A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions

Abstract

This paper presents a simplified model of the Helmholtz integral equation for bodies with axisymmetric shape and boundary conditions. By taking advantage of a body’s axisymmetric properties, the surface integral is reduced to a line integral along the generator of the body and an integral over the angle of revolution. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using a Gaussian quadrature formula. The analytical formulation leading to elliptic integrals deals directly with the singularities in the Green’s function and its normal derivative. Examples are shown for scattering from a single sphere and two spheres and radiation from a finite cylinder. The results are compared with analytical, approximate, and other accepted solutions.