Auto Spectrum. •

Select the Data Block with the Fourier Spectrum in it.

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Press the Add To button to add the PSD to the Data Block contain the Fourier and Auto spectra.

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Execute Format | Strip Chart and select "3" from the drop-down list.

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Tutorial Volume IB - Options

Fourier spectrum, Auto spectrum, and PSD in Strip Chart Format. Notice also that the units of the PSD are (g^2/Hz). This is a power (mean squared) quantity. •

Right click on the Traces spreadsheet and execute Show/Hide Columns from the menu.

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Check Window, Window Correction, and Window Value in the File | Options box, and click on OK.

Notice that the PSD Window Correction is set to Wide Band. Wide Band spectra are "normalized" (divided) by their Window Value. •

Change the PSD Window Correction to Narrow Band.

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Click on Yes in the dialog box that opens.

The original sine wave magnitudes were 1 g. The Fourier Spectrum peaks are 1 g, and the Auto spectrum peaks are 1 g^2. A PSD is the Auto spectrum "normalized" (divided) by the frequency resolution (df) of the spectrum. •

Execute File | Properties in the Data Block with the spectra in it.

Notice that the Frequency Resolution is 0.2 Hz. Therefore, the PSD peaks should be 5 (g^2/Hz), which is confirmed in the cursor values box on the Trace graphics.

Periodic Signals The three sinusoidal waveforms that were used to calculate the Fourier spectrum, Auto spectrum, and PSD are all in fact periodic in the sampling window that was used.

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Tutorial #6 - Signal Processing

Data Block Showing Zoomed Display of Sinusoidal Signal.

Sinusoidal Waveform Properties. â€˘

Execute File | Properties in the time domain window with the three sinusoidal signals n it to open its Properties dialog box.

In the previous sections, three spectra were calculated using, Spectrum Block Size = 1000 samples. Number of Averages = 11. Overlap processing = 10%. Each sampling window contained 2000 samples over a time period of T = 5 seconds. Assuming that the time waveform was not periodic in the sampling window, a Flat Top window was applied to the time

15

Tutorial Volume IB - Options waveforms in order to obtain accurate magnitudes in each spectral estimate, . However, the sinusoidal signal is periodic in the sampling window. •

The three sine waves complete exactly 100 (20 Hz), 150 (30 Hz), and 250 (50Hz) cycles in 5 seconds,

•

With overlap processing, the next sampling window starts after 10 (20 Hz), 15 (30 Hz), and 25 (50Hz) cycles of the sine have completed.

Since the sinusoidal signal is periodic in each sampling window, no leakage will occur in the calculated spectra.

Fourier spectrum, Auto spectrum, PSD of a Periodic Signal Using a Rectangular Window. •

Repeat the steps of the previous sections to calculate a Fourier spectrum, Auto spectrum, and PSD, but use a Rectangular window instead of a Flat Top window.

Notice that each spectrum at 20, 30 & 50 Hz are only one sample wide. Each spectrum is leakage free because the sine wave is periodic in each sampling window.

What is an ODS FRF? An ODS FRF is complex valued function of frequency that has magnitude & phase, like an FRF. An ODS FRF is created by combining the Auto spectrum of the roving response with the phase of the Cross spectrum between the roving response and a (fixed) reference response.

16

Tutorial #6 - Signal Processing

An ODS FRF. Advantages of ODS FRFs •

An ODS FRF is a true measure of the response of a machine or structure at each frequency.

•

An ODS FRF contains peaks at resonant frequencies.

•

A set of ODS FRFs can be used to obtain operating deflection shapes.

•

A set of ODS FRFs can be used to obtain operating mode shapes.

The ODS FRF provides the response (in displacement, velocity or acceleration units) at each DOF, together with the phase relative to a Reference response. A set of ODS FRF cursor values displayed in animation is the actual magnitude of the response at each DOF, with the correct phase relative to all other DOFs. When DeConvolution windowing is applied to a set of ODS FRFs, operating mode shapes can be obtained using FRF-based curve fitting.

ODS FRFs from Auto & Cross Spectra ODS FRFs can be calculated from time domain waveforms, or from Auto & Cross spectra. The source Traces can be stored either in one Data Block, or in two different Data Blocks. If the Trace DOFs also contain Measurement Set numbers, then each Measurement Set is processed independently of the others. Illustrative Example •

Open the Tutorial #6 - Z24 Bridge ODS FRFs.VTprj Project from the My Documents\ME'scopeVES\Tutorials folder.

This data was taken by impacting a bridge, but the impact forces were not measured. Three reference acceleration responses were measured together with 75 unique roving accelerometer responses. Because there weren't enough acquisition channels to simultaneously acquire all of the Roving responses, they were acquired in 9 separate Measurement Sets. Measurement Sets

17

Tutorial Volume IB - Options This Project file contains 9 Data Block files (BLK: APSs XPSs [1] to BLK: APSs XPSs [9]). Each Data Block file contains a separate Measurement Set of Auto & Cross Spectrum data. Each Measurement Set contains the following; •

Auto spectra for unique Roving responses.

•

Auto spectra of the three Reference responses.

•

Cross spectra between all Roving response and the three Reference responses.

To calculate ODS FRFs, Each Trace must be designated as either an Input or an Output, •

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

•

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

•

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

Checking the DOFs •

Open the BLK: APSs XPSs [1] window.

•

Drag the vertical blue splitter bar to the left to display the Traces spreadsheet, as shown below.

APSs XPSs [1].BLK Graphics & Trace Properties Spreadsheet. There are 63 Traces in this Data Block. •

Auto spectra for 3 Reference responses(1Z, -2Y & 2Z) are designated as Inputs in the Input Output column.

•

Auto spectra for 15 Roving responses, are designated as Outputs in the Input Output column.

•

45 Cross spectra (15 roving DOFs x 3 reference DOFs), are designated as Cross in the Input Output column.

Each Data Block (BLK: APSs XPSs [2] through BLK: APSs XPSs [9]) also contains Auto & Cross spectra,

18

•

Auto spectra for the same 3 Reference DOFs (1Z, -2Y & 2Z).

•

Auto spectra for unique Roving DOFs.

Tutorial #6 - Signal Processing •

Cross spectra between for each Roving and Reference DOF pair.

Calculate ODS FRFs In order to calculate ODS FRFs, all of the Auto & Cross spectra from the 9 Measurement Sets will be put into a single Data Block. •

Open the Data Block BLK: APSs XPSs [1] window.

•

Execute Edit | Paste Traces from File.

•

Select file BLK: APSs XPSs [2] in the dialog that opens, and click on Paste.

•

Repeat the above two steps to Paste the Traces from files BLK: APSs XPSs [3] through BLK: APSs XPSs [9] into the BLK: APSs XPSs [1] file.

Paste Traces from File Dialog Box. When completed, the BLK: APSs XPSs [1] window should contain 423 Traces from 9 Measurement Sets. To calculate ODS FRFs from the Auto & Cross spectra in BLK: APSs XPSs [1], •

Execute Transform | ODS FRFs. A dialog box will open, as shown below.

Transform | ODS FRFs Dialog Box. •

Select BLK: APSs XPSs [1] in both lists.

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Tutorial Volume IB - Options •

Check Auto Spectra in the Include section of the dialog box.

•

Click on the Calculate button.

When the ODS FRFs have been created, the File selection dialog box will open. •

Click on the New File button.

•

Enter "Bridge ODS FRFs" into the box and click on OK.

Notice that there are 423 Traces in the new Data Block; 297 ODS FRFs and 126 Auto spectra.

New Data Block Window Containing ODS FRFs & Auto Spectra.

Overlaying the Reference Auto Spectra In this example, one set of ODS FRFs for the entire Bridge structure was calculated from 9 independently acquired Measurement Sets of Auto & Cross spectra. Each Measurement Set was acquired while the Bridge was impacted, but the impact force level was not controlled. Therefore, the bridge response levels are most probably different for each Measurement Set. Whether or not the response levels are different can be determined by overlaying the Reference Auto spectra from all 9 Measurement Sets. •

Execute Edit | Sort Traces | By in the Data Block BLK: APSs XPSs [1] window.

•

Choose Input Output from the Sort Traces By drop down list in the dialog box that opens.

•

Click on Input in the Select From list to move it to the Sort Using list.

•

Press the Sort button followed by the Close button.

Now, 27 selected Auto spectrum Traces for Reference (Input) DOFs 1Z, -2Y & 2Z are displayed at the top of the Traces spreadsheet. •

Select the first 9 Traces (with DOFs 1Z[1] through 1Z[9]) in the Traces spreadsheet, as shown below.

•

Execute Format | Overlay Selected Traces.

It is clear for the overlaid Auto spectra that the excitation levels were different during the acquisition of the 9 Measurement Sets.

20

Tutorial #6 - Signal Processing

Overlaid Auto Spectra for Reference DOF 1Z. in 9 Measurement Sets.

Scaling ODS FRFs In a previous step, we saw from the overlaid Auto spectra for Reference DOF 1Z, that the response levels were different for the 9 Measurement Sets. In order to display ODS's from a this set of ODS FRFs, they must be re-scaled to account for the difference in the force levels, and hence the response levels, between all Measurement Sets. Scaling Method Each ODS FRF is re-scaled by first calculating an average Reference Auto spectrum for all Measurement Sets. Then, each ODS FRF is re-scaled by multiplying it by the average Reference Auto spectrum and divided it by the Reference Auto spectrum for its own Measurement Set. (See Transform | Scale ODS FRFs in the Signal Processing Commands section for details.) â€˘

Display the Band cursor, and drag the band to enclose the frequencies (4 to 12 Hz), as shown below.

NOTE: If the Line, Peak or Band cursor is displayed, re-scaling is done using only the data at the cursor or in the cursor band. Otherwise, all of the Trace data is used.

21

Tutorial Volume IB - Options

Reference Response 1Z Auto Spectrum With Band Cursor at (4 to 12 Hz). •

Execute Transform | Scale ODS FRFs.

When the scaling has been completed, the File selection box will open. •

Click on the New File button, enter "Scaled ODS FRFs" into the next dialog box, and click on OK.

ODS Animation ODS's can be displayed in animation directly from a Data Block of ODS FRFs. If an ODS is animated using data at or near a resonance peak, the ODS closely approximates an operating mode shape. Deleting Duplicate ODS FRFs Because three References were used, duplicate ODS FRFs were calculated from the 9 measurement Sets. Before ODS's can be displayed from the ODS FRFs, the duplicate ODS FRFs must be deleted from the Scaled ODS FRFs Data Block. •

Execute Edit | Sort Traces | By in the Scaled ODS FRFs Data Block window.

•

Choose "DOF" from the Sort Traces By drop down list.

•

Check Select All to move all of the DOFs from the Select From list to the Sort Using list.

•

Press the Sort button followed by the Close button.

Traces (M#1 to M#81) in the Traces spreadsheet contain only 9 unique ODS FRFs. The rest are duplicates which must be deleted.

22

•

Un-select all Traces.

•

Select M#1.

•

Scroll to M#81, hold down the Shift key, and click on M#81 to select all Traces from M#1 to M#81.

•

Scroll through the selected Traces and un-select 9 Traces with unique DOFs; (1Z:1Z, 1Z:-2Y, 1Z:2Z, -2Y:1Z, -2Y:-2Y, -2Y:2Z, 2Z:1Z, 2Z:-2Y, 2Z:2Z).

Tutorial #6 - Signal Processing NOTE: Measurement Set numbers are only required for calculating ODS FRFs. Once the ODS FRFs are calculated, Measurement Set numbers can be ignored. •

Execute Edit | Delete Selected Traces.

The Data Block should now contain 225 ODS FRF Traces, 75 Roving DOFs, each paired with three Reference DOFs. ODS Animation •

Open the STR: Z24 Bridge file.

•

Select "BLK: Scaled ODS FRFs" in the Animation Source list on the Toolbar.

•

Execute Draw | Animation Equations | Create Measured (Assign M#s).

•

Click on OK in each of the dialog boxes than open.

•

Execute Draw | Animation Equations | Create Interpolated.

•

Click on OK in each of the dialog boxes than open.

•

Execute Draw | Animate Shapes

in the Structure window.

A dialog box will open, informing you that the Animation source contains multiple References. •

Click on Yes.

Shapes can only be displayed in animation from one reference at a time. Shapes are displayed by selecting Traces by reference DOF (1Z, -2Y, or 2Z). The Trace Selection box will open which allows you to select Traces by choosing one of the reference DOFs. •

Choose reference DOF 1Z and click on Select.

Displaying Operating Mode Shapes •

Execute Format | Overlay Selected Traces.

•

Press the Real part button

•

Turn ON the Peak cursor and surround the peaks at 4.83 Hz in the Data Block window.

•

Select Traces from one of the other reference DOFs -2Y or 2Z.

to overlay the Real parts of the selected ODS FRFs.

Notice that the shape is the same no matter which Reference is selected. This is evidence of a resonance, or in this case an operating mode shape.

23

Tutorial Volume IB - Options

Animating an Operating Mode Shape at a Resonance.

24

Tutorial #7 - Basic Modal Analysis Modal Analysis Options NOTE: The commands in this chapter can only be executed if the VES-4000 Basic Modal Analysis option is enabled in your software. Check the Help | About box to verify authorization of this option. There are three Modal Analysis options in ME'scopeVES, each one building on the capabilities of the previous option, •

VES-4000 Basic Modal Analysis

•

VES-4550 Multi-Reference Modal Analysis

•

VES-4750 Operational Modal Analysis

ODS Analysis Versus Modal Analysis Modal analysis is used to characterize resonant vibration in machinery & structures. If a noise or vibration problem is due to the excitation of a structural resonance, then the structure either has to be isolated from the excitation source, or physically modified to reduce the level of vibration. •

ODS analysis shows how a machine or structure is vibrating, and where excessive vibration levels occur for various Points & directions.

•

Modal analysis indicates whether or not the excessive vibration is due to a structural resonance.

•

ODS's & mode shapes can be compared in ME'scopeVES to determine how a resonance is contributing to the overall vibration level occurring in a machine or structure.

What is FRF Curve Fitting? •

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.

•

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.

Curve Fitting Guidelines 1. Overlay the FRFs

25

Tutorial Volume IB - Options 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.

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.

26

Tutorial #7 - Basic Modal Analysis •

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.

Illustrative Example •

Open the Jim Beam.VTprj Project from the My Documents\ME'scopeVES\Demos folder.

•

Execute Modes | Modal Parameters

in the BLK: FRFs Data Block window.

When curve fitting is initiated, the following changes take place in the Data Block window; •

The Traces are displayed in the upper left corner.

•

The Mode Indicator is displayed in the lower left corner.

•

The Curve Fit menu is enabled, and a Curve Fitting Toolbar, (containing frequently used commands), is displayed in the Toolbar area.

•

The Curve Fit panel is displayed on the right side of the Data Block window.

The Curve Fit panel contains Curve Fitting tabs and the Modal Parameters spreadsheet. •

The Curve Fitting tabs contain controls for setting up and executing the curve fitting steps.

•

The Modal Parameters spreadsheet is for viewing and editing the modal parameter estimates extracted from the FRFs.

Modal parameter estimation is done in several steps, using the controls on the Curve Fitting tabs.

Data Block Showing Curve Fitting Panel. Splitter Bars

27

Tutorial Volume IB - Options During curve fitting, two additional splitter bars are displayed in the Data Block window. •

A vertical red splitter bar separates the Curve Fit panel from the Trace and Mode Indicator graphs.

•

A horizontal blue splitter bar separates the Trace and Mode Indicator graphs.

The size of the Curve Fit panel can be changed by dragging the red splitter bar horizontally, and the size of either graph can be changed by dragging the horizontal blue splitter bar vertically.

Deleting All Fit Data •

Execute Curve Fit | Delete All Fit Data

, and click on Yes in the dialog box that opens.

1. Counting Modal Peaks The first step of modal parameter estimation is to determine how many modes are represented by resonance peaks in a frequency band in the FRFs. NOTE: Each peak in an FRF is evidence of at least one mode. •

Scroll through the Traces by dragging the vertical scroll bar to the right of the Traces display.

There are two ways to determine the number of modes represented by peaks in the FRFs; 1. Overlay all of the Traces, visually inspect them for resonance peaks, and enter the number of peaks into the Modes box on the Mode Indicator tab. 2. Press the Count Peaks button on the Mode Indicator tab of the Curve Fit panel. Count Peaks Button The Count Peaks button on the Mode Indicator tab of the Curve Fit panel is used to count the resonance peaks in a set of FRFs. •

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 curve. The Real Part, Imaginary Part, or Magnitude of all (or selected) Traces of FRF data is used to calculate the Mode Indicator.

•

Press the OK button to calculate the Mode Indicator and count its peaks.

After the Mode Indicator has been calculated and its peaks counted, a graph of the Mode Indicator is displayed on the lower left in the window.

28

Tutorial #7 - Basic Modal Analysis •

The peaks above the noise threshold (horizontal line) on the Mode Indicator graph are counted.

•

Each modal peak is indicated with a red dot on the Mode Indicator.

•

The Modes box on the Mode Indicator tab contains the number of peaks counted.

Mode Indicator Showing 10 Resonance Peaks.

2. Estimating Frequency & Damping In many cases (especially with noisy data), it is better to build up a list of modal frequencies & damping by curve fitting in small cursor bands using as few modes as possible. In this example, since the FRFs are relatively noise free, frequency & damping for all 10 modes will be estimated at once. Fitting One FRF Notice that Global Polynomial method is chosen on the Frequency & Damping tab. •

Global curve fitting is done on all (or selected) Traces.

•

Local curve fitting is done on each Trace.

To estimate frequency & damping by curve fitting only the first Trace, •

Drag the vertical blue scroll bar (next to the Trace graph) to its top most position to display the first Trace.

•

Hold down the Ctrl key, and click on the Trace to select it.

Notice that a green background is displayed on the selected Trace. •

Press the Frequency & Damping button.

•

Click on No, and then Yes in the dialog boxes that open.

Frequency & damping estimates for 10 modes will be listed in the modal parameters spreadsheet, as shown below.

29

Tutorial Volume IB - Options

Frequency & Damping Curve Fit of One Trace. Frequency Lines The frequency estimate for each mode in the modal parameters spreadsheet is displayed as a vertical line on the Mode Indicator graph. The damping estimate for each mode is displayed as a horizontal line crossing the vertical frequency line where,

Width of the Damping Line = 2σ, σ = half power point (or 3 dB point) damping (in Hz) Half Power Point Damping The half power point damping (2σ) is approximately equal to the width of the resonance peak at 70.7 %

of the FRF peak magnitude value. Or, the half power point damping (2σ) is approximately equal to the width of the resonance peak at half (50%) of the FRF peak magnitude squared. The FRF magnitude squared is considered a power quantity. •

30

Execute Display | Zoom below.

and zoom the display around several resonance peaks, as shown

Tutorial #7 - Basic Modal Analysis

Zoomed Display of Frequency & Damping Estimates. Global Fitting All FRFs More accurate frequency & damping estimates are usually obtained by doing a Global curve fit on all (or several selected) FRFs. •

Execute Curve Fit | Delete SELECTED Modes modal parameters spreadsheet.

•

Hold down the Ctrl key and click on the selected Trace to un-select it.

•

Make sure that the Global method is selected on the Frequency & Damping tab.

•

Press the Frequency & Damping button.

•

Click on Yes in the dialog box that opens.

to delete the selected modes from the

New frequency & damping estimates are now added to the modal parameter spreadsheet. Notice that the Global estimates of modes 4, 5 & 6 are quite different than the estimates obtained by curve fitting only one FRF.

31

Tutorial Volume IB - Options

Global Frequency & Damping Estimates from 99 FRFs.

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)

32

Tutorial #7 - Basic Modal Analysis

Decay Constant

Loss Factor Quality Factor

3. Estimating Residues After modal frequencies & damping have been estimated, modal residues (mode shape components) are estimated during a second curve fitting step. •

Execute Display | mooZ to restore the full Trace display.

•

Press the Residues button on the Residues & Save Shapes tab.

•

Click on Yes in the dialog box that opens.

Residues Dialog Box. Estimates of residue magnitude & phase for all 10 modes and each FRF Trace are added to the modal parameter spreadsheet. •

Scroll through the Traces and release the mouse button to list the residues for the Trace being displayed.

33

Tutorial Volume IB - Options

Residue Curve Fit of 10 Modes and 99 FRFs. Fit Function After the frequency, damping, & residue have been estimated, a red Fit Function is also overlaid on each Trace, as shown above. •

The Fit Function is calculated using the modal parameter estimates.

•

If the modal parameters are accurate, then the Fit Function will lie on top of the FRF data.

Using the Band Cursor If the Band Cursor is displayed, curve fitting is done using data from within the cursor band It is often more convenient to curve fit using several cursor bands to avoid noise or non-resonance peaks in the FRFs. •

Execute Curve Fit | Clear Fit Function, and click on Yes in the dialog box.

•

Execute Display | Cursors | Band Cursor 10 resonance peaks, as shown below.

•

Press the Residues button again, and click on Yes in the dialog box.

and drag the edges of the band to enclose the

Notice that the red Fit Function is only displayed over the cursor band because only that data was used for curve fitting. The residue estimates will also be slightly different when residue curve fitting is done in cursor bands instead of using all of the FRF data.

34

Tutorial #7 - Basic Modal Analysis

Residue Curve Fitting in a Cursor Band.

Quick Fit When Curve Fit | Quick Fit is executed, the three curve fitting steps are carried out automatically; 1. If there is no Mode Indicator, a new Mode Indicator is calculated using the current method on the Mode Indicator tab, and its peaks above the noise threshold line are counted 2. Frequency & damping are estimated for the number of peaks counted, using the current curve fitting method on the Frequency & Damping tab. 3. A Residue is estimated for each mode in the modal parameters spreadsheet, using the current curve fitting method on the Residues tab. To use Quick Fit on the 99 Jim Beam FRFs, •

Execute Display | Cursors | Band Cursor to turn Off the Band cursor display.

•

Execute Curve Fit | Clear All Fit Data

•

Execute Curve Fit | Quick Fit

•

The Quick Fit results will be displayed, as shown below.

, and click on Yes in the dialog box that opens.

.

35

Tutorial Volume IB - Options

Quick Fit Results.

Saving Shapes The final step of curve fitting is to save the modal parameters into a Shape Table file. •

Press the Save Shapes button on the Residues & Save Shapes tab.

•

Press the New File button in the dialog box that opens to create a new Shape Table.

•

Enter "My Mode Shapes" into the next dialog box that opens, and click on OK.

The Shape Table window will open, listing the mode shapes of the 10 modes of the Jim Beam obtained from the Quick Fit.

36

Tutorial #7 - Basic Modal Analysis

Shape Table Showing 10 Mode Shapes.

Terminating Curve Fitting Curve fitting is complete when mode shapes have been saved into a Shape Table. To terminate curve fitting, •

Execute Curve Fit | Close

•

Or, execute Modes | Modal Parameters

. again.

NOTE: All curve fitting data is saved in the Data Block file. When the Project file is saved on disk, all curve fitting data is also saved.

Animating the Mode Shapes •

If the STR: Colored Jim Beam file is not open, open it from the Project Panel.

•

Close all other windows except the SHP: My Mode Shapes window.

•

Execute Window | Arrange Windows | For Animation

in the ME'scopeVES window.

NOTE: When Window | Arrange Windows | For Animation is executed, the active window retains its size and all other windows are arranged with it in the Work Area. •

Execute Draw | Animate Shapes in the STR: Colored Jim Beam window, or Tools | Animate Shapes in the SHP: My Mode Shapes window.

•

Press each of the Select Shape buttons in the Shape Table window to display each mode shape in animation.

37

Tutorial Volume IB - Options

Animating a Shape from "My Mode Shapes".

38

Tutorial #8 - Multi-Reference Modal Analysis 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.

•

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.

39

Tutorial Volume IB - Options •

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. 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. •

This test is the same as performing two or more single Reference modal tests, but is much faster.

•

The FRFs are elements from two or more rows of the FRF matrix in a MIMO model of the structure.

Illustrative Example In this example, the FRF data from a multi-reference roving impact test of a rectangular PVC plate will be curve fit to extract the experimental modal parameters of two closed coupled modes.

40

•

Open App Note #15 - Closely Coupled Modes.VTprj Project from the My Documents\ME'scopeVES\Application Notes folder.

•

Execute Draw | Animate Shapes in the STR: PVC plate window.

•

Click on OK in the dialog box that opens.

•

Execute Animate | Contours | Node Lines in the STR: PVC plate window.

•

Execute Display | Imaginary

•

Display the Peak cursor and surround the peaks at 187 Hz, as shown below.

and Format | Overlaid in the BLK: PVC plate window.

Tutorial #8 - Multi-Reference Modal Analysis

Animation from Reference 7Z. â€˘

Select reference 15Z.

Notice that the ODS changes as you select reference 7Z and then 15Z. This is a clear indication that the resonance peak at 187 Hz does not represent a single mode shape. NOTE: Mode shapes are independent of the reference used to obtain the FRF data. Therefore, the animated ODS at a resonance peak (an approximation of a mode shape) will not change if it is displayed from references of FRF data.

41

Tutorial Volume IB - Options

Animation from Reference 15Z. •

Drag the Peak cursor band to surround the peaks at 431 Hz.

•

Select reference 7Z and then reference 15Z.

Notice that the mode shape does not change when displayed from a different reference. This verifies that the 431 Hz peak represents a valid mode shape.

Multi-Reference Curve Fitting •

Execute Modes | Modal Parameters in the BLK: PVC plate window to initiate curve fitting.

•

Click on Yes in the dialog box that opens to un-select all Traces.

•

Execute Curve Fit | Delete All Fit Data

•

Turn Off the Peak cursor display.

•

Execute Format | Rows Columns, and Display | Bode

, and click on Yes.

.

Multi-Reference Mode Indicator With the Multi-Reference Modal Analysis option, the Multi-Reference CMIF (Complex Mode Indicator Function) and the Multi-Reference MMIF (Multivariate Mode Indicator Function) are added to the Mode Indicator methods. NOTE: A peak at or near the same frequency in two or more Multi-Reference Indicator curves indicates closely coupled modes or repeated roots.

42

Tutorial #8 - Multi-Reference Modal Analysis •

On the Mode Indicator tab, select the Multi-Reference CMIF method and press the Count Peaks button.

•

Scroll the Noise Threshold line upward until 7 peaks (7 modes) are counted on the two Mode Indicator curves, as shown below.

Multi-Reference CMIFs Showing 7 Resonance Peaks. Quick Fit NOTE: When a multi-reference Mode Indicator is selected, then a multi-reference Frequency & Damping and a multi-reference Residues curve fitting method is automatically chosen on each of their respective tabs. The Quick Fit command automatically executes commands on the Mode Indicator, Frequency & Damping, and Residues & Save Shapes tabs to complete the curve fitting process in one step. •

Execute Curve Fit | Quick Fit

.

The parameters for 7 modes are estimated by Quick Fit, and the modal parameters and Fit Functions are displayed as shown below. Notice that there are two closely coupled modes at 187 Hz and 189 Hz.

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Tutorial Volume IB - Options

Quick Fit Results For 7 Modes.

First Bending and First Torsional Mode In a previous section, ODS's were displayed from BLK: PVC plate Data Block for two different References (7Z & 15Z) revealed that the resonance peak at 189 Hz was not dominated by a single mode shape. Displaying shapes from any other resonance peak in BLK: PVC plate Data Block showed no change in the ODS between different references, indicating the presence of a single mode. MultiReference curve fitting was then performed on the FRF data in the BLK: PVC plate Data Block and modal parameters for two closely coupled modes (187 Hz & 189 Hz were extracted. •

Press the Save Shapes button on the Residues & Save Shapes tab.

•

Press the New File button in the dialog box that opens, enter "Quick Fit" into the next dialog box, and click on OK.

•

Execute Draw | Animate Shapes in the STR: PVC plate window.

•

Select SHP: Quick Fit in the Animation Source box on the STR: PVC plate window Toolbar.

Of the two closely coupled modes, the 187 Hz mode is the expected first bending mode, and the 189 Hz mode is the expected first torsional mode of the PVC plate.

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Tutorial #8 - Multi-Reference Modal Analysis

187 Hz First Bending Mode.

189 Hz First Torsional Mode.

Using the Stability Diagram As an alternative to counting peaks on multiple Mode Indicator curves, the Stability diagram can be used to extract closely coupled modes from FRF data.

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Tutorial Volume IB - Options •

Execute Modes | Modal Parameters in the BLK: PVC plate window to initiate curve fitting.

•

Execute Curve Fit | Delete All Fit Data data.

•

On the Stability tab, make sure that the Multi-Reference AF Polynomial method is selected.

•

Press the Stability button.

, and click on Yes to delete previous curve fitting

The Stability diagram is displayed on the Mode Indicator plot, as shown below. Poles (frequency & damping) estimates of curve fitting solutions from solutions for 1 mode up to 50 modes are displayed on the Stability diagram. Each Stable Group of poles has the same color, with the colors alternating between adjacent Stable Groups. NOTE: Each stable group of poles is colored using one of the top two Contour Colors in the File | Options box of Data Block window.

Stability Diagram. •

Press the Save Groups button on the Stable Groups tab.

•

Double click on the Select Mode column to un-select all modes.

•

Select the first two modes in the Modal Parameters spreadsheet.

•

Execute Curve Fit | Delete Selected Modes, and click on Yes in the dialog box to delete the first two modes.

Since Residues are already estimated with the AF Polynomial method, the Residue curve fitting step is not necessary. •

Press the Save Shapes button on the Residues & Save Shapes tab.

•

Press the New File button in the dialog box that opens, enter "Stability" into the next dialog box, and click on OK.

Comparing Mode Shapes A convenient way to numerically compare two mode shapes is to use the MAC calculation. •

46

Execute Display | MAC in the SHP: Stability window.

Tutorial #8 - Multi-Reference Modal Analysis â€˘

Choose SHP: Quick Fit in the dialog box that opens, and click on OK.

The MAC window will open showing a Bar Chart of the MAC values between each of the mode shape pairs in the SHP: Stability and SHP: Quick Fit files, as shown below.

MAC Values Window. â€˘

Position the mouse pointer on each vertical bar to display the MAC value between a pair of mode shapes.

All of the MAC values greater than "0.98", indicating that the mode shapes obtained with the Quick Fit method are essentially the same as those obtained from the Stability diagram.

47

Tutorial #9 - Operational Modal Analysis (OMA) OMA Simulation To simulate an OMA, a "round trip" will be performed using the modal model in the Jim Beam Demo Project file. The following steps will be carried out; 1. The MIMO Simulator in the Acquisition window will be used to simulate the excitation of the Jim Beam structure with a random force. 2. The acceleration responses of the Jim Beam due to the random excitation will then be "acquired" from the MIMO simulator using the Acquisition window. 3. Cross spectra between all responses and a (fixed) Reference response will be calculated. 4. The output-only Cross spectra will be curve fit to extract operating mode shapes. 5. The operating mode shapes will be compared with the mode shapes of the original modal model by displayed MAC values between each mode shape pair.

Connecting to the MIMO Simulator. •

Open the Jim Beam.VTprj Project from the MyDocuments/ME'scopeVES/Demos folder.

•

Execute File | New | Acquisition in the ME'scopeVES window.

•

Select Use MIMO Simulator in the dialog box that opens.

•

Select SHP: Mode Shapes in the next dialog box that opens.

The SHP: Mode Shapes file contains a modal model of the Jim Beam structure. The Acquisition window will be setup to excite the MIMO model with Burst Random excitation, •

On the Sources tab, make Source 1 active in the spreadsheet.

•

Select 5Z from the drop down list in the DOF column.

•

Make sure the Signal Type is Random, and the Burst Width is 60%, as shown below.

NOTE: Burst random excitation is used to insure that the Cross spectra calculated from the output signals of the MIMO Simulator are leakage-free.

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Tutorial Volume IB - Options

Acquisition Window Setup For Burst Random Excitation. •

•

On the Measurement tab. •

Select Time in the Domain section.

•

Check Time and un-check everything else in the Calculate section.

•

Set the Averages to "1" in the Averaging section.

On the Sampling tab •

•

•

Select 2045 for the Number of Samples in the Time section.

On the Channels spreadsheet •

In the Channels column, make channel 100 (the force channel) not active.

•

Click on the Units tab.

•

Double click on the Units column heading, and select (g) from the list in the dialog box

Execute Acquire | Front End Scope

.

Responses for 99 DOFs of the Jim Beam MIMO model due to burst random excitation applied at DOF 5Z are input to the Acquisition window from the MIMO Simulator, acting as a multi-channel acquisition front end. •

Scroll through the upper Traces to observe the accelerometer responses (MIMO outputs) displayed on Traces 1 through 99.

•

Scroll through the lower Traces in the window to observe the 99 accelerometer responses (MIMO Outputs).

NOTE: The lower Traces are the same as the upper Traces because Time was checked in the Calculate section on the Measurement tab, and Averages was set to "1".

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Tutorial #9 - Operational Modal Analysis (OMA) •

Execute Acquire | Stop (F6)

to terminate the Front End Scope acquisition.

Acquisition Showing Burst Random Output From The MIMO Simulator.

Acquiring Cross Spectra The Acquisition window will be changed to calculate 99 Cross spectra between each of the acquired accelerometer channels (MIMO outputs) and a single Reference channel (one of the MIMO outputs). •

•

•

On the Measurement tab, •

Select Frequency in the Domain section.

•

Check Cross Spectrum and un-check everything else in the Calculate section.

•

Enter 50 into the Averages box.

On the Channels spreadsheet, •

Make sure that Channel 100 in still in-active.

•

Channel 100 is the random force channel, which will not be acquired.

On the DOFs tab of the Channels spreadsheet, •

In the Input Output column, select Both in the drop down list for channel 45 (DOF 15Z).

NOTE: Channel 45 (DOF 15Z) is now designated as both a roving (Output) channel and a reference (Input) channel, Acquiring Data

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Tutorial Volume IB - Options The Acquisition window is now set up to acquire 99 channels of acceleration response data and calculate Cross spectra between each channel and the reference response channel 45 (DOF 15Z). •

Execute Acquire | Start (F5)

•

Click on OK in the dialog box that opens, to add no noise to the outputs.

.

50 Averages of Cross Spectra From 99 MIMO Simulator Responses. Acquisition of signals from the MIMO Simulator will continue until 50 estimates of Cross spectra have been calculated and averaged together using Linear averaging. The progress of data acquisition is indicated by the message "Average XX of 50", which is displayed on the Toolbar. When acquisition of the 50 estimates of the Cross spectra has completed, the message "Front End Ready" will be displayed on the Toolbar. •

Click on the lower Traces to make them active.

•

Execute Acquire | Save Traces (F9), and save the Cross spectra into a new Data Block file.

Curve Fitting Cross Spectra In the previous sections, 99 Cross spectra were calculated from 99 channels of acceleration data acquired from the MIMO Simulator.

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Tutorial #9 - Operational Modal Analysis (OMA)

Data Block of 99 Acceleration Cross Spectra. DeConvolution Window The 99 Cross spectra will now be curve fit to extract the 10 modes of the original modal model of the Jim Beam that was used by the MIMO Simulator. •

Execute Modes | Modal Parameters open,

to begin curve fitting. The following dialog box will

DeConvolution Reminder Dialog. The message in the dialog box says that a DeConvolution window must be applied to the Cross spectra before they can be curve fit. This window converts the Cross spectra to a form which can be curve fit using an FRF-based curve fitting method. •

Click on Yes to apply the DeConvolution window to the Cross spectra.

Curve Fitting •

Press the Stability button on the Stability tab.

When the calculation has completed, a Stability diagram containing pole estimates obtained from curve fitting model sizes from 1 to 50 is displayed on the Mode Indicator graph. •

On the Stable Groups tab, scroll the slider upward to increase the Min. No. of Stable Poles, and only 10 stable pole groups are displayed, as shown below.

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Tutorial Volume IB - Options

Stability Diagram Showing10 Stable Pole Groups. Fit Functions •

Press the Save Groups button on the Stable Groups tab.

•

Press the Residues button on the Residues & Save Shapes tab, and click on OK in the dialog that opens.

•

Scroll through the Traces to examine the red Fit Functions overlaid on the Cross spectra.

Fit Functions Overlaid on the Cross Spectra. Saving The Mode Shapes

54

Tutorial #9 - Operational Modal Analysis (OMA) •

Press the Save Shapes button on the Residues & Save Shapes tab.

•

Press the New file button in the dialog box that opens, enter "OMA Modes" into the next dialog that opens, and click on OK to save the modes a new Shape Table file.

Comparing Mode Shapes The final step of the "round trip" is to compare the OMA mode shapes with the original Jim Beam mode shapes that were used by the MIMO Simulator. The Modal Assurance Criterion (MAC) will be used to numerically compare mode shape pairs. •

Execute Display | MAC in the SHP: OMA Modes file.

•

Select the SHP: Mode Shapes Shape Table in the dialog box that opens.

•

Hover the mouse pointer over each vertical bar to display its MAC value.

It is clear from the MAC bar chart that all of the mode shape pairs have MAC values greater than 0.90, indicating that acquiring output-only data and curve fitting it can recover the modal parameters of a structure.

MAC Values Between Original Jim Beam and OMA Mode Shapes.

Summary of OMA Round Trip A modal model of the Jim Beam structure was used in a MIMO Simulator to simulate the acceleration response of the beam to a burst random excitation force. •

The burst random force was applied at DOF 5Z of the beam structure.

•

99 channels of acceleration response data were acquired from the MIMO Simulator in an Acquisition window.

•

99 Cross spectra were calculated in the Acquisition window between 99 Roving response DOFs and a Reference response at DOF 15Z.

•

The DeConvolution window was applied to the Cross spectra prior to curve fitting them using an FRF-based curve fitting method.

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Tutorial Volume IB - Options

56

â€˘

A Stability Diagram were used to obtain stable pole groups for the 10 modes.

â€˘

MAC values of mode shape pairs between the OMA modes and the original modal model were calculated and displayed in a 3D bar chart to verify the accuracy of the OMA mode shapes.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation What is a MIMO (Multi-Input Multi-Output) Model? NOTE: The commands in this chapter can only be executed if the VES-3550 MIMO Modeling & Simulation option is enabled in your software. Check the Help | About box to verify authorization of this option. Calculation of Transfer Functions, Outputs, and Inputs are all based upon use of a MIMO (Multi-Input Multi-Output) model of the dynamics of a structure. A MIMO model is a frequency domain model where 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 expressed with the equation:

{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). NOTE: Rows of the Transfer Function matrix correspond to Outputs, and columns correspond to Inputs. Each Input and Output corresponds to a measurement DOF (point & direction). Each Transfer Function is a Cross-channel function between two DOFs, an Input DOF and an Output DOF. Definitions Transfer Function •

A Transfer Function is defined as the Fourier spectrum of an Output divided by the Fourier spectrum of an Input.

Frequency Response Function (FRF) •

An FRF is defined as the Fourier spectrum of a displacement, velocity, or acceleration response (Output) divided by the Fourier spectrum of the excitation force (Input) that caused the response.

Transmissibility •

A Transmissibility is defined as the Fourier spectrum of an Output divided by the Fourier spectrum of an Input with the same units.

NOTE: An FRF and Transmissibility are special cases of a Transfer Function. MIMO Calculations

57

Tutorial Volume IB - Options Any one of the components of the MIMO model, (Inputs, Outputs, or Transfer Functions) can be calculated from the other two components using commands in the Transform | MIMO menu. •

Inputs and Outputs can be either time or frequency domain Traces.

•

Transfer Functions can be either experimentally derived or synthesized from modal parameters.

The MIMO model is also used to calculate and display in animation a sinusoidal ODS due to multiple sinusoidal excitation forces at the same frequency. (See the Transform | MIMO | Sinusoidal ODS command description for details.)

Frequency Response Functions (FRFs) Each FRF in a MIMO model defines the dynamic properties between a pair of DOFs of a structure, an Excitation DOF and a Response DOF. An FRF is defined as,

FRF = (Fourier spectrum of a response / Fourier spectrum of an excitation force) The Excitation force is typically measured with a load cell. Response motion is typically measured with an acceleration, velocity, or displacement transducer. Experimental Modal Analysis In an EMA, FRF measurements are usually made under controlled conditions where the test article is artificially excited using a broadband excitation signal. •

An impactor that applies a broad band impulsive force to the test article is commonly used for modal testing.

•

One or more shakers are attached to the test article and driven with broad band signals is also commonly used for modal testing.

Measuring Rows & Columns of the FRF Matrix An EMA requires that FRFs be measured from at least one row or column of the FRF matrix. •

If the Excitation is fixed and multiple Responses are measured, this corresponds to measuring elements from a single column of the FRF matrix.

•

If the Response is fixed and Excitation is provided at multiple DOFs (points & directions), this corresponds to measuring elements from a single row of the FRF matrix.

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.

58

•

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.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation •

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. 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. •

This test is the same as performing two or more single Reference modal tests, but is much faster.

•

The FRFs are elements from two or more rows of the FRF matrix in a MIMO model of the structure.

Illustrative Example FRFs can be calculated in two ways in ME'scopeVES, 1. From multiple Excitation force and response time waveforms. 2. From the Auto spectra of the forces, and the Cross spectra between all responses and the forces. Using Time Waveforms When FRFs are calculated from time waveforms, spectrum averaging is used to calculate estimates of the Cross spectra between all responses and excitation forces. During the calculation of these spectra, spectrum averaging using time domain windows, triggering & overlap processing is used. (See Spectrum Averaging in the Signal Processing chapter for more details.) To illustrate the calculation of FRFs using time domain waveforms, we will use the Data Block from the Z24 Bridge-2 Shaker.VTprj file. •

Open the Tutorial #10 - Z24 Bridge 2 Shaker.VTprj file from the My Documents\ME'scopeVES\Tutorials folder.

•

Open the BLK: Shaker Time Data file window.

This file contains 117 time domain Traces. Since all of the data could not be simultaneously acquired, it was taken in 9 Measurement Sets. •

All of the data in each Measurement Set was simultaneously acquired.

•

Each Measurement Set contains 2 Force signals for the same 2 reference (Input) DOFs (1Z & 2Z).

•

Each Measurement Set also contains the same 3 Roving response (Output) DOFs (1Z, -2Y & 2Z).

•

There are 72 unique Roving response DOFs, distributed among the 9 Measurement Sets.

A 2 Reference set of FRFs with 75 unique Roving response DOFs can be calculated from these Traces. The FRFs are calculated using MIMO processing, as depicted in the diagram below.

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Tutorial Volume IB - Options

Block Diagram for Multiple Reference FRF Calculation. Editing the Force and Response Trace Properties Notice that the Units column in the Traces spreadsheet in BLK: Shaker Time Data file is empty. NOTE: If transducer sensitivities and engineering units are not applied to the time domain Traces, the calculated FRFs will be un-calibrated, and the modal parameters extracted from them cannot be used for SDM or MIMO calculations since they will also be un-calibrated. •

Execute Edit | Sort Traces | Sort By in the BLK: Shaker Time Data window.

•

Select Input Output from the Sort By list in the dialog box that opens.

•

Select Inputs to place it in the Sort Using list on the right.

•

Press Sort to sort the Traces, followed by the Close button

Now, the Traces are ordered with the selected Input Traces as measurements M#1 to M#18, followed by the response Traces as measurements M#19 to M#117. •

Double click on the Units column header, and click on No in the dialog that opens.

•

Select (Lbf or N), whichever you prefer in the dialog box that opens, and click on OK.

The force Traces now have engineering units (Lbf or N), and are designated as Inputs to the MIMO model.

60

•

Right click on the Select column heading, and select Invert Selection from the menu.

•

Double click on the Units column header, and click on No in the dialog that opens.

•

Select (g) in the dialog box that opens, and click on OK.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation

BLK: Shaker Time Data Window Showing Engineering Units & MIMO Input Output Traces.

Calculating MIMO FRFs FRFs will be calculated using the multiple reference time domain Traces in the BLK: Shaker Time Data window. •

The bridge was excited simultaneously by 2 shakers.

•

The shakers were driven by un-correlated broad band random signals with frequency spectra over the span of (3 to 30 Hz).

•

The forces applied to the bridge and the acceleration responses due to the forces were simultaneously acquired in 9 Measurement Sets.

•

The Block Size of the Shaker Time Data.BLK file is 65536, (65536 samples per Trace).

•

The data was acquired at a 100 Hz sampling rate, (equivalent to a 0.01 second time increment between samples and a total time length of 655.35 seconds per Trace).

To verify these properties, •

Right click on the Trace graphics area and select Data Block Properties from the menu.

FRFs with a Block Size of 2000 samples will be calculated from this data. This means that only 4000 time domain samples are required per spectrum calculation, so spectrum averaging with overlap processing can be used. •

Double click on the Select column in the Traces spreadsheet in the BLK: Shaker Time Data window until all Traces are un-selected.

•

Execute Transform | Calculate | Transfer Functions. The following dialog box will open,

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Tutorial Volume IB - Options

•

Make sure that BLK: Shaker Time Data is chosen in both the {Outputs} and {Inputs} source lists, as shown above.

•

Check the Coherence box in the Include section.

•

Click on the Calculate button. The Spectrum Averaging box will open.

•

Make the following selections in the Spectrum Averaging dialog box, Spectrum Block Size = 2000 Number of Averages = 20 Averaging: Linear Time Domain Window: Hanning

Notice that the Percent Overlap = 19%. This means that with each successive block of 4000 time domain samples used to calculate a spectral estimate contains 19% of the samples that were used in the previous block of samples. Hanning Window

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Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation Because the Time Domain Window selection is Hanning, a Hanning window will be applied to each block of 4000 time domain samples before the FFT is applied to it. Use of the Hanning window is necessary to minimize the effects of leakage due to the non-periodicity of the random signals in each sampling window. (See Time Domain Windows in the Signal Processing Commands chapter for details.) •

Click on the OK button to calculate the FRFs & Coherences.

When the calculations are completed, a dialog box will open allowing you to save the results. •

Click on the New File button.

•

Enter "MIMO FRFs" into the dialog box, and click on OK.

The BLK: MIMO FRFs window will open displaying the calculated FRFs and Coherences.

MIMO FRFs and Coherences Removing Measurement Sets NOTE: Measurement Set numbers are only required for performing the FRF and Coherence calculations. To remove the Measurement Sets from the DOFs, •

Right click on the Traces spreadsheet and execute Select None to un-select all Traces

•

Double click on the DOFs column header in the Traces spreadsheet

•

Select Delete and check Measurement Set in the DOF Generator dialog box (as shown below), and click on OK

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Tutorial Volume IB - Options

Displaying FRFs and Coherences Together Notice (on the Title bar) that the new Data Block contains 495 Traces. •

198 FRFs (75 unique roving DOFs plus 24 duplicate roving DOFs times 2 reference DOFs)

•

198 Partial Coherences (75 unique roving DOFs plus 24 duplicate roving DOFs times 2 reference DOFs)

•

99 Multiple Coherences (75 unique roving DOFs plus 24 duplicate roving DOFs)

The FRFs and Coherences are mixed together, and need to be sorted by DOF.

64

•

Execute Edit | Sort Traces | Sort By

•

Choose Measurement Type from the Sort Traces By list in the dialog box.

•

Select FRF, Partial Coherence, Multiple Coherence to place them in the Sort Using list,as shown below

•

Press Sort to sort the Traces.

•

Choose Roving DOF from the Sort Traces By drop down list.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation •

Click on Select All to place all of the Roving DOFs in the Sort Using list on the right

•

Press Sort to sort the Traces, followed by the Close button

Notice that the first 18 M#s are nine duplicate copies of the same two FRFs with DOFs 1Z:1Z and 1Z:2Z. •

Select all 9 of the FRFs with DOFs 1Z:1Z

•

Execute Format | Overlay Traces to display the selected Traces.

The overlaid FRFs are displayed below. From this display it is clear that the nine FRFs for DOFs 1Z:1Z are duplicates on one another. Therefore, eight of the nine duplicate FRFs, as well as the Partial Coherences and Multiple Coherences, should be deleted.

Overlaid FRFs for DOFs 1Z:1Z. Deleting Duplicate Traces Multiple Coherence •

Execute Edit | Sort Traces | Sort By, and select Measurement Type from the Sort By list in the dialog box.

•

Select Multiple Coherence to place it in the Sort Using list on the right.

•

Check Renumber M#s

•

Press Sort to sort the Traces, followed by the Close button

•

Select Traces M#1 through M#27, and un-select only three of them (with DOFs 1Z, -2Y, 2Z)

FRFs •

Execute Edit | Sort Traces | Sort By, and select Measurement Type from the Sort By list in the dialog box.

•

Select FRF to place it in the Sort Using list on the right.

•

Check Renumber M#s

•

Press Sort to sort the Traces, followed by the Close button

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Tutorial Volume IB - Options •

Select Traces M#1 through M#54, and un-select only six of them (with DOFs 1Z:2Z, 1Z:1Z, 2Y:2Z, -2Y:1Z, 2Z:2Z, 2Z:1Z)

Partial Coherence •

Repeat the steps for deleting duplicate FRFs, but Sort By Partial Coherence instead, to delete the duplicate Partial Coherences (with DOFs 1Z:2Z, 1Z:1Z, -2Y:2Z, -2Y:1Z, 2Z:2Z, 2Z:1Z)

When all of the duplicate Traces have been deleted, the Data Block should contain 375 Traces, 5 Traces for each of 75 unique Roving DOFs. 2 FRFs, 1 Multiple Coherence, 2 Partial Coherences The Traces will be sorted again so that each group of 5 Traces consists of 2 FRFs (for both reference DOFs), followed by 1 Multiple Coherence, followed by 2 Partial Coherences (for both reference DOFs). •

Execute Edit | Sort Traces | Sort By, and select Measurement Type from the Sort By list in the dialog box

•

Select FRF, Multiple Coherence, Partial Coherence to place them in the Sort Using list

•

Press Sort to sort the Traces

•

Select Roving DOF from the Sort By list in the dialog box

•

Check Select All to place all Roving DOFs in the Sort Using list, as shown below

•

Press Sort to sort the Traces, followed by the Close button

•

Execute Format | Strip Chart and choose 5 from the drop down list.

In the figure below, it is clear that the shaker at 1Z contributes more to the response at Roving DOF 1Z than the shaker at 2Z. Not only does FRF 1Z:2Z have more noise in it than FRF !Z:!Z, but the Partial Coherences clearly indicate this. Each pair of Partial Coherences shows how the two shakers contribute to the overall response at each Roving DOF. The Multiple Coherence shows that the two shakers together caused most of the response at DOF 1Z in the frequency span (3 to 40Hz) frequency range. The rest of the response is caused by extraneous noise.

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•

Partial Coherence shows the percentage contribution (0 to 1) of each shaker (Input) to each response (Output).

•

Multiple Coherence shows the total contribution (0 to 1) of both Inputs to each Output.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation

MIMO FRF s and Coherences Displayed Together.

Animating Shapes from Multiple Reference FRFs A multiple reference set of FRFs is ideal for verifying that each resonance peak is evidence of a single mode of vibration. Since only the FRFs are needed for displaying shapes in animation, they will be copied to a separate Data Block. •

Execute Edit | Select Traces | Select By in the BLK: MIMO FRFs window.

•

Choose Measurement Type from the drop down list in the dialog box that opens, and select FRF from the selection list.

•

Press the Select button followed by the Close button

•

Execute Edit | Copy Traces to File

•

Press the New File button in the dialog box that opens.

•

Enter "Multi-Ref FRFs" into the dialog box, and click on OK.

The BLK: Multi-Ref FRFs window will open containing 150 FRFs; 75 roving DOFs paired with 2 reference DOFs (1Z & 2Z). Creating Measured Equations (Assigning M#'s) To animate shapes directly from the FRFs, an animation equation must be created for each Point & direction on the structure model where a response was actually measured. This is done by assigned each M# in BLK: Multi-Ref FRFs to a DOF on the Bridge model. •

Execute Tools | Create Animation Equations (Assign M#'s) in the BLK: Multi-Ref FRFs window.

•

Select STR: Z24 Bridge in the dialog box that opens.

•

Click on OK in the dialog boxes that open.

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Tutorial Volume IB - Options When the Measured animation equations (equations for Measured DOFs) have been created, the following dialog box will open. There are only 150 FRFs in the Multi-Ref FRFs Data Block so normally 150 Animations equations would be created to assign each FRF to a DOF of the structure. However, multiple Points on the railings of the bridge model where numbered with the same Point number. Therefore, a total of 218 Animation equations were created.

Creating Interpolated Equations Next, Animation equations must be created for all un-measured DOFs of the Bridge model. Otherwise, they won't move during shape animation. •

Execute Draw | Animation Equations | Create Interpolated in the STR: Z24 Bridge window.

•

Click on Yes and OK in the dialog boxes that open.

When the Interpolated animation equations have been created, the following dialog box will open.

Displaying ODS's •

Close all windows in ME'scope except BLK: Multi-Ref FRFs and STR: Z24 Bridge

•

Execute Window | Arrange Windows in the ME'scopeVES window.

•

Execute Draw | Animate Shapes

•

A dialog box will open saying that BLK: Multi-Ref FRFs has multiple references. Click on OK.

in the Structure window.

Selecting a Reference Next, the Edit | Select Traces | Select By dialog box will open where you must select Traces from one of the two references.

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•

Choose one of the references (1Z or 2Z) and click on the Select button.

•

Press the Imaginary part button

•

Execute Format | Overlaid.

•

Drag the (Line or Peak) cursor to a resonance peak to display the ODS at the resonance.

in the BLK: Multi-Ref FRFs window.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation Multiple Reference FRFs Verify Single Modes When an ODS is displayed on a structure model directly from multi-reference FRF data at a resonance peak, there are two possible outcomes; â€˘

Choose reference 1Z in the Edit | Select Traces | Select By dialog box, and click on the Select button

â€˘

Choose reference 2Z in the Edit | Select Traces | Select By dialog box, and click on the Select button

If the ODS does not change when a different reference is selected, this is evidence that the ODS is being dominated by a single mode shape.

ODS from Reference 1Z Using the Peak Cursor.

MIMO Outputs (Forced Response) The forced response of a structure due to multiple excitation forces can be calculated using MIMO Modeling & Simulation. The following block diagram depicts this process when forces are specified as time domain waveforms.

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MIMO Outputs Block Diagram Three different commands in ME'scopeVES can be used to calculate forced responses, 1. Tools | Sinusoidal ODS in a Shape Table window uses mode shapes to calculate ODS's due to multiple sinusoidal forces at a single frequency. 2. Transform | MIMO | Sinusoidal ODS in a Data Block window uses FRFs or mode shapes to calculate ODS's due to multiple sinusoidal forces at a single frequency. 3. Transform | MIMO | Outputs in a Data Block window uses FRFs or mode shapes, and a Data Block of time or frequency domain force Traces to calculate a Data Block of forced response Traces. Each of these methods is used to calculate forced responses in the following sections.

Sinusoidal ODS using Mode Shapes •

Open the Tutorial #10 - Sinusoidal ODS.VTprj Project from the My Documents\ME'scopeVES\Tutorials folder.

•

Open SHP: Mode Shapes from the Project Panel and display its mode shapes in animation.

This structure has a bending mode at 461 Hz and a torsional mode at 493 Hz. •

Display each of these two mode shapes in animation to verify them as the first bending and first torsional modes.

Simultaneous Excitation Forces Assume that the Jim Beam is excited simultaneously by two 500 Hz sinusoidal forces, one applied at Point 5 in the vertical direction (DOF 5Z) of the top plate, and the second force is applied at the Point 15 in the vertical direction (DOF 15Z) . Our intuition would say that the forced response ODS should be dominated by the torsional mode at 493 Hz, since it is closest to the excitation frequency. However, we will see that the mode shape determines which modes will be excited by the sinusoidal forces. In-Phase Forces To calculate the sinusoidal ODS due to two in-phase sinusoidal excitation forces at DOFs 5Z & 15Z, •

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Un-select all shapes in the SHP: Mode Shapes window.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation •

Execute Edit | Copy Shapes to File.

•

Click on the New File in the dialog box that opens, enter "Copy of Mode Shapes" in the next dialog box, and click on OK.

•

Execute Tools | Sinusoidal ODS in the SHP: Mode Shapes window.

•

Setup the Tools | Sinusoidal ODS dialog box as shown below.

•

Execute Draw | Compare Shapes in the STR: Colored Jim Beam window.

•

Select the 460 Hz shape in the SHP: Copy of Mode Shapes window.

In-Phase Forced Response at 500 Hz Excites Bending Mode. The MAC value between the sinusoidal ODS at 500 Hz (due to the two in-phase forces) and the 460 Hz mode is 0.84, indicating that the 460 Hz mode shape is being excited by the 500 Hz forces. •

Select the 493 Hz shape in the SHP: Copy of Mode Shapes window.

The MAC value between the sinusoidal ODS at 500 Hz and the 493 Hz mode is 0.10, indicating that the 493 Hz mode is not being excited by the 500 Hz forces, even though it is closer in frequency to the excitation frequency than the 460 Hz mode. Out-of-Phase Forces •

In the Tools | Sinusoidal ODS dialog box, change the Phase of the second force to 180 degrees.

•

Press the Animate Shape button.

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Out-of-Phase Forced Response at 500 Hz Excites Torsional Mode. Now, the MAC value between the sinusoidal ODS at 500 Hz (due to the two out-of-phase forces) and the 493 Hz mode is 0.99, indicating that the 493 Hz mode clearly dominates the response due to the 500 Hz forces.

Sinusoidal ODS using FRFs To illustrate the use of the Transform | Calculate | Sinusoidal ODS command in a Data Block window, •

Open the Jim Beam.VTprj file from the Demos fly out tab.

FRFs can be either measured (acquired experimentally) or synthesized from modal parameters. For this illustration, they will be synthesized from modal parameters. Synthesizing FRFs The modal parameters in the SHP: Mode Shapes file will be used to synthesize FRFs. Since we want to calculate the response due to two sinusoidal forces (applied at DOFs 5Z & 15Z of the Jim Beam structure), FRFs must be synthesized with reference DOFs 5Z & 15Z in order to calculate forced responses due to forces applied at these DOFs.

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•

Execute Tools | Synthesis FRFs in the SHP: Mode Shapes file window.

•

In the dialog box that opens, select the first Roving DOF, scroll to the bottom of the Roving DOF list, hold down the Shift key and select the last Roving DOF.

•

Hold down the Ctrl key, and select Reference DOFs 5Z & 15Z, as shown below.

Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation

Synthesize FRFs Dialog Box. •

Click on OK, select Displacement in the dialog that opens, and click on OK.

•

When the final dialog box opens, enter "5Z 15Z FRFs" as a file name, and click on OK.

A new Data Block window will open containing 198 FRF Traces with DOF pairs between 99 Roving DOFs and 2 Reference DOFs.

Synthesized FRFs For References 5Z & 15Z. In-Phase Forces To calculate the forced response ODS due to two in-phase sinusoidal excitation forces applied at DOFs 5Z & 15Z, •

Execute Transform | MIMO | Sinusoidal ODS in the BLK: 5Z 15Z FRFs window.

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Setup the dialog box as shown below, and press the Animate Shape button.

•

Execute Draw | Compare Shapes in the STR: Colored Jim Beam window.

•

Select the 460 Hz shape in the SHP: Mode Shapes window.

The MAC value indicates that the 460 Hz mode shape dominates the in-phase forced response ODS, as shown below. •

Select the 493 Hz shape in the SHP: Mode Shapes window.

Because the 460 Hz mode is a bending mode with approximately equal shape components at DOFs 5Z & 15Z, it is excited by the in-phase forces. On the other hand, the nearby 493 Hz mode has equal and opposite shape components at DOFs 5Z & 15Z, and therefore is not excited.

In-Phase Sinusoidal ODS Dominated by 460 Hz Bending Mode. Out-of-Phase Forces •

Change the Phase of the second Force to 180 degrees, and click on Animate Shape.

Now, the torsional mode at 493 Hz mode is easily excited by the two out-of-phase forces, because its mode shape components at DOFs 5Z & 15Z are also out-of-phase

Forced Response using Time Waveforms The Transform | MIMO | Outputs command in the Data Block window requires the following;

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Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation 1. Multiple excitation forces (Inputs) as either time or frequency domain Traces in a Data Block file. 2. Either FRFs between all Input & Output DOF pairs, or a modal model with mode shape DOFs for all required Inputs & Outputs. Transform | MIMO | Outputs calculates either time or frequency domain forced responses (Outputs) with the same X-Axis properties as the Inputs. •

Open the Jim Beam.VTprj file from the Demos fly out tab.

•

Open SHP: Mode Shapes from the Project Panel and display its mode shapes in animation.

This structure has a 460 Hz bending mode and a 493 Hz torsional mode. •

Display these two mode shapes in animation to verify them as the first bending and the first torsional modes.

Synthesized Sinusoidal Forces MIMO Modeling & Simulation will be used simultaneously excite the Jim Beam structure model with two 500 Hz sinusoidal forces, one applied at DOF 5Z and the other at DOF 15Z. One of the forces will be synthesized as a time waveform in a Data Block file using the File | New | Data Block command in the ME'scopeVES window. •

Execute File | New | Data Block in the ME'scopeVES window.

•

Enter "Sinusoidal Forces" into the dialog box that opens, and click on OK.

•

Set up the parameters in the dialog box as shown below, and click on OK.

•

Spin the mouse wheel to Zoom the Data Block window to display the sine wave (of amplitude +1) more clearly.

To add the second sinusoidal force Trace to the Data Block,

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Execute Edit | Paste Traces from File.

•

Select the BLK: Sinusoidal Forces file in the dialog box that opens, and click on Paste.

Next, the sinusoidal Input forces need to be defined by editing their Trace DOFs, Units, and Input Output properties. •

In the Traces spreadsheet, double click on the Units column heading, select (Lbf or N) in the dialog box that opens, and click on OK.

•

Click on the DOFs cell for M#1 and enter 5Z.

•

Click on the DOFs cell for M#2 and enter 15Z.

•

Double click on the Input Output column header, and select Input in the dialog box that opens.

Two In-Phase 500 Hz Sinusoidal Forces. Using a Modal Model The BLK: Sinusoidal Forces file with two in-phase sinusoidal forces in it will be used together the modal model in the SHP: Mode Shapes file to calculate time domain forced response waveforms. •

Open the SHP: Mode Shapes file from the Project panel.

•

Execute Transform | MIMO | Outputs in the BLK: Sinusoidal Forces window.

•

Select the SHP: Mode Shapes file in the Transfer Functions list, and BLK: Sinusoidal Forces in the Inputs list.

•

Click on Calculate.

•

Select Displacement and click on OK in the dialog that opens.

•

Press the New File button in the dialog box that opens next, enter "Forced Responses" into the dialog, and click on OK.

Animating the In-Phase Forced Response Time domain Forced Response ODS's are displayed by sweeping the Line cursor through the BLK: Forced Responses Data Block.

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Tutorial #10 - Multi-Input Multi-Output (MIMO) Modeling & Simulation •

Close all windows except the STR: Colored Jim Beam and the BLK: Forced Response window.

•

Execute Window | Arrange | For Animation in the ME'scopeVES window.

•

Execute Draw | Animate Shapes

•

Make sure the Sweep Animation is enabled, and adjust the animation speed to a slow sweep.

in the STR: Colored Jim Beam window.

Sweep Animation Showing In-Phase Forced Response at 500 Hz. Notice that the 500 Hz ODS looks like the 460 Hz mode shape. Calculating its MAC values with the shapes in SHP: Mode Shapes will verify how much alike the two shapes are. •

Press Animate | Step animation.

•

Press the arrow keys

•

Execute Tools | Save Shape in the BLK: Forced Responses window, and save the shape into a New File.

•

Execute Display | MAC in the new Shape Table, and select SHP: Mode Shapes in the dialog box that opens.

on the Toolbar in the STR: Colored Jim Beam window to pause the

to clearly display the deformed shape.

The MAC value = 0.90 in the figure below indicates that the time domain ODS correlates strongly with the 460 Hz mode shape. this means that the 460 Hz mode is dominating the time domain ODS.

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MAC Plot Showing In-Phase Forced Response Correlated With 460 Hz Mode.. Out-of-Phase Response To calculate the ODS due to two out-of-phase sinusoidal forces, one of the Traces in the BLK: Sinusoidal Forces file will be multiplied by "-1" to change its phase by 180 degrees. •

Select one of the Traces in the BLK: Sinusoidal Forces window.

•

Execute Tools | Math | Scale Traces By Mag Phs

•

Select Scale By Mag & Phs from the drop down list.

•

Enter Multiply magnitude by "-1" in the dialog box that opens, and click on OK.

•

Select BLK: Sinusoidal Forces in the next dialog box that opens, and click on Replace.

The BLK: Sinusoidal Forces window now has two out-of-phase 500 Hz sine waves in it. •

Execute Transform | MIMO | Outputs, and repeat the steps above to display ODS's due to the out-of-phase forces using sweep animation.

This forced response ODS looks like the 493 Hz mode shape. It's likeness to this mode shape can be verified numerically by saving the shape and displaying its MAC values with respect to the mode shapes in SHP: Mode Shapes.

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Tutorial #11 - Acoustics Creating an Acoustic Surface NOTE: The commands in this chapter can only be executed if the VES-6000 Acoustics option is enabled in your software. Check the Help | About box to verify authorization of this option. An Acoustic Surface is a special type of SubStructure that is used to display acoustic data. 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 automatically calculated when the surface is generated.

•

A normal vector (at right angles) to the surface is also calculated for each measurement Point.

•

The surrounding area and normal of a Point are used to calculate Sound Power through the surface from Intensity data.

Rectangular Surface •

Execute File | Project | New to start a new Project.

•

Execute File | New | Structure to create a new Structure window.

•

Execute File | Options in the Structure window.

•

On the Units tab in the File | Options box, choose Meters from the Length Units list, and click on OK.

•

Execute Draw | Drawing Assistant

•

On the SubStructure tab, double click on the Editable Acoustic Surface.

•

On the Dimensions tab, enter the following changes.

in the Structure window.

Width: 1 m Points: 5 Height: 1 m Points: 6

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Acoustic Surface Showing Areas & Normals. â€˘

Execute Display | Points | Acoustic Normals to display the acoustic normal at each Point.

Each of the 30 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.

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Tutorial #12 - Direct Data Acquisition Using the Acquisition Window NOTE: The commands in this chapter can only be executed if one of the VES-7xx Direct Data Acquisition options is enabled in your software. Check the Help | About box to verify authorization of this option. The Acquisition window option in ME'scopeVES allows you to acquire data directly from a multi-channel acquisition front end. A test can be setup ahead of time in an Acquisition window using multiple Measurement Sets. A Measurement Set is used to define all of the data that is simultaneously acquired from a structure. Each Measurement Set contains all of the front end channel settings required to acquire a set of data from the structure. In an Acquisition window, you can do the following; 1. Setup a multi-channel test using a 3D model of the test structure prior to performing the test. 2. Acquire multi-channel time domain Traces, and calculate time or frequency domain functions for each Measurement Set. 3. Save all time or frequency measurements into an accumulator Data Block. During acquisition, or following its completion; •

Operating Deflection Shapes can be displayed in animation directly from the Acquisition window.

•

Or Mode Shapes can be extracted in the accumulator Data Block by curve fitting frequency domain measurements.

Illustrative Example To illustrate some of the capabilities of the Acquisition window, FRF measurements will be calculated by acquiring data from a Data Block file of pre-recorded data. •

Open Tutorial #12 - Random Shaker Test.VTprj from the My Documents\ME'scopeVES\Tutorials folder.

•

Open the BLK: Random Shaker Test Data Block file.

The BLK: Random Shaker Test file contains the following, •

32 Traces of random time domain data with a Block Size of 20,000 samples.

•

Two Measurement Sets of data, each Set with 15 Output Traces (accelerometer responses) and one Input Trace (force) at 1Z.

•

Measurement Set [1] has Output DOFs from 1Z through 15Z.

•

Measurement Set [2] has Output DOFs 16Z through 30Z.

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BLK: Random Shaker Test. This data is typical of data that would be acquired during a random shaker test using a 16-channel data acquisition system, recorder or analyzer. •

Measurement Set [1] was acquired with accelerometers attached at Points 1 through 15 in the Z direction.

•

Measurement Set [2] was acquired with accelerometers attached at Points 16 through 30 in the Z direction.

Each Measurement Set will be processed separately to calculate FRFs & Coherences between the excitation force channel and each of the 15 acceleration response channels. Creating a Plate Model The Data Block data was acquired by attaching a shaker to one corner of a rectangular aluminum plate, and attaching accelerometers at Points in a 5 by 6 grid of Points on the plate. To create a model for the test structure, •

Execute File | New | Structure in the ME'scopeVES window.

•

Execute Draw | Drawing Assistant in the empty Structure window.

The Drawing Assistant tabs are displayed to the right of the vertical blue splitter bar. •

On the SubStructure tab, double click on the Editable Plate SubStructure .

A vertical Plate SubStructure is added to the Structure window. •

On the Dimensions tab, enter the following parameters, Width = 15 Points = 5 Height = 18 Points = 6

NOTE: Length units can be either English or Metric. Only the relative values of the dimensions are important for drawing a structure model however. •

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On the Position tab, enter 45 into the Rotate Degrees box, and click twice on the Y up arrow.

Tutorial #12 - Direct Data Acquisition The plate model should now be a horizontal 5 by 6 grid of test Points. To number the test Points, •

Execute Draw | Points | Number Points. The Number Points dialog box will open, as shown below.

•

Click near each Point to number it. Number all 30 Points, as shown below.

•

Click on the Close button in the Number Points dialog box to terminate Point numbering.

Point Numbering on the Plate Model.

Acquiring Data from a Data Block Instead of acquiring data from front end acquisition hardware, prerecorded data will be acquired from the BLK: Random Shaker Test Data Block file. Each Trace in the Data Block will provide a channel of acquired data. •

Execute File | New | Acquisition in the ME'scopeVES window.

•

In the dialog box that opens, select Data Block File, as shown below, and click on OK.

•

In the next dialog box that opens, select BLK: Random Shaker Test, and click on OK.

. Connect To Front End Dialog box. In an Acquisition window,

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Time domain Traces of data are acquired as blocks of data from the front end, and are displayed in the upper graph area.

•

Calculated time or frequency domain Traces derived from the upper Traces are displayed in the lower graph area.

Notice that the Acquisition window is already setup to acquire data for Measurement Set [1]. In the Channels spreadsheet, 16 channels are active and have the proper Input Output and Units. •

Click on the Setup, Units, and DOFs tabs below the Channels spreadsheet to examine the channel parameters.

•

Channel 1 is the force channel with DOF 1Z [1], with units of N.

•

Channels 2 through 16 are acceleration channels with DOFs 1Z [1] through 15Z [1], and units of g.

No data is displayed in the upper or lower Trace graphics areas yet because data has not been acquired from the Data Block yet.

Acquisition Window Connected to BLK: Random Shaker Test. •

In the Time section on the Sampling tab, enter 2000 for the Number of Samples.

•

In the Domain section on the Measurement tab, choose Time, and check Time in the Calculate section.

•

Execute Acquire | Front End Scope

.

Using the Front End Scope, data is continuously being acquired from the 16 active front end channels in blocks of 2000 samples each. Since Time was checked in the Calculate area, the same time domain Traces are displayed in both the upper (acquired) and lower (calculated) Trace areas. •

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Execute Acquire | Stop (F7)

to stop the acquisition.

Tutorial #12 - Direct Data Acquisition

Acquisition Window Using Front End Scope. Applying a Hanning Window Since the acquired data is random, each sampling window of time domain data (2000 samples) is nonperiodic in its sampling window. The Digital Fourier Transform (DFT) of this type of random data will have leakage in it. NOTE: To reduce the effects of leakage in the DFT of a random signal, a Hanning window must be applied to each channel of acquired data before the FFT is applied to it. •

In the Window Type column on the Setup tab In the Channels spreadsheet, notice that all of the Channels are set to Rectangular.

To reduce leakage in the DFTs, a Hanning window will be applied to all channels of data, •

On the Setup tab In the Channels spreadsheet, double click on the Window Type column heading.

•

Choose Hanning from the drop down list in the dialog box that opens, and click on OK.

•

Execute Acquire | Front End Scope

to acquire data again.

Notice that the lower graph Traces are smoothly tapered to zero at the ends of the sampling window. This is the effect of multiplying each upper Trace by a Hanning window.

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Lower Traces With Hanning Window Applied.

Calculating FRFs and Coherence With the Hanning window applied to each channel, data can now be acquired and FRFs and Coherences calculated between the Input (force) channel and each Output (acceleration) channel. •

Choose Frequency in the Domain section on the Measurement tab, and check FRF and Coherence in the Calculate section.

•

In the Averaging section, select the Linear averaging method, and change Averages to 10.

•

On the Trigger tab, make sure that Free Run is selected.

The Acquisition window is now ready to acquire time domain data from BLK: Random Shaker Test, and calculate FRFs and Coherences. Overlap Processing 10 successive sampling windows (with 2000 samples each) will be acquired, and the average value of 10 sets of spectral data will be calculated for each Trace in Measurement Set [1]. Each Trace in the Data Block file has 20000 samples of data in it. Therefore, there is exactly enough data for calculating 10 averages using 2000 samples per average or sampling window. If the number of averages is increased above 10 however, overlap processing of the data must take place. Overlap processing means that each successive sampling window of 2000 samples will contain some samples from the previous window of samples. In other words, the acquisition sampling window blocks are overlapping. NOTE: Overlap processing allows more spectrum averages to be calculated from a fixed total number of samples. •

On the Measurement tab, click on the Up arrow next to the Averages box to increase it to 11.

Notice that Percent Overlap is 10% for 11 averages. The Percent Overlap will continue to increase as the number of averages is increased. •

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Execute Acquire | Start

, or press the F5 key on the keyboard to acquire data.

Tutorial #12 - Direct Data Acquisition Acquisition will start, and FRFs and Coherences will be calculated from blocks of acquired time domain data. Acquisition will continue until 11 blocks of data have been acquired and post-processed. As data is being acquired, the current number of averages is displayed on the Toolbar. •

When all of the averages have been completed, the message "Front End Ready" will be displayed on the Toolbar.

Displaying the Results •

Execute Format | Group by DOF.

Each FRF and Coherence pair (with the same DOFs) will be displayed together in the lower graph area, as shown below. •

Scroll through the lower graph Traces to display each FRF and Coherence pair.

FRF & Coherence Overlaid. Notice that the Coherence drops in several places. The Coherence drops for the following reasons; •

At anti-resonances, or frequencies where the FRF is close to zero.

•

At resonances, or frequencies where the FRF has peaks and the effect of leakage is greatest.

The drop at anti-resonances is expected since the structural response is close to zero. The drop at the resonances is due to the remaining effects of leakage. Remember, the Hanning window only reduces leakage effects, but does not eliminate them completely. Leakage Effects on Random Data You can observe the drastic effects of leakage on random data by removing the Hanning window from the acquisition post-processing. •

On the Setup tab in the Channels spreadsheet, double click on the Window Type column heading, and select Rectangular for all channels.

•

Execute Acquire | Start

, or press the F5 key to acquire data again.

Larger Block Size Reduces Leakage

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Tutorial Volume IB - Options Acquiring random data using a large Block Size (number of samples in the sampling window), will also reduce the effects of leakage. •

In the Time section on the Sampling tab, enter 8000 for the Number of Samples.

•

Execute Acquire | Start

, or press the F5 key to acquire data again.

Using a Hanning window and a large Block Size further reduces the effects of leakage. •

On the Setup tab in the Channels spreadsheet, double click on the Window Type column heading, and select Hanning for all channels.

•

Execute Acquire | Start

, or press the F5 key to acquire data again.

To re-acquire data and calculate FRFs and Coherences with a Block Size of 1000 (half of the time domain Block Size); •

In the Time section on the Sampling tab, enter 2000 for the Number of Samples.

•

Execute Acquire | Start

, or press the F5 key to acquire data again.

Saving Measurement Set [1] The 15 FRFs calculated from Measurement Set [1] will be saved into in a new accumulator Data Block. •

Click on the lower graph to make it active.

NOTE: The active Graph is indicated a darker background color, and by the yellow half of the Display | Active Graph tool . The active Graph can also be chosen by clicking on its tab (upper or lower) on the Traces spreadsheet. •

Drag the vertical blue splitter bar to the left, and select the FRFs in the Traces spreadsheet, as shown below.

•

Execute Acquire | Save Traces

•

Enter a name Plate FRFs for the new Data Block into the dialog box, and click on OK.

.

Measurement Set [1] FRFs Selected.

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Tutorial #12 - Direct Data Acquisition Notice that the Data Block that you saved the FRFs into is now listed on the Acquisition Toolbar. This Data Block has become the accumulator Data Block for saving successive Measurement Sets of data.

Acquiring Measurement Set [2] Now that Measurement Set [1] has been acquired and saved into an accumulator Data Block, Measurement Set [2] can be acquired and added to the accumulator Data Block. •

Execute Measurement Set | Next

to advance to Measurement Set [2].

NOTE: The current Measurement Set "2" is displayed in the Active column of the Channels spreadsheet as "MS 2 of 2" •

On the Setup tab In the Channels spreadsheet, double click on the Window Type column heading.

•

Choose Hanning from the drop down list in the dialog box that opens, and click on OK.

•

Execute Acquire | Start

, or press the F5 key to acquire Measurement Set [2].

Saving Measurement Set [2] FRFs •

Click on the lower graph to make it active.

•

Select the FRFs in the Traces spreadsheet.

•

Execute Acquire | Save

.

Measurement Set [2] FRFs Selected. The Measurement Set [2] FRFs are added to the accumulator Data Block.

ODS Animation

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•

Execute Tools | Create Animation Equations in it.

•

Select Match Structure and Source DOFs in the dialog box that opens, and click on OK.

in the Data Block window with the 30 FRFs

A next dialog box will report that 30 Measured animation equations were created. •

Click on OK.

•

Execute Draw | Animate Shapes

•

Execute Window | Arrange | For Animation

•

Drag the Line cursor to each resonance peak in the Data Block to display the ODS, which is an approximation of a mode shape.

in the Structure window containing the Plate model. in the ME'scopeVES window.

Shape Animation From Random Shaker FRFs.

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Tutorial #13 - Structural Dynamics Modification (SDM) Modeling Structural Changes NOTE: The commands in this chapter can only be executed if the VES-5000 Structural Dynamics Modification option is enabled in your software. Check the Help | About box to verify authorization of this option. Modal analysis is used to characterize and further understand noise & vibration problems in operating machinery and structures. If a noise or vibration problem is due to the excitation of a structural resonance, there are only two options available; 1. Isolate the structure from its excitation forces. 2. Physically modify the structure to reduce its response levels. When masses, stiffeners, dampers, tuned absorbers, or other physical additions such as stiffening plates or beams are attached to a structure, its resonant vibration will change. When a SubStructure is attached to another SubStructure, or the boundary conditions of the structure are changed, its modes of vibration will also change, The Structural Dynamics Modification (SDM) method allows you to model additions (or subtractions) of physical elements to a structure, and calculate the new modes of the modified structure. All structural modifications are converted internally to changes in the mass, stiffness or damping properties of the structure. These mass, stiffness and damping changes are used together with the modes of the unmodified structure to calculate the modes of the modified structure.

Block Diagram of the SDM Method.

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.

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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.

•

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.

•

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.

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•

An FEA Triangle is defined between 3 Points

•

An FEA Quad is defined between 4 Points

Tutorial #13 - Structural Dynamics Modification (SDM) 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.

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.

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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.

Adding FEA Objects to a Structure Model FEA Objects can be added to a structure model either one at a time, or by using the FEA Assistant. •

See the Tutorial - Experimental FEA chapter for details on using the FEA Assistant.

Adding An FEA Object All FEA Objects are either added at a Point or between two or more Points on a structure model. •

Select the type of FEA Object from the Edit | Objects list on the Structure window Toolbar.

The FEA Objects spreadsheet will be displayed on the right of the vertical blue splitter bar. •

Drag the vertical blue splitter bar to the left to display the FEA Objects spreadsheet.

•

Execute Edit | Add Object

•

Click on a sufficient number of end Points to add the FEA Object.

•

For example, a Spring requires 2 end Points and an FEA Quad plate requires 4 end Points.

.

After an FEA Object is added to a structure model, it is displayed on the model and added to the FEA Objects spreadsheet. •

Select FEA properties for the new FEA Object from the drop down list in its cell in the FEA Objects spreadsheet.

Illustrative Example To illustrate the use of SDM, an FEA spring will be added between the top and bottom plates of the Jim Beam structure in the Jim Beam.VTprj Project, and the new modes of the structure calculated. •

Open the Jim Beam.VTprj Project from the My Documents\ME'scopeVES\Demos folder.

•

Execute Animate | Draw Structure the animation.

•

Execute Display | Point Labels

in the STR: Colored Jim Beam window to terminate

to display the Point numbers on the model.

The FEA Spring will be attached between Points 5 and 20. •

Choose FEA Springs from the Edit | Object Type list on the Toolbar.

•

Execute Edit | Add Object

•

Click near Point 5 to select it, and then near Point 20 to add an FEA Spring to the model.

•

Execute Edit | Add Object

•

Open the SHP: Mode Shapes window from the Project Panel.

to initiate the Add Object operation.

again to terminate the Add Object operation.

NOTE: Since each mode shape DOF (M#) in SHP: Mode Shapes has a Measurement Type = UMM Mode Shape, this file contains a modal model of the unmodified structure.

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Shape Table Containing UMM Mode Shapes Changing Engineering Units To use SDM, the engineering units of the mode shape DOFs (M#s) in the Shape Table must be compatible with the units in the Structure window containing the model with FEA Objects attached to t. The current engineering units in the SHP: Mode Shapes table are (in)/(lbf-sec). To change from English to Metric engineering units; •

Double click on the Units column heading in the DOFs spreadsheet in the SHP: Mode Shapes window.

•

Enter "m/N" in the dialog box that opens, and click on OK.

•

Click on Yes in the next dialog box that opens, to re-scale the mode shapes to the new units (m)/(N-sec).

•

Execute File | Structure Options in the STR: Colored Jim Beam window.

•

On the Units tab, select Mass, Length, and Force units to match the units in SHP: Mode Shapes.

Spring properties must be defined in the FEA | Properties List before they can be assigned to a particular FEA Spring. •

Execute FEA | Properties in the STR: Colored Jim Beam window, and select the Springs tab in the dialog box that opens.

•

Execute Edit | Add

•

If you are using English units, enter 1.0 E+06 (lbf)/(in) in the stiffness column of the spreadsheet.

•

If you are using Metric units, enter 1.7513 E+08 (N)/(m) in the stiffness column of the spreadsheet.

•

Return to the FEA Property column in the Spring Objects spreadsheet and select Spring_1 from the drop down list.

to add a new spring property to the spreadsheet.

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Jim Beam Structure with FEA Spring Attached The model is now ready to perform an SDM calculation with the stiffener (FEA Spring) attached between the top & bottom plates of the Jim Beam.

Calculating New Modes In the previous section, a very stiff spring was added between the top & bottom plates of the Jim Beam structure. This stiffener will affect all modes that have any relative motion between Points 5 & 20 in the vertical direction. •

Execute SDM | Calculate New Modes

•

Select SHP: Mode Shapes in the dialog box that opens.

•

Click on Yes in the dialog box that opens next, and No in the next dialog box.

in the STR: Colored Jim Beam window.

When the calculation is complete, a dialog box will open asking you to select a Shape Table for storing the new mode shapes of the modified structure.

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Tutorial #13 - Structural Dynamics Modification (SDM) •

Click on the New File button, and type "Spring 5Z 20Z" in the dialog box that opens.

The new Shape Table file window will open, listing the new mode shapes.

Shape Table Containing New Modes of the Modified Structure.

Animating the New Mode Shapes •

Close all windows except STR: Colored Jim Beam, SHP: Mode Shapes, and SHP: Spring 5Z 20Z.

•

in the ME'scopeVES window to display the Execute Window | Arrange | For Animation Structure on the left and the Shape Tables on the right.

NOTE: The window that was active before Window | Arrange | For Animation is executed will retain its size after this command is executed. To initiate comparison animation between the unmodified and modified structure mode shapes, •

Execute Draw | Compare Shapes

•

Click on a Shape in the SHP: Spring 5Z 20Z window to animate it.

•

Click on a shape in the SHP: Mode Shapes window to animate it.

in the STR: Colored Jim Beam window.

Notice that the mode shapes are the same for Shape 1 (165 Hz) and Shape 2 (225 Hz) in both Shape Tables. Because there is little or no relative motion between the upper and lower plates for these two modes, they were not affected by the stiffener. •

Click on Shape 3 (441 Hz) in SHP: Spring 5Z 20Z.

This is a new mode of the modified structure which clearly shows the effect of the stiffener. The unmodified structure had modes at 347 & 460 Hz, both of which no longer exist in the modified structure.

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Comparison of the Unmodified (347Hz) and Modified (440Hz) Mode Shapes. Truncated Modal Model The modal model that was used by SDM had only 10 modes in it, yet it was used to represent the entire dynamics of the unmodified structure. A real Jim Beam structure would have more than 10 modes. Therefore, this modal model is called a truncated model because the higher frequency modes of the real structure are not included in the model. When a truncated modal model is used with SDM to calculate the new modes of a modified structure, the highest frequency mode (or modes) in the solution are called computational modes, and have unrealistic mode shapes. â€˘

Click on Shape 10 in SHP: Spring 5Z 20Z to display its shape.

It is clear from the animated mode shape for Shape 10 that it is a computational mode because its mode shape does not show the effect of the stiffener. The highest frequency mode (or modes) in an SDM solution always shift to higher unrealistic frequencies. This occurs in order to account for the absence of the higher frequency modes in the truncated modal model of the unmodified structure. In other words, the truncated modal model is not a complete model of the structural dynamics. The computational modes appear at higher frequencies (with unrealistic mode shapes) to absorb the effects of the modification that would normally be absorbed by the missing modes. The SDM method provides useful solutions for the lower frequency modes, even when a truncated modal model is used to model the dynamics of the unmodified structure.

Modal Sensitivity The SDM | Modal Sensitivity command allows you to examine how sensitive the modes of a structure are to the amount of a particular structural modification. With this command, you can determine how much of certain FEA Object properties are required in order to change the modal parameters of a structure so that its new modes are close to some target modal parameters that you specify. To perform a Modal Sensitivity search, you provide the following, 1. Target modal parameters (frequencies & damping) for the modified structure.

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Tutorial #13 - Structural Dynamics Modification (SDM) 2. A solution space of FEA properties over which to search for the best solution. NOTE: The Best solution is a set of FEA properties that minimizes the difference between the modal parameters of the modified structure and the target modal parameters. The FEA Object properties found by the Modal Sensitivity search can then be used with the SDM | Calculate New Modes command to calculate new modes for the modified structure. Illustrative Example We saw in the previous example that adding a very stiff (1E6 lbf/in) spring between the top & bottom plates of the Jim Beam structure had no affect on the first two modes, but created a new mode at 441 Hz which didn't exist in the unmodified structure. Modal Sensitivity will now be used to determine how much spring stiffness is necessary between the top & bottom plates to obtain new modes for the structure with the third mode at 440Hz. NOTE: If you don't have a Jim Beam structure model with an FEA Spring attached between Points 5 & 20, repeat the steps in the previous sections of this chapter. Target Frequency •

Execute SDM | Modal Sensitivity in the STR: Colored Jim Beam window.

•

Select SHP: Mode Shapes (the modal model of the unmodified structure) in the dialog box that opens.

•

Click on OK and Yes in the two following dialog boxes. The Modal Sensitivity window will open.

•

On the upper spreadsheet, enter "440" into the Target Frequency cell in the third row, as shown below.

•

Press the Select Mode button in the third row of the upper spreadsheet. (This is the target mode that will be used to calculate an Error function for ordering the solutions.)

•

On the lower spreadsheet, enter "1e4"(lbf/in) for the Property Minimum, and "2e6"(lbf/in) for the Property Maximum, (or the equivalent values if you are using different engineering units).

NOTE: To change from English units to different engineering units, follow the instructions under Changing Engineering Units in the Adding Objects to a Structure section. •

Enter "1000" for the Property Steps, as shown below.

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Modal Sensitivity Window. •

Execute Solution | Start Calculation, and click on Yes in the dialog boxes that follow.

1000 SDM solutions will be calculated and ordered from the Best to the Worst according to how close the third modal frequency is to the Target frequency (440Hz). Solution Scroll Bar After the search process has been completed, a scroll bar will be displayed on the right hand side of the window. The solutions are displayed 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.

The Solution Value for the best solution (shown below), is only 47850 (lbf/in) of stiffness, which is substantially less that the 1E6 (lbf/in) required to create the third mode at 441Hz. This illustrates the "brick wall" effect when trying to stiffen structures to increase modal frequencies. Brick Wall Effect: In this case, it took only 47,850 (lbf/in) of stiffness between the top & bottom plates to increase the third mode to 440Hz, but it took 1,000,000 (lbf/in) of stiffness to move it to 441Hz.

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Tutorial #13 - Structural Dynamics Modification (SDM)

Best Modal Sensitivity Solution. Unrealistic Solutions •

Scroll through the other solutions and observe the Solution Frequency of the third mode.

Notice that there are many other solutions that also yield a third mode close to 440 Hz. However, some of the worst solutions (with the scroll near the bottom of the Solution scroll bar), are unrealistic. This is a manifestation of using a truncated modal model. These unrealistic solutions occurred because the truncated modal model for the unmodified structure was not sufficient to model its dynamics together with certain FEA Spring stiffness modifications. Saving a Solution •

Scroll the Solution scroll to the top of the Solution Scroll bar.

•

Execute Solution | Save Solution in FEA Properties. This saves the stiffness as the FEA Property of Spring_1.

•

Execute SDM | Calculate New Modes, and select SHP: Mode Shapes in the dialog box that opens.

•

Click on the New File button, and enter "440 Hz Target" in the dialog box that opens.

Mode Shape Comparison •

Close are windows except STR: Colored Jim Beam, SHP: Mode Shapes & SHP: 440 Hz Target.

•

in the ME'scopeVES window to display the Execute Window | Arrange | For Animation Structure on the left and the Shape Tables on the right.

NOTE: The window that was active before Window | Arrange | For Animation is executed will retain its size after this command is executed. To initiate comparison animation between the unmodified and modified structure mode shapes, •

Execute Draw | Compare Shapes

in the STR: Colored Jim Beam window.

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Select SHP: Mode Shapes in the Animation Source list on the Toolbar, and SHP: 440 Hz Target in the Comparison Source list.

•

Execute Animate | Compare Shapes | Synchronize MAC.

•

Click on Shapes in SHP: Mode Shapes to display Shape pairs with highest MAC together.

Comparison of Third Modes Sowing Effect of Spring Stiffener.

Adding a Tuned Absorber The SDM | Add Tuned Absorber command can be used to attach one or more tuned vibration absorbers to a structure. A tuned absorber is used to suppress the amplitude of a particular mode of vibration. The components of a tuned absorber are its mass which is connected by a spring & damper to the structure. A tuned absorber should be designed to absorb energy from the structure, thereby reducing the vibration amplitude of the structure at the tuned frequency. A tuned absorber will cause a single resonance peak will split into two resonance peaks with lower amplitudes. A tuned absorber requires the following two items, 1. A structure model containing the attachment Point. 2. A Shape Table containing a modal model of the unmodified structure. A tuned absorber is defined by the following items, 1. Absorber mass. 2. Absorber frequency. The frequency should be close to the frequency of the resonance to be suppressed. 3. Absorber damping (optional). An estimate of the percent of critical damping of the absorber. Illustrative Example A tuned absorber will be added to the top plate of the Jim Beam structure in the Jim Beam.VTprj Demo Project.

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Tutorial #13 - Structural Dynamics Modification (SDM) •

Open the Jim Beam.VTprj file from the Demos fly out panel.

•

Click on the SHP: Mode Shapes file in the Project fly out panel to open its window.

The tuned absorber will be added to Point 15 in the Z (vertical) direction, and tuned to reduce the amplitude of the third mode (347 Hz). To observe the third mode resonance peak, a driving point FRF will be synthesized using the modal model in SHP: Mode Shapes. •

Execute Tools | Synthesize FRFs in the SHP: Mode Shapes window.

•

Un-select all mode shapes.

•

In the dialog box that opens, check Driving Points Only.

•

Select Roving DOF 15Z, and click on OK.

•

Select Acceleration response in the dialog box that opens, and click on OK.

•

Enter "Driving Point 15Z" In the New File dialog box that opens, and click on OK.

•

In the Data Block window that opens, color the Trace Blue, as shown below.

Driving Point FRF (15Z:15Z) Showing Resonance Peak at 347 Hz. •

Execute FEA | FEA Object List in the STR: Colored Jim Beam window.

•

Hide all FEA Objects on the structure.

•

Execute SDM | Add Tuned Absorber in the STR: Colored Jim Beam window to open the Tuned Absorber dialog box. •

Select DOF [15] Z in the DOF list.

•

Enter "0.1" Lbm in the Mass column.

•

Select 347 Hz in the Frequency list.

•

Enter "1" % in the Damping column, as shown below.

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•

Click on Calculate New Modes.

•

When the calculation is complete, enter "TA Modes" as the new Shape Table name in the dialog box that opens.

To observe the effect of the tuned absorber, the driving point FRF at 15Z will be synthesized using the TA Modes and overlaid on the driving point FRF synthesized using SHP: Mode Shapes. •

Execute Tools | Synthesize FRFs in the SHP: TA Modes window.

•

In the dialog box that opens, check Driving Points Only.

•

Select Roving DOF 15Z, and click on OK.

•

Select Acceleration response in the dialog box that opens, and click on OK.

•

In the dialog box that opens, select the "Driving Point 15Z" and click on Add To.

•

Execute Format | Overlaid in BLK: Driving Point FRFs.

Driving Point FRF (15Z:15Z) Without (Blue) and with (Red) Tuned Absorber. It is clear from the overlaid FRF Traces that the high amplitude peak at 347 Hz has been split into two lower amplitude peaks, one on each side of the original 347 Hz peak.

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Tutorial #14 - Experimental Finite Element Analysis (FEA) Experimental FEA NOTE: The commands in this chapter can only be executed if the VES-8000 Experimental FEA option is enabled in your software. Check the Help | About box to verify authorization of this option. Experimental FEA is used to add finite elements to the same 3D structure model that is used for displaying experimental mode shapes in animation. In this chapter, a finite element model will be constructed by adding plate elements to a model of the Jim Beam test article. The FEA model will then be solved for its analytical modes, and they will be compared with the experimental modes of the structure. FEA Prior to a Modal Test Prior to performing an experimental modal analysis (EMA), building a finite element model and solving for its FEA modes provides the following information to assist you in setting up the test, 1. The number and density of modes in a certain frequency range. 2. The approximate modal frequencies. 3. The dominant direction of motion of each mode shape. Spatial Aliasing When the number of test points & directions on a test article is not sufficient to distinguish one mode shape from another, this is known as spatial aliasing. To illustrate spatial aliasing, •

Open the Tutorial #14 - Experimental FEA.VTprj Project from the My Documents\ME'scopeVES\Tutorials folder.

•

Click on Shape 1 in the Shape Table window to display the 165 Hz mode shape.

Notice that the dominant direction of motion of this mode is in the global X direction. •

Execute Animate | Direction | X direction to disable the X direction of mode shape animation.

•

Execute Animate | Direction | Y direction to disable the Y direction of mode shape animation.

Now, when only the Z direction of this mode is displayed in animation, it "looks like" a rigid body mode of the beam. This doesn't not satisfy our intuition, because it would be very unusual for a structure like this to have a rigid body mode at 165 Hz. If experimental data were only acquired from the Jim Beam in the Z direction, this apparent rigid body mode shape would have been extracted from the data. Clearly, the X & Y directions are needed in order to determine the dominant direction of motion of this mode shape. If X & Y experimental data were not acquired, this would be a case of spatial aliasing. NOTE: Spatial aliasing occurs when a test article has not been spatially sampled in enough Points & directions to adequately define the dominant motion of its mode shapes.

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165 Hz Mode - Z Direction Only. Being able to observe the dominant direction of motion of each mode shape of a structure before performing a modal test is very useful for avoiding spatial aliasing. By providing a set of mode shapes beforehand, an FEA model is helpful for choosing a sufficient number of excitation and response points & directions (DOFs).

Creating an FEA Model The actual Jim Beam structure was constructed from three 3/8 inch thick aluminum plates, fastened together with cap screws. The dimensions of the Jim Beam are 12 in. long by 6 in. wide by 4.5 in. high. The following steps will be carried out to create an FEA model from the experimental STR: Colored Jim Beam model. 1. Create a 2D profile SubStructure of the Jim Beam. 2. Extrude the profile into a 3D surface model containing surfaces Surface Quad Objects. 3. Mesh the surface model to create more Surface Quads. 4. Use the FEA Assistant to add an FEA Quad plate to the model wherever there is a Surface Quad. 5. Enter element properties for the FEA Quad plates. 6. Solve for the analytical modes of the FEA model. Creating a 2D Profile To create a 2D profile from the Colored Jim Beam model, •

Execute Animate | Draw Structure the animation.

•

Turn Off the display of all surfaces.

•

Execute Edit | Objects Type | Points

•

Hold down the Ctrl key, and select 11 Points on the edges of the Photo model, as shown below.

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in the STR: Colored Jim Beam window to terminate

.

Tutorial #14 - Experimental Finite Element Analysis (FEA)

Points Selected to Form a 2D Profile. When completed, there should be 5 selected Points on the upper edge of the top Plate, 1 selected Point on the back plate, and 5 selected Points on the lower edge of the bottom plate. •

Execute Edit | Copy Objects to File.

•

Click on the New File button in the dialog box that opens, and enter "FEA Plate Model" into the next dialog box that opens.

The STR: FEA Plate Model window will open containing the 11 selected Points. In order to extrude a 2D profile into a 3D model, •

Lines must be added between all Points on the profile.

•

A SubStructure must be defined for the profile.

NOTE: Some of the Points will already be connected with Lines. To add Lines between pairs of Points, •

Select Lines from the Edit | Objects Type | Lines

•

Execute Edit | Add Object

•

Starting at one end of a Line to add, click on a Point and then on an adjacent Point to add a Line between them.

•

Repeat the above step until all of the Points on the profile are connected with Lines, as shown below.

•

Execute Edit | Add Object

in the STR: FEA Plate Model window.

.

again to terminate the Add Lines operation.

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Profile With Lines Connecting all Points. Creating a SubStructure for Extruding the Profile •

Double click on the Select Lines column heading in the Objects spreadsheet to select all of the Lines.

•

Execute Draw | SubStructure | Add Selected Objects to SubStructure in the STR: FEA Plate Model window.

•

Click on the New Substructure button in the dialog box that opens.

•

Enter "Surface Model" into the next dialog box that opens, and click on OK.

Next, the Profile will be scaled to the proper size, and then extruded into a 3D surface model. NOTE: After scaling it to English units, the SubStructure can be re-scaled to different engineering units if desired. •

Execute Draw | Drawing Assistant

•

Select the SubStructure in the SubStructures spreadsheet.

•

On the Dimensions tab, un-check Lock Aspect Ratio, and enter the following dimensions X: 12.0 (in), Y: 0.0 (in), Z: 4.5 (in)

•

On the Position tab, press the To Global Origin button to center the SubStructure about the global origin.

•

On the Extrude tab, enter Length 6 (in), Points 3, and click on the Extrude button.

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in the STR: FEA Plate Model window.

Tutorial #14 - Experimental Finite Element Analysis (FEA)

Extruded Surface Model. Changing Engineering Units The current engineering units in the Structure window are English units. To change from English to other engineering units; •

Execute File | Structure Options in the STR: FEA Model window.

•

On the Units tab, select the desired Mass, Force, & Length units, and click on OK.

When you change the Length units, a dialog box will open. •

Click on Yes in the dialog box to re-scale the structure model to the new Length units.

Adding FEA Quads to the Surface Model An FEA model will be created by adding FEA Quad plate elements to the previously created structure model. The FEA Assistant will be used to add an FEA Quad Object wherever there is a Surface Quad. •

Execute FEA | FEA Assistant

•

Select the Surface Model SubStructure.

•

On the Add FEA Elements tab, press the New button on the same line as the Plates button.

•

Select the Plates tab in the dialog box that opens, and execute Edit | Add.

in the STR: FEA Model window.

A new plate has been added to the Plate Properties spreadsheet. •

In the Material column, click on the cell in the new plate row, and select Aluminum from the drop down list.

•

In the Thickness column, enter "0.375" (in) into the cell, as shown below.

If you are using different Length engineering units than inches, 1. Change Length units to inches in the File | Structure Options dialog box. 2. Enter a thickness of "0.375" (in) into the FEA Properties Plate spreadsheet. 3. Change back to your Length engineering units in the File| Structure Options box.

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Tutorial Volume IB - Options The plate thickness will then be displayed in your Length engineering units. •

Click on the close button

•

Press the Plates button on the Add FEA Elements tab to add the FEA Quad plate elements to the SubStructure.

in the FEA Properties box.

NOTE: When the Plates button is pressed, an FEA Quad will be added to the Substructure wherever there is a Surface Quad. 20 FEA Quads should be added. Meshing the FEA Quads The structure model in the STR: FEA Plate Model window should have 20 FEA Quads attached to it. To improve the accuracy of the FEA modes, the FEA model will be meshed to create more FEA Quads. Each FEA Quad will be replaced with four FEA Quads, therefore creating a total of 80 FEA Quads. •

Select the Surface Model SubStructure in the STR: FEA Plate Model window.

•

Execute Draw | Mesh Objects | Mesh All Edges.

•

Enter "1" in the dialog box as shown below, and click on OK.

The structure model should now contain 80 FEA Quads and 105 Points, as shown below. You can check them by displaying their Object spreadsheets. The FEA Quad labels will be displayed as shown below. The FEA model is now ready to be solved for its FEA mode shapes.

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Structure Model with 80 FEA Quads Attached.

Solving for the FEA Modes NOTE: In order to compare the FEA & EMA mode shapes using MAC values, the 33 Points on the FEA model that coincide geometrically with the test Points on the Jim Beam Photo model must have the same Point numbers. •

Execute Display | Display Objects | FEA Objects | Show Objects in the STR: FEA Plate Model window.

•

Execute Draw | Points | Number Points.

•

Press the Clear All button in the Number Points box to clear all of the existing Point labels.

•

Click near each of the 33 Points to number it, as shown below.

•

When you are finished numbering Points, click on the Done button.

The 33 numbered Points on the FEA Plate Model should coincide with the 33 test Points on the original STR: Colored Jim Beam model.

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Point Numbering on the FEA Plate Model. The Plate Model is now ready to be solved for its FEA modes. •

Execute FEA | Calculate FEA Modes.

•

Click on Yes in the dialog box that opens.

•

Enter the values (shown below) in the next dialog box that opens, and click on OK.

Calculate FEA Modes Dialog Box. After the modes of the Jim Beam have been calculated, a dialog box will open allowing you to name the Shape Table file into which to store the FEA modes. •

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Enter "FEA Modes" into the dialog box, and click on OK.

Tutorial #14 - Experimental Finite Element Analysis (FEA)

FEA Modes Shape Table. Notice that there are the 6 rigid body FEA modes of the structure, with frequencies at or near "0" Hz. The first mode with a significant frequency is mode shape 7. Notice also that eac mode shape has 630 DOFs; 315 translational and 315 rotational DOFs. NOTE: The FEA model has 105 Points (or Nodes) in it. Mode shapes were calculated with six DOFs per Node (3 translational and 3 rotational DOFs) times 105 Nodes gives a total of 630 DOFs.

Comparing FEA & EMA Mode Shapes Only the translational DOFs of the FEA mode shapes are displayed in animation and compared with the EMA mode shapes at matching DOFs. There are two ways to compare mode shapes; 1. Graphically with the animated comparison display. 2. Numerically by calculating the MAC value for each pair of FEA & EMA mode shapes. Creating Animation Equations •

Execute Tools | Create Animation Equations in the SHP: FEA Mode Shapes window.

•

Select the STR: FEA Plate Model in the dialog box that opens, and click on OK in the dialog boxes that follow.

In the STR: FEA Plate Model window, •

Execute File | Structure Options, and make sure Sources on Right and Display MAC are checked on the Animation tab.

•

Execute Draw | Compare Shapes.

•

Choose SHP: Mode Shapes in the Comparison Source list, and STR: Colored Jim Beam in the Comparison Structure list on the Toolbar.

•

Execute Window | Arrange Windows | For Animation

•

Execute Animate | Compare Shapes | Synchronize MAC

in the ME'scope window.

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Click on each Shape button in the SHP: FEA Modes window or in the SHP: Mode Shapes window to display its shape in animation.

Both models will animate together, with the EMA shapes displayed on the Colored Jim Beam model and the FEA shapes displayed on the FEA Plate Model. The MAC values between the FEA & EMA mode shapes are listed in the table below. Even though each FEA modal frequency is significantly less than its corresponding EMA modal frequency, the MAC values between FEA modes 8 through 17 and EMA modes 1 through 10 indicate that these mode shape pairs are "closely matched" with one another.

FEA Mode Number

FEA Modal Frequency (Hz)

EMA Mode Number

EMA Modal Frequency (Hz)

MAC Value

8

149

1

164

0.97

9

211

2

224

0.97

10

309

3

347

0.95

11

415

4

460

0.93

12

449

5

493

0.96

13

590

6

635

0.94

14

996

7

1109

0.91

15

1090

8

1211

0.90

16

1170

9

1323

0.86

17

1390

10

1555

0.84

FEA & EMA Modal Frequencies and MAC Values.

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Comparison of FEA Mode Shape 8 and EMA Mode Shape 1. Out-of-Phase Animation •

Drag the horizontal scroll bar at the bottom of the Structure window to the left to overlay the two mode shapes during animation.

Two mode shapes may be closely correlated (indicated by a MAC value close to 1.0), but have different phases. When this occurs, the two shapes will not lie on top of one another during comparison animation. Even though their MAC value is close to "1", one shape may be animating 180 degrees outof-phase with the other shape. If two mode shapes are animating out-of-phase with one another, •

Execute Animate | Compare Shapes | Flip Right Sign.

Shape Normalization If flipping the sign of the right shape still does not correct the out-of-phase animation, then normalizing the shapes will cause them to overlay more closely during comparison animation. (See the Display | Complexity Plot command description in the Multi-Reference Modal Commands chapter for more details on shape normalization. To normalize the shape during animation, •

Execute Animate| Shapes | Normalized.

Mode Shape MAC Values The Modal Assurance Criterion (MAC) value provides a numerical comparison of two mode shapes. MAC Rules •

A MAC equal to 1.0 means that the two shapes are identical.

•

A MAC greater than 0.90 means that the two shapes a similar.

•

A MAC less than 0.90 means that the two shapes are different.

Matching DOFs

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Tutorial Volume IB - Options The EMA mode shapes of the Jim Beam are defined in three directions (X, Y, Z) at 33 points, or 99 DOFs. The FEA mode shapes of the Jim Beam are defined in three directions (X, Y, Z) at 105 points, but only 33 of those Points have Point numbers & directions that match with the EMA mode shapes. NOTE: In order to calculate MAC values between a pair of shapes, both shapes must have shape components with the same DOFs (Point numbers & directions). Recall that 33 Points on the FEA Plate Model were numbered to match the same 33 geometric Points on the Colored Jim Beam model. Also, both models have the Measurement Axes at each of these 33 Points oriented in the same (X, Y, Z) directions. Consequently, the FEA mode shapes have components with DOFs (1X, 1Y, 1Z) through (33X, 33Y, 33Z) that match the shape components of the EMA mode shapes. Hence, MAC values can be calculated between mode shape pairs in these two Shape Tables but using shape components for the matching DOFs. MAC Bar Chart •

Execute Display | MAC in the SHP: Mode Shapes window.

•

Select SHP: FEA Modes in the dialog box that opens, and click on OK.

•

Hover the mouse pointer over each of the vertical bars to display the MAC value for a shape pair.

MAC Plot for FEA & EMA Mode Shapes. MAC Comparison in Z Direction Only Since most of the mode shapes have dominant motion in the Z direction, it is instructive to compare MAC values for only the Z directions of the DOFs. •

Execute Edit | Select DOFs | By in the SHP: Mode Shapes Shape Table.

•

Select Direction from the drop down list in the dialog box that opens, and Z in the list below it.

•

Press the Select button followed by the Close button.

•

Execute Display | MAC in the SHP: Mode Shapes window.

•

Select SHP: FEA Modes in the dialog box that opens, and click on OK.

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MAC Plot for Z Direction Only. Notice that all the MAC values (except the first one) are now greater than 0.9. This means that the FEA & EMA shapes are essentially the same in the Z direction, at their common Points. NOTE: The dominant motion of the first mode is in the Y direction and it has very little motion in the Z direction. Therefore, its MAC value is less than 0.9 in the Z direction.

Point Matching Example We were careful to number 33 Points on the FEA Plate Model so that they had the same numbers as the corresponding geometric Points on the Colored Jim Beam model. This insured that the FEA mode shapes would have 99 DOFs in common with the EMA mode shapes. Therefore, meaningful MAC calculations between FEA & EMA mode shape pairs were obtained. If the nodes (Points) of an imported FEA modal are numbered differently than the Points on an experimental model, then the FEA & EMA mode shapes cannot be compared using MAC values. NOTE: To compare FEA & EMA mode shapes using MAC values, the common geometric Points on the FEA & EMA models must have the same Point numbers and the same measurement axes. The FEA | Point Matching command is used to renumber common To illustrate Point Matching, some of the Point numbers on the FEA model will be changed so that they are different from the Point numbers on the EMA model. •

Terminate animation, and execute Draw | Points | Number Points in the STR: FEA Model window.

•

Press the Clear All button In the dialog box to clear all of the Point labels on the FEA model.

•

Click on Points in the first several rows of points on the upper plate of the Jim Beam to number them, as shown below.

NOTE: This Point numbering is arbitrary, so you can number as many Points as you desire. •

After you have numbered some Points, click on Close in the Number Points box.

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FEA Model Showing Re-Numbered Points. The FEA model now has some numbered Points, and many un-numbered Points. •

Execute FEA | Calculate FEA Modes in the STR: FEA Plate Model window.

•

Click on Yes in the dialog box that opens.

•

Enter the parameters shown in the dialog below, and click on OK.

•

Enter "New FEA Modes" into the dialog box that opens next, and click on OK.

•

Execute Tools | Create Animation Equations (Assign M#s) in the SHP: New FEA Modes window.

•

Select the STR: FEA Plate Model in the dialog box that opens, and click on OK in the dialog boxes that follow.

Comparing Mode Shapes •

Execute Draw | Compare Shapes

•

Choose SHP: Mode Shapes in the Comparison Source list, and STR: Colored Jim Beam in the Comparison Structure list on the Toolbar.

•

Execute Window | Arrange Windows | For Animation

in the STR: FEA Plate Model window.

in the ME'scopeVES window.

The FEA & EMA mode shapes will be displayed side-by-side in animation, as shown below.

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Click on each Shape button in the SHP: Mode Shapes and SHP: New FEA Modes windows to display different shape pairs.

Comparison of New FEA Mode Shape 8 & EMA Mode Shape 1. Notice that when a matching pair of mode shapes is displayed, their mode shapes look the same as before, but their MAC values are very low. NOTE: The MAC values between matching mode shapes are low (below 0.90) because the DOFs of the mode shape pairs do not match.

Aligning the FEA & EMA Models In the previous section, the Points on the FEA Model were re-numbered to make them different from the geometrically close Points on the EMA Model. After re-numbered and solving again for the FEA modes, we saw from the shape comparison animation that the numerical comparison of like mode shapes using MAC values was no longer valid. The FEA | Point Matching command is used to re-number Points and align Measurement Axes between dissimilar FEA and EMA models so that mode shape MAC values are valid. Prior to executing FEA | Point Matching, the FEA & EMA models must be geometrically aligned. This is done by creating two SubStructures from the two models, and copying them into a new Structure window where they can be aligned.

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Tutorial Volume IB - Options Creating Two SubStructures •

Execute Edit | Objects | Points

•

Execute Edit | Select Objects | Select All

•

Execute Draw | SubStructure | Add Selected Objects to SubStructure.

•

Press the New SubStructure button in the dialog box that opens, and enter "FEA SubStructure" into the next dialog box that opens.

•

Repeat the steps above in the STR: Colored Jim Beam window, but enter "EMA SubStructure" into the last dialog box that opens.

in the STR: FEA Plate Model window. .

To geometrically align the two SubStructures, •

Select the FEA SubStructure in the STR: FEA Plate Model window.

•

Execute Edit | Copy Objects to File.

•

Press the New File button in the dialog box that opens, and enter "Point Matching" into the next dialog box that opens.

•

Copy the EMA SubStructure into the STR: Point Matching window with the FEA SubStructure.

The STR: Point Matching window should contain the two SubStructures, as shown below.

FEA & EMA SubStructures Before Geometric Alignment. Aligning the SubStructures •

Execute Draw | Drawing Assistant in the STR: Point Matching window.

•

Select the FEA SubStructure.

•

On the Position tab, press the To Global Origin button.

•

Select the EMA SubStructure.

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Tutorial #14 - Experimental Finite Element Analysis (FEA) •

On the Position tab, press the To Global Origin button.

The two SubStructures are now geometrically aligned, and are ready for Point Matching.

EMA & FEA SubStructures After Geometric Alignment.

Using the Point Matching Command The FEA | Point Matching command carries out the following steps, 1. Locate each Point on the FEA model geometrically closest to each Point on the EMA model. 2. Re-number each EMA Point using the Point number of its matching FEA Point. 3. Re-number each EMA shape DOF using the re-numbered EMA Point. 4. Copy the Measurement Axes of each EMA Point to its matching FEA Point. 5. Transform the FEA mode shape components at each FEA Point into the Measurement Axis coordinates of the matching EMA Point. NOTE: The FEA SubStructure must precede the EMA SubStructure in a SubStructure spreadsheet before executing the FEA | Point Matching command. •

Select both FEA SubStructure & EMA SubStructure in the STR: Point Matching window.

•

Make sure that both the SHP: FEA Modes and SHP: Mode Shapes windows are open.

•

Execute FEA | Point Matching.

•

In the dialog box that opens, select SHP: FEA Modes in the left list and SHP: Mode Shapes in the right list as shown below, and click on OK.

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Point Matching Dialog Box. When Point Matching is completed, a series of dialog boxes will open, asking it you want to save each of the Point matched SubStructures and Shape Tables into new files. •

Click on Yes to save each new file.

•

Name the FEA SubStructure "Matched FEA Structure" and the mode shapes "Matched FEA Modes" in the dialog boxes that open.

•

Name the EMA SubStructure "Matched EMA Structure" and mode shapes "Matched EMA Modes" in the dialog boxes that open.

Creating Animation Equations •

Execute Tools | Create Animation Equations (Assign M#s) in the SHP: Matched FEA Modes window.

•

Select Matched FEA Structure in the dialog box that opens, and click on OK in the dialog boxes that follow.

•

Execute Tools | Create Animation Equations (Assign M#s) in the SHP: Matched EMA Modes window.

•

Select Matched EMA Structure in the dialog box that opens, and click on OK in the dialog boxes that follow.

Comparing Shapes •

Execute Draw | Compare Shapes

•

Choose SHP: Matched EMA Modes in the Comparison Source list, and STR: Matched EMA Structure in the Comparison Structure list on the Toolbar.

•

Execute Window | Arrange Windows | For Animation

•

Click on each Shape button in the SHP: Matched FEA Modes and SHP: Matched EMA Modes windows to display different shape pairs and verify their MAC values.

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in the STR: Matched FEA Structure window.

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Tutorial #14 - Experimental Finite Element Analysis (FEA)

Mode Shape Comparison After Point Matching. MAC Bar Chart The MAC values between all FEA & EMA mode shape pairs can be displayed in a MAC Bar chart. •

Execute Display | MAC in the SHP: Matched FEA Modes window.

•

Select SHP: Matched EMA Modes, and click on OK.

The MAC Bar Chart below confirms that each Point matched EMA mode shape has a high MAC value with its corresponding FEA mode shape.

MAC Bar Chart of Point Matched FEA &EMA Mode Shapes.

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Tutorial #15 - FEA Model Updating Targeted FEA Model Updating NOTE: The commands in this chapter can only be executed if the VES-9000 FEA Model Updating option is enabled in your software. Check the Help | About box to verify authorization of this option. FEA Model Updating involves changing properties of an FEA model so that its FEA modes more closely match a set of experimental modal parameters. This is called Targeted Model Updating because you can do the following; 1. Select FEA & EMA modal frequency and mode shape pairs to be matched. 2. Select FEA element properties to be updating. 3. Select elements in portions of an FEA model to be updating. FEA model updating uses the SDM method to rapidly calculate new FEA modes due to changes in each FEA property. The SDM method requires the following, •

The FEA elements that will be modified on the FEA model.

•

FEA mode shapes of the un-modified structure.

The FEA Model Updating exhaustive calculation procedure guarantees that the best solution in a userdefined solution space will be found. The calculation process orders the solutions from best to worst. The best solution is the one that minimizes the difference between the FEA & EMA modal parameters for each selected mode pair. However, any of the solutions (element property changes) can be used to calculate the new modes of the updated FEA model.

Illustrative Example To illustrate FEA Model Updating, the thickness of the vertical plate on the FEA model of the Jim Beam structure will be updated so that its modal frequencies more closely match its experimental (EMA) frequencies. The FEA modes of the Jim Beam were calculated in the previous tutorial, Tutorial #14 Experimental FEA. The FEA modes are also contained in the Tutorial #15 - FEA Model Updating.VTprj file in the ME'scope/Tutorials folder. •

Open the Tutorial #15 - FEA Model Updating.VTprj file from the My Documents\ME'scopeVES\Tutorials folder.

•

Open the STR: Colored Jim Beam and SHP: EMA Modes windows.

•

Open the STR: FEA Plate Model and SHP: FEA Modes windows.

Comparing Shapes

First, the FEA & EMA mode shapes will be compared, both in animation and numerically using the Modal Assurance Criterion (MAC) value between mode shape pairs. •

Execute File | Structure Options in the STR: Colored Jim Beam window.

•

In the Animation tab, check both Sources on Right and Display MAC.

•

Execute Draw | Compare Shapes

•

Choose SHP: FEA Modes in the Comparison Source list and STR: FEA Plate Model in the Comparison Structure list on the Toolbar.

in the STR: Colored Jim Beam window.

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Tutorial Volume IB - Options •

Execute Window | Arrange Windows | For Animation

.

The FEA & EMA mode shapes will be displayed side-by-side in animation, as shown below. •

Click on each Shape button in the SHP: FEA Modes window to display its mode shape.

Comparison of EMA Mode Shape 1 & FEA Mode Shape 8. Notice that each of the first 6 FEA modes is a rigid body mode shape. That is, there is very little flexible motion of the plate structure in the first 6 mode shapes. •

Click on FEA mode 7 (61 Hz) to display its mode shape. This is the first (lowest frequency) flexible body mode of the FEA model.

•

Click on each of the EMA modes, and notice that FEA mode 7 does not match any of the EMA mode shapes.

NOTE: MAC values of 0.90 or greater indicate a close match (or strong correlation) between a pair of mode shapes. A MAC value less than 0.90 indicates that two mode shapes are different. •

Execute Animate | Shapes | Normalize.

•

Execute Animate | Compare Shapes | Synchronize by MAC.

Notice that each FEA mode shape (8 through 17) closely matches with one of the EMA mode shapes (1 through 10). However, notice also that each FEA modal frequency is significantly less than the frequency of its matching EMA mode. This means that the stiffness of the FEA model is less than the stiffness of the real Jim Beam test article.

Preparing for FEA Model Updating Several steps are needed before Model Updating can be performed. 1. Delete the FEA Rigid Body Shapes The first six modes in the SHP: FEA Modes file have rigid body mode shapes. Since only the frequencies of several flexible body FEA modes with be compared with their corresponding EMA modes, the rigid body modes will be deleted from the FEA modal model. •

126

Select Shape 1 in the Shapes spreadsheet of the SHP: FEA Modes window.

Tutorial #15 - FEA Model Updating •

Hold down the Shift key and select Shape 6. Shapes 1 to 6 are now selected.

•

Execute Edit | Delete Selected Shapes, and click on Yes to delete the first six rigid body modes.

2. Add an EMA Shape There is no EMA mode shape to match the 62 Hz FEA mode shape. In order to pair the FEA & EMA mode shapes correctly, another shape must be added to SHP: EMA Modes. •

Execute Edit | Add Shapes in the SHP: EMA Modes window, and click on OK in the dialog box that opens.

A new 0 Hz mode has been added to the end of the SHP: EMA Modes file. •

Execute Edit | Sort Shapes | Ascending to move the 0 Hz mode to Shape 1 in the window.

Now the 11 modes in SHP: EMA Modes can be matched one for one with the first 11 modes in SHP: FEA Modes. 3. Select FEA Quads on the Vertical Plate To update the thickness of only the FEA Quad Objects on the vertical plate of the FEA plate model, the FEA Quads on the top & bottom plates will be hidden to remove them from the calculations. •

Execute Edit | Object Type | FEA Quads

•

Execute Edit | Select Objects | Selection Box.

•

Draw a selection box to enclose all of the FEA Quads on the vertical plate, as shown below

in the STR: FEA Plate Model window.

FEA Plate Model Showing FEA Quads Selected on Back Plate. •

Execute FEA | FEA Objects List in the STR: FEA Plate Structure window.

•

Right click on the Select column header and execute Invert Selection from the menu.

•

Double click on the Visible column in the spreadsheet, click on No in the dialog box that opens, and click on OK.

The FEA Quads on the top & bottom plates are now hidden and therefore will be ignored during FEA Model Updating.

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FEA Objects List Showing Hidden FEA Quads. 4. Check the Engineering Units FEA Model Updating requires the STR: FEA Plate Structure, SHP: FEA Modes and SHP: EMA Modes files have consistent engineering units. •

Check the Units column in the DOF spreadsheet in both the SHP: FEA Modes and SHP: EMA Modes windows to verify the shape units.

NOTE: (in/lbf-sec) are typical English units for UMM mode shapes. To change engineering units in a Shape Table, •

Double click on the Units column heading in the DOFs spreadsheet, enter different units (for example, m/N-sec) into the dialog box that opens, and click on OK.

•

Click on Yes in the next dialog box that opens, to re-scale the shapes to the new engineering units.

To check the engineering units of the FEA Plate Structure, •

Execute File | Structure Options in the STR: FEA Plate Structure window.

•

On the Units tab, select the Mass, Force, & Length Units that are consistent with the units in the Shape Tables, and click on OK.

In English Units, the dimensions of the Jim Beam are 12 inches long by 6 inches wide by 4.75 inches high. In Metric Units, the dimensions of the Jim Beam are 30.5 centimeters long by 15.25 centimeters wide by 12 centimeters high.

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Tutorial #15 - FEA Model Updating Calculating Solutions The FEA model, plus the FEA & EMA mode shapes are now ready to perform FEA Model Updating. Model Updating is done by evaluating and ordering a potentially large number of solutions over a userdefined solution space. •

Execute FEA | FEA Model Updating in the STR: FEA Plate Structure window.

•

Select SHP: FEA Modes in the FEA Shapes list and SHP: EMA Modes in the EMA Shapes list, and click on OK.

FEA Model Updating Shape Table Selection Dialog Box. The FEA Model Updating window (shown below) will open. It contains two spreadsheets separated by a red horizontal splitter bar. Upper Spreadsheet •

FEA modal frequencies are listed in the first column.

•

EMA frequencies are listed in the second column.

•

MAC value for each FEA & EMA mode shape pair is listed in the third column.

The first FEA mode (61 Hz) has no matching EMA mode. Mode pairs 2 through 6 have similar mode shapes, but the FEA frequencies are less than the EMA frequencies. Error Function The plate thickness solutions are ranked from Best to Worst according to a Solution Error function. The Solution Error function includes two terms for each pair of modes, 1. The difference between the Updated FEA & EMA frequency, for each selected mode pair. 2. If Yes is selected in the Include MAC column of the upper spreadsheet, then a second term (1 MAC value) is added to the Solution Error for each selected mode pair.

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FEA Model Updating Window Before Solutions are Calculated. NOTE: In this example, the thickness of the vertical plate should be increased in order to increase the frequencies of the FEA modes so that they more closely match the EMA frequencies. •

Select the 5 modes shown in the FEA | Model Updating window above to use these mode pairs in the Solution Error.

Lower Spreadsheet The lower spreadsheet lists the properties of all visible FEA Objects on the FEA model. Solution Space The solution space (over which solutions will be calculated) is user-defined in the lower spreadsheet. A solution space should be defined that surrounds the current property value, in this case the plate thickness value (0.375 in). In the lower spreadsheet, •

Enter 0.30 into the Property Minimum cell for Plate_1.

•

Enter 0.60 into the Property Maximum cell for Plate_1.

•

Enter 10 into the Property Steps cell for Plate_1.

•

Depress the Select Property button for Plate_1 to update this property during calculations.

Calculate Model Updating Solutions •

Execute Solution | Start Calculation in the FEA | FEA Model Updating window.

•

Click on OK to calculate 10 SDM solutions using plate thicknesses between 0.30 & 0.60 in.

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Tutorial #15 - FEA Model Updating

FEA Model Updating Window After 10 Solutions are Calculated.

Calculating Updated FEA Modes After all of the solutions have been evaluated, a Solution scroll bar will be displayed on the right hand side of the FEA Model Updating window. Solution Scroll Bar Each of the 10 solutions can be displayed by using the scroll bar on the right side of the window. •

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.

Graphics Display •

Execute Display | Bar Charts in the FEA | Model Updating window.

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Graphical Solution Display. Frequency Bar Chart The upper left bar graph shows two bars for each mode pair. •

The blue bar is the Percent Error between the FEA & EMA (Target) frequencies.

•

The green bar is the Percent Error between the Solution (Updated FEA) & EMA (Target) frequencies.

•

Hover the mouse pointer over each bar graph to display its numerical values.

It is clear from the bar graph that FEA model updating significantly reduced the percent error between the Updated FEA and the EMA frequencies, for the selected mode pairs. MAC Bar Chart The upper right bar graph displays MAC values using two bars for each mode pair. •

The blue bar is the MAC between the FEA & EMA mode shapes.

•

The red bar is the MAC between the Solution & EMA mode shapes.

•

Hover the mouse pointer over each bar graph to display its numerical values.

In this example, the MAC values changed very little, indicating that the mode shapes did not change. Lower Bar Charts The lower bar chart displays the Current & Solution values of the FEA properties. •

Hover the mouse pointer over each bar graph to display its numerical values.

Calculating Modes of the Updated Model

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Tutorial #15 - FEA Model Updating •

Drag the Solution scroll bar on the right side of the FEA Model Updating window to display the desired Solution.

•

Execute Solution | Save Solution in FEA Properties to save the property values as Updated properties.

•

Execute FEA | Calculate Updated FEA Modes.

•

Select SHP: FEA Modes in the dialog box that opens, and click on OK.

•

Click on Yes to continue the calculation, and save the new modes into a new Shape Table.

133

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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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.

136

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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Tutorial Volume IB - 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 138

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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Tutorial Volume IB - 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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Tutorial Volume IB - 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))

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Tutorial Volume IB - 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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Tutorial Volume IB - 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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Tutorial Volume IB - 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 Parameters Spreadsheet ... 29, 33

Add Object ......................................... 96

O

C

Object List .................................... 81, 96

Complex Exponential ......................... 29

P

D

Polynomial.................................... 29, 33

Damping ............................................. 25

R

F

Residue ........................................ 25, 33

FEA Object ................................... 93, 96

S

FRF .................................................... 57

Shape

G

Mode Shape ................. 25, 36, 39, 58

Grid .................................................... 81

Sound Power ...................................... 81

I

SPL .................................................... 81

Intensity .............................................. 81

Surface Area ...................................... 81

M Modal Frequency ......................... 25, 36

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