Vertical time-harmonic coupling vibration of an impermeable, rigid, circular plate resting on a finite, poroelastic soil
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RESEARCH PAPER
Vertical time-harmonic coupling vibration of an impermeable, rigid, circular plate resting on a finite, poroelastic soil layer Shiping Zhang1,2,3 • Ronald Y. S. Pak4 • Junhui Zhang1,2,3 Received: 30 March 2020 / Accepted: 2 September 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Boer’s poroelastic model Contact stresses Dynamic compliance Fredholm’s integral equation Poroelastic media Rigid circular plate
& Junhui Zhang [email protected] Shiping Zhang [email protected] Ronald Y. S. Pak [email protected] 1
National Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science and Technology, Changsha 410114, Hunan, China
2
Hunan International Scientific and Technological Innovation Cooperation Base of Advanced Construction and Maintenance Technology of Highway, Changsha University of Science and Technology, Changsha 410114, Hunan, China
3
School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan, China
4
Department of Civil, Environmental, and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, USA
1 Introduction The study associated with the dynamic interactions of plates and surrounding materials has been always a subject of considerable interest in the field of applied mechanics and geo
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