Analytical Solutions for Harmonic Wave Propagation in Poroelastic Media

Abstract

This paper presents several analytical solutions for problems of harmonic wave propagation in a poroelastic medium. The pressure‐solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. Then these equations are solved for several particular situations. Closed‐form analytical solutions are obtained for several basic problems: independent plane harmonic waves; radiation from a harmonically oscillating plane wall; radiation from a pulsating sphere; and the interior eigenvalue problem for a sphere, for the cases of both a rigid surface and a traction‐free surface. Finally, a series solution is obtained for the case of a plane wave impinging on a spherical inhomogeneity. This inhomogeneity is composed of poroelastic material having different properties from those of the infinite poroelastic medium in which it is embedded, and the incident wave may be composed of any linear combination of Biot “fast” and “slow” waves.