ME scope Application Note 18 Simulated Multiple Shaker Burst Random Modal Test

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1 ME scope Application Note 18 Simulated Multiple Shaker Burst Random Modal Test The steps in this Application Note can be duplicated using any Package that includes the VES-4600 Advanced Signal Processing and VES-700 Multi-Channel Acquisition options. Click here to download the ME scope Project file for this App Note. INTRODUCTION In this Application Note, you will use the Multiple Input Multiple Output (MIMO) calculation and data acquisition features of ME scope to simulate a modal test using two shakers driven with burst random signals. The dynamics of the structure under test will be modeled using a modal model. This exercise will simulate a shaker test using 2 uncorrelated random signals and an ME scope acquisition window with 101 data acquisition channels.the following steps will be carried out in this exercise 1. Synthesize two burst random force time-domain waveforms using the File New Data Block command 2. Use the Data Block with the burst random signals together with the modal model of Jim Beam in the Transform MIMO Outputs command to calculate 99 forced response time-domain waveforms for the Jim Beam structure 3. Use the Acquisition window to "acquire" the time-domain force & response time-domain waveforms from a Data Block file, and calculate multiple reference FRFs, Multiple Coherences, and Partial Coherences 4. Curve fit the multiple reference FRFs and compare MAC values between the resulting mode shapes and the modes of the original modal model MODAL MODEL Click on this link and open the AppNote18.VTprj Project file for this App Note This Project file contains the structure file, STR: Colored Jim Beam, for animating mode shapes from the Shape Table, SHP: Mode Shapes. Notice that the Shape Table has 10 modes in it, ranging in frequency from 165 Hz to 1550 Hz. Each mode shape has 99 DOFs that define the resonant deformation of the structure in three directions (X, Y, Z) at 33 Points. Also, the mode shapes are scaled to Unit Modal Masses (UMM). This constitutes a modal model, which defines the dynamics of the structure, between any two DOFs where mode shape components are defined. This modal model is a truncated dynamic model since it only includes the first 10 (lowest frequency) modes of the structure. The real Jim Beam structure, which is made out of three aluminum plates attached together with 6 screws, has many more modes above 2000 Hz. Nevertheless, it is assumed that these 10 modes will adequately represent the dynamics of the structure from 0 to 2000 Hz. Page 1 of 15

2 A mode shape of the Jim Beam Structure FORCED RESPONSE SHP: UMM Mode Shapes of the Jim Beam To calculate the forced response of the structure, two burst random force time-domain signals will be synthesized using the File New Data Block command. The forces will be applied to Points 5 & 15, the two corners of the top plate, in the vertical (Z) direction. Then, the Transform MIMO Outputs command will be executed in the Data Block window with the force waveforms in it. The forces, together with the modal model for the Jim Beam, will be used to calculate the forced response of the Jim Beam. The modal model will be used to synthesis FRFs between the shaker excitation DOFs and 99 outputs (response DOFs) of the structure. The synthesized FRFs with then be multiplied by the Fourier spectra of the two excitation forces (inputs) to obtain the Fourier spectra of the 99 responses (outputs). Finally, the response spectra will be Inverse Fourier transformed to yield the forced response time-domain waveforms of the structure. CREATING THE BURST RANDOM EXCITATION SIGNALS Burst random excitation signals are ideal for modal testing large structures using multiple shakers because both the acquired force and response signals are completely containing within their sampling window time-period T. Page 2 of 15

3 Hence, the FRFs calculated from these signals are leakage free, and do not require any special time-domain windowing (such as a Hanning window). Furthermore, burst random excitation can be combined with spectrum averaging to reduce the effects of extraneous noise and non-linearities from the FRFs. FRFs calculated from burst random excitation and spectrum averaging are a best linear approximation of the dynamics non-linear real world structures. A set of these FRFs is more suitable for curve fitting using linear FRF-based curve fitting methods. A burst random signal is the same as a pure random signal, but it is shut off prior to the end of the sampling window time T. This is done to allow the damped response of the structure to decay to near-zero before the end of the sampling window. Therefore, when burst random excitation is used, both the excitation and response signals will be completely contained within the sampling window time-period T. To create a Data Block with the two burst random force time waveforms in it Execute Animate Draw in the Structure window to terminate the animation Execute File New Data Block in the ME scope window. A dialog box will open Enter the following parameters into the dialog box, Block Size: 2000 samples Fmax: 2000 Hz Pre Trigger Delay (Samples): 10 Number of Averages: 50 On the Random tab, enter, Number of M#s: 2 RMS Magnitude: 1 Burst Random Width (%): 60 Click on OK and enter Burst Random Forces in the dialog that opens A new Data Block window will open with the two burst random signals in it. Use the Display Zoom command in the Data Block window to display the random signals as shown below Page 3 of 15

4 Zoomed Data Block Window Showing 2 Burst Random M#s. Since 50 averages were specified, each M# contains 50 unique burst random signals arranged one after another. Each burst random signal is 2000 samples long, and is defined over a sampling window period of T = 0.5 seconds. With 50 burst signals in succession, there are 100,000 samples in each M#. You can check this with the File Data Block Properties command. Each random burst will excite the structure differently, so averaging 50 response spectra together will average out any noise and non-linearities, leaving only linear, noise-free spectra. A burst random width of 60% means that the signal is shut off at 60% of T, or 0.3 seconds. A burst random width should be chosen to ensure that the structural response has decayed to near zero in T = 0.5 seconds. We will see that this burst random width will ensure that the responses of the Jim Beam structure have decayed sufficiently in 0.5 seconds. The response decay is a function of the modal damping. The mode with the lightest amount of damping will dictate how quickly the response decays to near-zero. Rule of Thumb: Structural response decay is near-zero when its amplitude is 1% or less of the peak response amplitude in the burst random response. Next, the DOFs and units of the force signals must be defined. Click on the M#s spreadsheet cell for (M#1) and enter 5Z for its DOF Click on the M#s spreadsheet cell for (M#2) and enter 15Z for its DOF Double click on the Units column heading. In the dialog box that opens, choose lbf from the drop down list, and click on OK and No to change the units to force units Double click on the Input Output column heading. In the dialog box that opens, choose Input from the drop down list, and click on OK to designate each force as an Input to the structure MIMO model. With these changes, two 1-lbf RMS forces will be applied to the structure, one at 5Z and the other at 15Z. DIFFERENTIATING THE MODE SHAPES To simulate a real-world shaker test, the responses should be calculated in acceleration units. The UMM mode shapes in SHP: Mode Shapes have displacement units associated with them. To differentiate theses mode shapes to acceleration units, first they must be re-scaled to Residue mode shapes. Execute Tools Scaling UMM to Residue Shapes in the SHP: Mode Shapes window Hold down the Ctrl key and select both 5Z and 15Z in the dialog box that opens, and click on OK Page 4 of 15

5 Click on New File in the next dialog box, and enter "Residue Mode Shapes" in the following dialog box Execute Tools Differentiate twice in the SHP: Residue Mode Shapes window Double click on the Units column in the lower spreadsheet in SHP: Residue Mode Shapes, and enter g/lbf-sec in the dialog box as shown below Click on Yes in the next dialog box to re-scale the residues to acceleration units. The forced responses of the structure can now be calculated in acceleration units using the residue mode shapes. CALCULATING THE FORCED RESPONSES To calculate the forced responses, Execute Transform MIMO Outputs in the BLK: Burst Random Forces window. Verify that BLK: Burst Random Forces is listed under Inputs, and that SHP: Residue Mode Shapes is selected under Transfer Functions as shown below Page 5 of 15

6 Click on Calculate Click on the New File in the next dialog, enter Burst Random Responses, and click on OK Burst Random Responses. A new Data Block window will open displaying 99 M# forced responses. Use the Display Zoom command in the BLK: Burst Random Responses window to display the M#s more clearly From the responses, it is clear that shutting off the burst random signals at 60% of each sampling window length was sufficient to allow the structural response to decay to near-zero before the end of each sampling time (T = 0.5 seconds). Next, the response time waveforms will be merged with the force waveforms in a single Data Block called BLK: Simulation. Then, using an Acquisition window, data will be "acquired" from BLK: Simulation to simulate multi-channel acquisition from actual front-end hardware. To save the force signals into a new Data Block, Execute M#s Copy to File in the BLK: Burst Random Forces window In the dialog box that opens, click on New File, enter Simulation in the dialog box that opens, and click on OK Execute M#s Paste from File in the BLK: Simulation window Page 6 of 15

7 In the dialog box that opens, select Burst Random Responses, and click on Paste SIMULATED DATA ACQUISITION Data acquisition from a multi-channel acquisition front-end will now be simulated by acquiring 101 channels of time domain data from the BLK: Simulation window. To acquire the data: Execute File New Acquisition in the ME scope window, and click on OK in the dialog box that opens. A new (empty) Acquisition window will open. Execute Acquire Connect to Front End in the Acquisition window. Select Data Block file, and click on OK Select BLK: Simulation in the next dialog box, check Configure Acquisition from source, and click on OK After the Acquisition window has been connected to the BLK: Simulation window, the Channels spreadsheet will list 101 channels, corresponding to the 101 M#s in the BLK: Simulation Data Block. Also, the properties of the M#s in BLK: Simulation will have been copied into the Channels spreadsheet On the Sampling tab, change the Number of Samples to 2000 and set Averages to 50 On the Measurement tab, check FRF (Transfer Function) and Coherence The Acquisition window is now ready to acquire 50 averages of data from BLK: Simulation and calculate multireference FRFs, together with Multiple & Partial Coherences for the 99 responses caused by the 2 excitation forces. Page 7 of 15

8 Acquisition Window Setup to Acquire 50 Averages. Compare the time and frequency sampling parameters on the Sampling tab with those used to create the Data Block with 2 force M#s. These parameters should be the same as those used to create the Burst Random forces. In this simulation, there is no need to trigger on an input signal. Each excitation burst and the resulting responses will be properly acquired because each acquisition window of 2000 samples has the same length, T = 0.5 sec. Notice in the Window column of the Channels spreadsheet that all channels are using a Rectangular window. This is the default time domain window. It is also called a Uniform, None or Boxcar window. NOTE: A Rectangular window does not alter the time domain data before it is transformed with the FFT. To acquire the multi-channel data Execute Acquire Start in the ACQ: Acquisition 1 window As the data is acquired, the number of averages is displayed on the Toolbar. The acquired time waveforms are displayed in the upper graphics area, while the calculated FRFs & Coherences are displayed in the lower graphics area. When 50 averages of data have been acquired, the display on the Toolbar will display Front End Ready. Notice that a total of 495 FRFs & Coherences have been calculated. To sort the M#s by DOF: Right click on the lower graphical area, and execute M# Sort from the menu In the dialog box that opens, make the selections shown below and click on Sort Page 8 of 15

9 To display all of the measurements associated with each response DOF of the structure Right click on the lower graphical area, execute Format Strip Chart from the menu, and select (5) from the drop down list. The following 5 M#s will be displayed for each Roving DOF 2 FRFs between the Roving DOF and each force (Input) DOF 1 Multiple Coherence function 2 Partial Coherence functions between the Roving DOF and each Reference (force) DOF. Multiple Coherence measures how much of the measured response is linearly related to (correlated with or caused by) the two measured forces. A value of 1 indicates that each response is completely correlated with the two forces. Since the responses were calculated from the two forces using 10 mode shapes, the responses are perfectly correlated with the forces. Each Partial Coherence measures how much of a measured response is due to each of the measured forces. The sum of the Partial Coherences is always close to 1 for each frequency. Notice that, for each frequency, if the FRF from one reference has a very high value and the FRF from the other reference has a low value, the Partial Coherence corresponding to the FRF with high value will be high while the Partial Coherence corresponding to the other FRF has a low value. This is indicating that force is more easily applied to a structure at DOFs and frequencies where the structure has a larger response (it is more compliant) than at DOFs and frequencies where it is very stiff and less compliant. CURVE FITTING THE FRFS In order to curve fit the multi-reference FRFs, they must be saved into a Data Block file. Right click on the lower graphical area of the Acquisition window, and execute M# Select Select By from the menu In the dialog box that opens, make the selections shown below and click on Select Page 9 of 15

10 Right click on the lower graphical area of the Acquisition window, and execute Tools Save M#s As from the menu In the dialog box that opens, click on the New File button, enter "Multi-Ref FRFs" in the next dialog box as shown below, and click on OK The new Data Block should have 198 FRFs in it, 99 Roving DOFs paired with Reference DOF 5Z and 99 Roving DOFs paired with Reference DOF 15Z Page 10 of 15

11 To curve fit the FRFs, Right click on the graphical area of the BLK: Multi-Ref window, and execute Curve Fitting from the menu When Curve Fitting is enabled in a Data Block window the following four areas are displayed 1. The FRFs in the upper left graphics area 2. The Mode Indicator function in the lower left graphics area 3. The Curve Fitting tabs on the upper right 4. The Modal Parameters spreadsheet on the lower right Select Multiple Reference CMIF on the Mode Indicator tab as shown below Right click on the graphical area of the BLK: Multi-Ref window, and execute Curve Fit Quick Fit from the menu Multi-Reference curve fitting will be performed on the FRFs. When it is completed, modal parameter estimates will be displayed in the Modal Parameters spreadsheet, and a red Fit Function will be overlaid on each FRF. Use the vertical scroll bar on the right of the FRF graphics to scroll through the FRFs and their modal parameters Press the Save Shapes button on the Residue, Save Shapes tab, to save the modal parameters into a new Shape Table file In the dialog box that opens, click on the New File button, enter "Multi-Ref Mode Shapes" in the next dialog box as shown below, and click on OK Page 11 of 15

12 COMPARING MODE SHAPES The Multi-Ref mode shapes can be compared with the original UMM mode shapes in two ways 1. Displaying MAC or SDI bar charts between the two Shape Tables 2. Displaying correlated shape pairs in Comparison animation MAC Comparison Right click in the spreadsheet area of the SHP: Multi-Ref Mode Shapes window, and execute Display MAC from the menu In the dialog box that opens, select SHP: Mode Shapes as shown below, and click on OK The M# selection box will open in which you can select a Reference DOF (5Z or 15Z) and display the MAC bar values between the two Shape Tables. All of the diagonal bars have values of "1", indicating that each of the 10 multi-reference mode shapes correlates perfectly with each of the original UMM mode shapes. MAC measures the co-linearity of a pair of mode shapes. MAC = 1 means that the two mode shapes are linearly dependent, that is they both lie on the same straight line. Page 12 of 15

13 Repeat the above steps but execute Display SDI instead All of the SDI bars have values at or close to "0". SDI measures the difference between a pair of mode shapes. SDI = 1 means that the two mode shapes are components with equal values. SDI = 0 means that two mode shapes have components with different values. Animated Shape Comparison To compare the Multi-Ref mode shapes with the original UMM mode shapes in animation, Right click in the M#s spreadsheet area of the SHP: Multi-Ref Mode Shapes window, and execute M#s Select Select None from the menu Right click again in the M#s spreadsheet area of the SHP: Multi-Ref Mode Shapes window, and execute M#s Sort By from the menu Make the selections in the dialog box that opens as shown below Close all windows except STR: Colored Jim Beam, SHP: Multi-Ref Mode Shapes and SHP: Mode Shapes Page 13 of 15

14 Right click again in the graphics area of the STR: Colored Jim Beam window, and execute Draw Compare Shapes from the menu Execute Windows Arrange Windows For Animation in the ME'scope window Select any shape in the SHP: Multi-Ref Mode Shapes window to display its corresponding shape in the SHP: Mode Shapes window with the Maximum MAC value Page 14 of 15

15 CONCLUSIONS A two-shaker 101-channel modal test was simulated by acquiring time domain force and response signals from a Data Block file using an Acquisition window. The forced responses (Outputs) were calculated using the Transform MIMO Outputs command and the following data 1. Two synthesized uncorrelated burst random excitation forces (Inputs) 2. A modal model of the Jim Beam with ten scaled Residue mode shapes having acceleration numerator units The simulated force & response time waveforms were acquired from a Data Block by the Acquisition window, and multiple reference FRFs, plus Multiple & Partial Coherences were calculated using 50 averages. The multiple reference FRFs were then curve fit, and the resulting mode shapes compared with the original UMM mode shapes using in the simulation. The mode shapes resulting from curve fitting the FRFs were nearly identical to the original UMM mode shapes. These results verify that a multiple shaker modal test using burst random excitation yields leakage free FRFs that preserve the linear dynamic properties of a structure. The Multiple Coherences were all at or near a value of 1, indicating that the measured responses were linearly related to the measured forces at all frequencies. In this case, there were no other unmeasured forces or extraneous noise contributing to the measured responses. The two Partial Coherences (one for each force Input) summed to values at or near 1 for all frequencies, again indicating that the measured forces were linearly related to the measured responses. The Partial Coherences further showed the percentage of each force that caused each response as a function of frequency. Page 15 of 15