An analytical approach for verifying BEM formulation involving acoustic radiation and scattering from a rigid sphere in a half space.

摘要

The solution of acoustic radiation and scattering in a half space has been well formulated using the Boundary Element Method (BEM). Problems in this class include the radiation of sound from vibration bodies near reflecting surfaces and the scattering of sound from objects in air that are in close proximity to rigid surfaces. The BEM solution uses a modified Green's function in the Helmholtz Integral formulation, which eliminates the discretization over the infinite plane. Hence the numerical approximation are confined to the body or obstacle. This is the main advantage of the BEM formulation for a half space. This paper presents an analytical approach for solving acoustic radiation and scattering in a half space for a rigid sphere to verify the BEM formulation. Firstly, the image of the sphere as well as the image of the field point are defined with respect to the infinite plane. Then, an ad hoc solution is assumed for the radiating sphere above the infinite plane. The ad hoc solution involves a constant and the distance between the center of the sphere to the field point and also the distance between the center of the image of the sphere to the field point.