SYMMETRIZATION OF THE CONTAINED COMPRESSIBLE-FLUID VIBRATION EIGENPROBLEM

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.