1  Introduction

Acoustic shields, screens or barriers are sometimes used as a means to reducing the noise from machines, engines or roads. When it comes to determining a mathematical model for an acoustic shield, the main property to take into account is that the shield is a thin structure and, because it is thin, its vibratory motion can become coupled to the acoustic field. Thus a shield is equivalent to a discontinuity in the sound pressure field and the shield contributes to the acoustic field through coupling. Because of its topology, the shield is termed a shell.
The traditional boundary element method (BEM) is only suitable for computing the acoustic field exterior to non-thin bodies [1-3]. One purpose of this paper is to extend the BEM for the solution of three-dimensional acoustic radiation problems, as considered in references [4-8], to acoustic-vibratory systems involving vibrating bodies and thin, acoustically coupled shells. This is brought about by first introducing an integral equation which unifies the direct boundary integral equation of Burton and Miller [9] - which reformulates the Helmholtz equation exterior to bodies only - and the integral equation given in Ben Mariem and Hamdi [10] and Warham [11] - which reformulates the Helmholtz equation exterior to shells only. The resulting equation is termed the boundary and shell integral equation, which is a reformulation of the Helmholtz equation exterior to a set of bodies and shells. On the application of an integral equation method, a numerical method termed the boundary and shell element method (BSEM) is derived.
The acoustic radiation model that is considered in this paper is that of a set of vibrating bodies and shells lying in an acoustic medium. The dynamic properties of the shells are governed by the linear equations of motion and they may be directly forced. In this paper the boundary and shell integral equation which governs the acoustic field is stated. It is shown how a particular BSEM can then be derived by approximating the surface of the bodies and shells by a set of triangles and by approximating the boundary functions by a constant on each triangle and then applying the classical technique of collocation. The in vacuo vibratory properties of each shield are assumed known. A Fortran library subroutine ABSEMGEN which is able to compute the properties of the three-dimensional acoustic field around a set of vibrating bodies and coupled shells is described. The results from applying ABSEMGEN to test problems having the general form of a cube with a vibrating face shielded by a square are given.