Finite Element Analysis of Structure-Acoustic Systems; Formulations and Solution Strategies

This thesis is concerned with the finite element analysis of the small-amplitude coupled vibration problem of an acoustic fluid enclosed in a flexible and/or rigid container structure. The governing equations for linear elastic solids and inviscid acoustic fluids are derived by a continuum mechanics approach. Modified equations for an acoustic fluid interpenetrating a rigid incompressible porous material are given.

The coupled structure-acoustic vibration problem is discretized by a finite element technique resulting in eleven formally equivalent symmetric and unsymmetric systems of equations. The advantages and restrictions connected to the use of various formulations are discussed with respect to the undamped problem. Suitable formulation found for the coupled analysis is then generalized to also incorporate various damping effects.

Non-modal reduction techniques that use a set orthogonolized load-dependent Krylov vectors are described and are successfully applied to proportionally or non-proportionally damped structure-acoustic problems. The basic idea is that, in the case of spatially invariant loading situations, the information of the loading distribution is used in a procedure where the original system of equations is transformed into a much smaller system without solving the corresponding eigenvalue problem.

Matrix-vector iteration schemes based on the Lanczos algorithm are used for the reduction of the symmetric systems of equations, whereas for the unsymmetric systems an iteration scheme based on the Arnoldi algorithm is developed. The applications of the Lanczos process and the Arnoldi process respectively to harmonic and transient analysis of structure-acoustic systems are new and are illustrated in numerical examples for both structural and fluid loading.