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SUMMARYThe goal of this work is to examine the efficacy of interpolatory model order reduction on frequency sweep problems with many forcing vectors. The adaptive method proposed relies on the implicit interpolatory properties of subspace projection with basis vectors spanning the forced response of the system and its derivatives. The algorithm is similar to a recently proposed adaptive scheme in that it determines both interpolation location and order within the frequency domain of interest. The bounds of efficiency of the approach as the number of forcing vectors grows are explored through the use of rough floating operation counts. This, in turn, guides choices made in the adaptive algorithm, including a new technique that prevents excessive subspace growth by capitalizing on subspace direction coupling. In order to demonstrate the algorithm's utility, a series of frequency sweep problems drawn from the field of structural acoustics is analyzed. It is demonstrated that increased order of interpolation can actually degrade the efficiency of the algorithm as the number of forcing vectors grows but that this can be limited by the subspace size throttling procedure developed here. Copyright © 2014 John Wiley & Sons, Ltd.

This paper outlines a strategy for identifying and exploiting the lack of dynamic coupling between potential modifications to a vibroacoustic system. Often a designer develops a set of modifications and wishes to determine those that perform the best relative to some metric, in particular, we consider performance metrics that rely on the steady state forced response of the structure over a frequency band of interest. In this case, the effects of coupling are shown to appear as a force residual and therefore may be neglected if sufficiently small. When modifications are uncoupled from one another, the computational cost of analyzing all possible modified systems can be greatly reduced. For example, if up to 4 of 7 potential modifications are allowed to be applied to a system, there are 98 possible modified systems that need to be analyzed to determine the optimal combination. However if all of the modifications are found to be uncoupled, then only seven modified systems need to be analyzed to generate the results for all possible modified systems. An example problem demonstrates the benefits of uncoupling between modifications.

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