3 Using Hybrid Modal Substructuring with a Complex Transmission Simulator to Model an Electrodynamic Shaker 33 Fig. 3.12 Prediction vs. truth drive point FRF at the beam tip assembled structure. Reference [12] provides several checks and criterion for determining a viable mode selection. In the current work, the first 54 modes of the experimental subsystem were used, spanning from 0 to 5000 Hz. For the TS, the first 35 modes were used, which corresponds to the number of FEM modes up to 6500 Hz. These were the FEM modes of the TS that were found above to agree very well with experiment. The analytical subsystem (TS plus beam) was represented by its first 48 modes, which spans 0–6700 Hz. This was chosen so that the TS and analytical models were roughly removing and then adding the same range of dynamic information. The resultant natural frequencies and mode shapes of the hybrid structure predicted by the TSM were used to reconstruct drive point FRFs for easy visual comparison with the truth data. It should be noted that, for this work, damping was not accounted for in the FEMs, and thus zero damping is predicted. For the FRF reconstruction, a damping ratio of .25% was applied to all modes. Figure 3.12 shows a comparison between the predicted and truth drive point FRFs at the tip of the beam in the vertical direction. The transmission simulator method has successfully transferred in the first three cantilever beam modes in this direction, as given by the three large modal peaks in the FRFs. These predicted modes are quite accurate with respect to frequency out to around 3000 Hz, after which the results vaguely resemble the truth data, but are inaccurate. Figure 3.13 shows the predicted and truth drive point FRFs at the top left corner of the half cube, next to the beam. As with the beam tip, the prediction is quite accurate and is in good agreement with the truth data. The results again become somewhat less accurate past 2500 Hz. This shows that the dynamics of the half cube were successfully preserved through the substructuring process and that complex transmission simulators can be handled quite effectively. 3.7 Conclusion A framework for implementing the transmission simulator method on an electrodynamic shaker has been applied to a system containing a complex transmission simulator. It was shown that a cantilever beam, representing a mock test article, could be assembled onto a relatively complicated half cube shaker fixture, the TS, while preserving the dynamics of the half cube in the process. This was done by first creating FEMs of each subsystem and utilizing Effective Independence to determine an efficient set of roving hammer points to collect experimental modal data. From the steps laid out in previous work, the experimental and FEM data was passed through CMS to produce a prediction for the built-up system of the shaker, half cube, and the beam. When compared to truth data, the results were shown to be accurate out to near 3000 Hz. Thus, the predictions are quite good in the target range for this shaker, in that the dynamics of the half cube have been preserved while the beam has been successfully coupled onto the half cube.
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