Symmetrization of the contained compressible‐fluid vibration eigenproblem

Abstract

This paper studies the symmetrization of the problem of coupled vibrations of an acoustic fluid enclosed in an elastic container. The container structure is discretized by a displacement finite element formulation and the acoustic fluid by a displacement‐potential formulation. The vibrations of this physically conservative coupled system are governed by an unsymmetric algebraic eigenvalue problem. Eight equivalent symmetric forms of this problem are exhibited. The fluid‐pressure formulation leads to a similar unsymmetric eigenproblem, which in turn can be converted to another eight equivalent symmetric forms.