Modal reduction for exterior acoustic and vibroacoustic problems

Abstract

Modal analysis, mode superposition and modal reduction are considered standard approaches for interior acoustic problems as well as for pure vibration problems. Things are different for exterior problems. Only a few methods are known to formulate a linearized eigenvalue problem for unbounded acoustic problems. Even fewer techniques on modal superposition and reduction are found in the literature. This talk will review such techniques which are either based on conjugate Astley-Leis infinite elements or on boundary elements for the unbounded region. While the results appear to be promising, a number of open questions need to be solved in this context. Among others, it is yet unclear which modes are actually required for a modal reduction and how to find a method to just evaluate these modes and the related eigenvalues. The situation is different for vibroacoustic radiation problems with clear resonances. In such cases, a modal reduction is able to substantially accelerate the solution process. Future work might lead to modal reduction using modes from non-linear eigenvalue problems which are known from the numerous papers on the boundary element methods published over the last decade.