11 Improved Expansion Results Using Regularized Solutions 121 Table 11.4 Modal superposition parameters used with the coupled components model Overall properties Parameter Value Units Sample rate 4000 Hz Sample size 3000 Sample time 0.75 s Pulse length 0.005 s Pulse amplitude 10 lbf Fig. 11.19 Modal superposition schematic of the coupled components model and the response of the input force in the time and frequency domain adequate excitation up to 400 Hz to cover the first ten modes of the coupled components model (7–389 Hz), which were solely considered in the expansion process. The quality of the results was quantified by computing the TRAC of the expanded time responses with the reference time responses. The reference time responses correspond to the analytical time domain responses superimposed with the noise of the considered test case. The TRAC values of all DOF computed for each noise severity case is presented in Fig. 11.20. Inspecting the TRAC values of each test case for all DOF, the values exhibit a clear trend of decreasing TRAC value with increasing noise severity. Starting from the lowest severity of noise, the TRAC values of nodes 50 through 76 (mid-span of system beam A between the coupling points to subsystem beam B) and 143 through 184 (first 40 inches of subsystem beam B) are low. Lower TRAC values at the aforementioned nodes, as opposed to all other nodes, are likely due to the lack of instrumentation. The TRAC values have dropped below 0.9 for most nodes in component beam C by the third level of severity, and for most nodes in system beam A by the fourth level of severity indicating a poor correlation. The effects of noise on the expanded time domain responses are shown using node 202 as an example. Node 202 corresponds to the second to last node of the component beam C, shown in Fig. 11.21a. The results of the least severe noise case, case 1 with noise amplitude 0.005, are provided in Fig. 11.21b and the results of the most severe noise case,
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