ME'scopeVES Application Note #15 - Multi-Reference Curve Fitting to Find Closely Coupled Modes

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App Note #15

www.vibetech.com

25-Feb-14

ME’scope Application Note #15 Multi-Reference Curve Fitting To Find Closely Coupled Modes INTRODUCTION In this note, the VES-4500 Multi-Reference Modal Analysis Option will be used to estimate the modal parameters of two closely coupled modes in a plate structure. Closely Coupled Modes: A structure is said to have two or more closely coupled modes is they are represented by only one resonance peak in a set of FRF or spectral data. In this note, the mode shapes of two closely coupled modes of a rectangular plate will be identified from a multireference set of FRF measurements. The plate, shown in the Figures below, is made of Poly Vinyl Chloride (PVC). The two Figures show the operating deflection shape (ODS) of the plate at 190 Hz, when displayed from two different Reference DOFs, 7Z and 35Z. These two ODS’s are clearly different!

A 2-reference set of FRFs can be used to identify 2 closely coupled modes, if there are any. But, the first question to ask is, “How do we know if the structure has any closely coupled modes?” This question can be answered by displaying the operating deflection shapes (ODS’s) from each reference DOF in animation. The animated shape capability of ME’scope will be used to discover the first evidence of closely coupled modes. Property of Mode Shapes: All mode shapes are inherent properties of a structure. This means that they do not depend on the Reference DOFs used to acquire a multireference set of FRFs. ME’scope displays in animation the ODS data at the cursor position in a Data Block of FRFs. If the structure is “lightly damped”, the ODS is a close approximation of a mode shape when the cursor is placed at a resonance peak. Using the above property of mode shapes, the ODS should not change if displayed from one Reference DOF versus another in a multi-reference set of FRFs. If the ODS at a resonance peak does not change when displayed from different references in a multi-reference set of FRFs, this is a strong indication of a single mode. If on the other hand, the ODS is different when displayed from different references, this is an indication of closely coupled modes.

Figure 1. 190 Hz ODS From Reference 7Z.

Figure 1 shows the ODS at 190 Hz from the FRFs from Reference 7Z. Figure 2 shows the ODS at 190 Hz from the FRFs from Reference 35Z. Clearly, these are different shapes, indicating the ODS is not dominated by a single mode, hence it must the summation of contributions from closely coupled modes. Another clue that the ODS is not dominated by a single mode is that 190 Hz is the lowest frequency resonance on the structure. In almost all cases, the fundamental (lowest frequency) mode of a structure is the first bending or first torsional mode. These two modes have very simple mode shapes, unlike the ODS shown in Figure 1 & 2.  Open App Note 15 - Closely Coupled Modes.VTprj from the ME’scope\Application Notes folder. This Project contains a Structure file with the plate model, and a Data Block with 70 FRFs that were acquired from the plate.

Figure 2. 190 Hz ODS From Reference 35Z.

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