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

Abstract

In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. 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 specified 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 densities, the second-part solution is 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 semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.

Formulation and accuracy of On-Surface Radiation Conditions for acoustic multiple scattering problems

“…Consequently, the physics emerging from such global phenomenae present some specific and unusual behaviors. Various numerical techniques [1,2,9,14,15,20,26,27,30,32,36,53] can be considered for predicting the multiple scattering behavior of a complex configuration. One possible approach is based on rigorous integral equation formulations.…”

µ-diff: A matlab toolbox for multiple scattering problems by disks

“…Multiple scattering is known to be a very complicated and challenging problem in terms of computational method [1,2,3,7,8,16,22,23,28,30,36,51] since the incident wave is multiply diffracted by all the single scatterers involved in the geometrical configuration. As a consequence, the scattered wavefield has a highly complicated structure and exhibits some particular physics properties.…”

Multiple scattering of an acoustic wave from a network of cylindrical rods encased in a solid viscoelastic medium

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