Acoustic Array Systems

Appendix

Acoustic Boundary Element Method

A.1 Introduction

The sound field at a spatial domain is determined from the source, scatterer, and boundaries inside or around the zone of concern. The source would be a vibrating object or a cloud of aerodynamic fluctuations. The scatterer might be an irregular body having rigid or flexible surfaces, and the reflecting boundary would change the phase of incident sound, absorbing some amount of sound and reflecting the rest. The Kirchhoff–Helmholtz integral equation provides the general solution of the sound radiation and scattering problems, which represents the sound field constructed by the monopole and dipole source distributions on a vibrating surface. The acoustic boundary element method (BEM) based on the Kirchhoff–Helmholtz integral formulation has been widely used to solve the radiation and scattering problems with irregularly shaped geometry, which has no closed form solutions in separable coordinates. Because the Kirchhoff–Helmholtz integral equation is solved on the boundary of the domain, there is a reduction in spatial dimensions by one compared with other numerical modal methods, such as finite element method (FEM) and finite difference method (FDM). This means that, for a three-dimensional sound radiation and propagation problem, boundary element modeling can be carried out only on the two-dimensional boundaries of the domain. Furthermore, for exterior problems of infinite extent, the discretization can be limited to the ...