Radiation and scattering of acoustic waves from axisymmetric bodies in a half space using boundary element method

This paper presents a BEM (Boundary Element Method) formulation suitable for solving acoustic radiation and scattering problems involving axisymmetric bodies in a half space. The method is based on the Helmholtz Integral Equation wherein some modifications are introduced by taking advantage of the axisymmetric properties of the body in question. This work proposes some further development to the previous published papers involving axisymmetric bodies in that the present formulation includes the half space phenomenon. By using appropriate Green's function, the integral over the infinite plane is avoided. Then the integral consisting of the acoustic velocity potential and the half space Green's function is reduced to line integral over the generator of the body and an integral over the angle of revolution by virtue of the axisymmetric properties. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using simple Gaussian quadrature formula. The present formulation is also extended to include axisymmetric bodies mounted in an infinite baffle. A modified geometrical coefficient in the Helmholtz Integral Equation is presented in which the integration is simplified in the same way. Simplification proposed in this paper offers conveniency in the discretization scheme and reduces computing time compared to the three dimensional formulation. Test cases are shown involving spherical and cylindrical shape bodies in which comparison with analytical solution where available or three dimensional calculation is also demonstrated.