Acoustic scattering by a pair of poroelastic spheres

Abstract

An exact analysis for sound scattering by two interacting fluid-saturated porous-elastic spheres that are insonified by plane waves at arbitrary angles of incidence is outlined. The novel features of the Biot dynamic model for description of poroelastic material behaviour along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorem for spherical wave functions are employed to develop a closed-form solution in the form of infinite series. The prime objective is to investigate the dynamic poroelasticity effects on acoustic scattering and its associated field quantities. The analytical results are illustrated with a numerical example in which two identical water-saturated aluminium foam spheres are insonified by a plane wave at broadside and end-on incidence. The basic acoustic field quantities, such as the form function amplitude and the scattered far-field pressure directivity pattern, are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, and the proximity of the two spheres are examined. Limiting cases involving two rigid as well as two elastic spheres are considered and fair agreements with well-known solutions are established.