Transient Finite Element Analysis of the Exterior Structural Acoustics Problem

Considerable progress has been made in the development of numerical methods for the time-harmonic exterior structural acoustics problem involving solution of the coupled Helmholtz equation. In contrast, numerical solution procedures for the transient case have not been studied so extensively. In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. In the fluid domain, a mixed two-field finite element approximation, based on a specialization of the Hu-Washizu principle for elasticity, is proposed and employs pressure and displacement potential as independent fields. Since radiation dissipation renders the coupled system nonconservative, a variational formalism based on the Morse and Feshbach concept of a “mirror-image” adjoint system is used. The variational formalism also accommodates viscoelastic dissipation in the structure (or its coatings) and this is considered in the paper. Very accurate results for model problems involving a single layer of fluid elements have been obtained and are discussed in detail.