FINITE-ELEMENT SOLUTION OF THE TRANSIENT EXTERIOR STRUCTURAL ACOUSTICS PROBLEM BASED ON THE USE OF RADIALLY ASYMPTOTIC BOUNDARY OPERATORS

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 we propose a finite element formulation 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 is proposed and employs pressure and displacement potential as independent fields. The variational statement of the interaction problem is developed from a Hamiltonian approach, thus allowing specialization to different alternative formulations. 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. Accurate results for model problems involving a single layer of fluid elements have been obtained and are discussed in detail.