Rigid disc vibration in a multi-layered transversely isotropic poroelastic half-space underlying a liquid layer

Abstract

Vertical vibration of a rigid disk embedded in a multi-layered poroelastic medium is considered in this paper, for the first time. The whole medium is underlying a liquid layer with finite depth to evaluate the submarine structures. Extended reflection and transmission matrix are introduced for layered porous media. The governing differential equations are simplified by virtue of Fourier and Hankel integrals transformations. Scalar potential functions are used to decouple the complex equations. By the definition of the suitable boundary conditions between layers, and solving the equations, the Green's functions of the medium can be reached. The disk surface of the rigid disk is assumed as a set of the concentric rings with equal displacements. The Green's functions are applied to generate the set of equations of the rings. The accuracy of the proposed method is sensitive to determine the number of the rings which make the surface of the disk.