12 Expansion of Coupled Structural-Acoustic Systems 135 Fig. 12.4 Representative acoustically-dominated mode (mode 38, 1969 Hz) response is essentially nonexistent, so the addition of noise masks the insignificant acoustic response. When expansion is performed, noise is being expanded, so the compared acoustic responses are not expected to look the same. The acoustic-dominated mode 38 expansion is shown in Fig. 12.7, with the major contributors to the mode highlighted. The imaginary acoustic expansion (the dominant response in this mode) matches closely with the actual mode in shape and magnitude. The expanded real portion of the structural mode is also a fairly close match to the real structural response, with some slight differences in amplitude. The expanded imaginary structural response and the expanded real acoustic response do not look similar to their counterparts. However, again this is likely due to the small, insignificant response values that were poorly expanded in the presence of noise. The coupled mode 66 expansion is shown in Fig. 12.8, with the major contributors to the mode highlighted. The expanded real portion of the structural mode is very similar to the real structural response. The expanded imaginary acoustic response is similar to the actual imaginary acoustic response, with some differenced around the center of the cylinder. These differences could be due to mode truncation. Although more acoustic than structural modes were included in the expansion, the coupled mode is fairly high in frequency, and the mode set used for expansion might not span the space of the acoustic response. Again, the very small valued portions of the expanded mode (imaginary structural response and real acoustic response) did not closely resemble the actual mode. Overall, the coupled expansion was shown to be a success for the dominant portions of the mode shapes. Expansion using complex modes generated from the QEVP solver was able to be used in traditional SEREP equations. However, some of the
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