Vertical time-harmonic coupling vibration of an impermeable, rigid, circular plate resting on a finite, poroelastic soil layer

Abstract

Studies associated with dynamic plate–medium interactions generally assumed the plate structures to be permeable for the sake of convenience. But the effect and applicability of such an assumption are still unclear, and then the pore fluid pressure on the plate and medium interfaces cannot be obtained. In this paper, the mentioned problems are discussed by studying the coupling steady-state vibration of an impermeable, rigid, circular plate resting on a finite, fluid-saturated, poroelastic soil layer underlain by rigid base and subjected to a vertical time-harmonic loading. The semi-analytical solutions for the dynamic compliance, displacements, stresses, especially the contact stress including effective stress and pore fluid pressure of the plate and the layer, are proposed. In developing these solutions, the linearly poroelastic model established by de Boer is used to describe the mechanical behaviour of the porous medium. By means of four scalar displacement potentials and the Fourier–Hankel transformation to solve the equations of motion of the poroelastic layer, and then imposing boundary and interfacial conditions, a pair of coupling Fredholm’s integral equations of the second kind formulating the plate–medium interaction are derived and evaluated with numerical methods. The proposed solutions are then verified by comparing with the existing special solutions and the FEM calculation results. Numerical examples are also performed to examine the effects of the permeability of both the plate and the poroelastic layer and the thickness of the layer on the dynamic response of the coupling system.