than or equal to 5 %. Third, the magnitudes of the launcher tip frequency responses of the simulated and experimentally determined data are compared to assess how closely the two match one another in terms of the location and amplitude of the dominant peaks. This assessment is mostly qualitative, because the model is not capable of capturing all of the real dynamic behaviors of the structure and other spurious behaviors introduced by non-physical phenomenon (i.e., noise) that are evident in an experimentally determined dataset. However, if the dominant modes identified from the experimental data are well represented in the model (i.e., MAC numbers near unity), the model does not introduce significant spurious modes, and the appropriate levels of damping are included in the FE model, then the frequency response of the FE model simulated data should be very close to the frequency response derived from experiment. This indicates that in the area of interest, the model is a good approximation of the real system. An underlying assumption with this modal correlation procedure is that launch vehicle tip-off rates are largely a function of the launcher rail tip dynamics. It is possible that there may be additional locations other than the rail tip where it will be necessary for a dynamic launcher FE model to accurately simulate the experimental frequency response. If other such locations are identified, the frequency response of these areas will be considered as criterion in the modal correlation procedure. Figure 14.8 shows the frequency response at the launcher tip for both a poor and well-correlated model. 14.10 Modal Correlation Results After several cycles of updating and comparing the FE model results to the experimentally derived parameters, overall correlation can be achieved. Table 14.2 shows the resonance frequencies derived from the experimental and simulated datasets, the MAC numbers, and percent frequency error for each mode. The simulated data are generated from the most recent iteration of the correlated launcher FE model. The results in Table 14.2 show that of the 22 experimentally derived mode shapes, 17 of the modes derived from the FE model can be correlated to test data (i.e., MAC number greater than 0.75). The launcher model does not correlate the fundamental 2.36-Hz rail mode, although that is likely the result of problems with noise in the experimental dataset in the “near-DC” frequency range and not model error. It is encouraging that the frequency error associated with this mode appears to be very small. Of the 17 correlated modes, 10 show frequency errors at or below 5 %. Also, of the 22 experimentally derived modes, only 2 could not be correlated to modes derived from the FE model. As detailed previously, after an analysis of the baseline frequency response is completed, the model is updated and then re-evaluated until the modal correlation criteria are met. In the context of the current work, the launcher has undergone four such iterations, and the rail tip frequency response of the most recent model is shown in Fig. 14.9. Figure 14.9a shows the frequency response in the rotated Y direction to a strike at P01. The dominant peaks in the experimental data occur at 5.5, 13, 17, 58, and 93 Hz, and the simulated response aligns well with the actual response. Fig. 14.8 Frequency response magnitude at the launcher tip of (a) poorly correlated model and (b) a well-correlated model 14 A Novel Method to Correlate a Rocket Launcher Finite Element Model Using Experimental. . . 163
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