Teaching boundary element methods in acoustics

Abstract

The boundary element method (BEM) provides a powerful tool for the numerical solution of sound fields, because (1) it maps the domain equation on the boundary and thus reduces the problem dimension by one, (2) it provides a nonreflecting boundary on an arbitrary radiating surface, and (3) pressure, velocity, and intensity can be calculated at every field point from the boundary data. The author’s concept of teaching BEM in a graduate engineering course is to provide a link with subjects taught in undergraduate engineering mechanics such as rod vibrations, reciprocity principle, influence functions, and finite elements (FE). These subjects are generalized to the field equations of acoustics and elastodynamics. The associated integral equations are derived from the dynamic reciprocity principle. Their kernels are fundamental solutions which turn out to be influence functions of a full space. Boundary formulations of rods and beams recall well-known FE matrices. The fluid–structure interaction of interior and exterior acoustics is formulated by adopting the unsymmetric allocation approach of BEM and a symmetric hybrid BEM which is based on a multifield varational principle. Waves and vibrations in a flexible pipe and the sound radiation from a vibrating tire are treated as examples.