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.

本文首次考虑了嵌入多层多孔弹性介质中的刚性磁盘的垂直振动。整个介质位于具有有限深度的液层下面，以评估海底结构。针对层状多孔介质引入了扩展的反射和透射矩阵。借助Fourier和Hankel积分变换简化了控制微分方程。标量势函数用于解耦复数方程。通过定义各层之间合适的边界条件并求解方程，可以实现介质的格林函数。假设刚性磁盘的磁盘表面是一组具有相等位移的同心环。应用格林函数生成环的方程组。