Dynamic Green’s Functions for an Infinite Acoustic Field with Multiple Spheres Subjected to the Robin Boundary Conditions

Abstract

A semi-analytical approach is presented to solve three-dimensional dynamic Green’s function for an infinitely extended acoustic field with multiple spheres subjected to the Robin boundary conditions. The multipole expansions of the acoustic field induced by a time-harmonic point source are expanded with spherical wave functions. As an alternative to the complex addition theorem, the multipole expansion is computed in a straightforward way. By taking the finite number of terms, an algebraic system is constructed and is used to obtain Green’s function. This result of one sphere agrees with the available analytical solution. For the case of more than one sphere, the proposed results are verified by the numerical method such as the boundary element method (BEM). It indicates that the present solution is more accurate than that of the BEM and shows a fast convergence. Finally, the parameter study is performed to explore the influences of the exciting frequency of the point source, the surface admittance, the number and the separation of spheres on the dynamic Green’s functions. The proposed results can be applied to solve the acoustic scattering problems and to increase the application of boundary integral equation method in the way of numerical Green’s functions.