Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

Abstract

In this paper, we employ the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from a point sound source. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free-space fundamental solution. The other is a typical boundary value problem (BVP) with boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null-field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier boundary densities, the second-part solution can be easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semi-analytical solution of the Helmholtz problem. An example was demonstrated to validate of the present approach. The parameters of size and spacing between cylinders are considered. The results are well compared with the available theoretical solutions and experimental data.