Boundary integral solutions of three dimensional acoustic radiation problems

Abstract This paper is concerned with the development of a procedure for generating the sound fields radiated by arbitrarily shaped, three dimensional bodies from an integral representation of the solutions of the Helmholtz equation. The method of Burton and Miller is employed to eliminate the non-uniqueness in the external Helmholtz formulae which occurs at the internal eigenfrequencies of the geometry under consideration. Also, a representation of the most singular component in the Burton and Miller formulation is developed resulting in an integral equation which is amenable to numerical solutions. A simple numerical scheme is introduced which reduces the large amounts of computer storage and time normally required for the solution of similar problems. This numerical scheme is then used to obtain solutions for the radiated sound field generated by a vibrating piston set in a sphere. The numerical solutions for the surface and far field sound patterns are compared with exact analytical solutions and deviations of 10% at most are noted. Since the symmetry of the sphere was not taken advantage of in these computations, the numerical schemes employed are applicable to general three dimensional sound radiation problems.