13 Expansion Methods Applied to Internal Acoustic Problems 145 Fig. 13.5 Time expansion shown as time histories at the two expanded b-set DOF Fig. 13.6 Time expansion shown as PSDs at the two expanded b-set DOF (PSD) of that time response, in Fig. 13.6. Using either metric, the expanded response of the two b-set DOF in this acoustic domain match very well with the actual response, indicating that SEREP is a useful method for acoustic expansion of not only mode shapes, but transient responses as well. A typical artifact of mode-based expansion methods is mode truncation errors that are caused by not including enough modes in the mode shape matrices used to make the SEREP transformation matrix. The effects of mode truncation are demonstrated in Fig. 13.7 where just three modes were used to populate the transformation matrix. This is exactly the expected behavior, with the expanded response matching well at low frequencies and not as well at higher frequencies. The results from SEREP expansion of the acoustic response in terms of modes and time responses show that SEREP is effective for internal acoustic problems as well as structures. While this isn’t surprising, it is useful to see the technique demonstrated with this atypical application in mind. Just like with structural system expansion, acoustic system expansion is sensitive to problem setup considerations such as mode truncation, as demonstrated here, and also factors such as a-set DOF and mode selection. For systems with a small number of active modes, such as some automobile cabins or small rocket payload sections, this expansion technique could be effective in generating full-field responses from a small number of measurements.
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