Abstract
In this paper, dynamic response of an elastic circular plate, under axisymmetric time-harmonic vertical loading, resting on a transversely isotropic poroelastic half-space is investigated. The plate-half-space contact surface is assumed to be smooth and fully permeable. The discretization techniques are employed to solve the unknown normal traction at the contact surface based on the solution of flexibility equations. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results corresponding to the deflections of a circular plate, with different degrees of flexibility, resting on a transversely isotropic poroelastic half-space are presented.
Highlights
Biot [1] proposed a theory of wave propagations in a poroelastic material, which is a two-phase material consisting of an elastic solid with voids filled with water
The dynamic responses of rigid foundations under vertical loading were investigated by Kassir and Xu [2] for rigid strips, Jin and Liu [3], Zeng and Rajapakse [4] and Ai et al [5] for rigid circular plates, and Halpern and Christiano [6], Senjuntichai et al [7,8] and Keawsawasvong and Senjuntichai [9] for rigid rectangular plates
This paper presents dynamic interaction between an elastic circular plate under vertical loading and a transversely isotropic poroelastic half-space
Summary
Biot [1] proposed a theory of wave propagations in a poroelastic material, which is a two-phase material consisting of an elastic solid with voids filled with water. The interpretation of material properties of transversely isotropic poroelastic media was later presented by Cheng [14] in order to illustrate the relations between the results obtained from the laboratory measurement and the parameters in the transversely isotropic poroelastic materials proposed by Biot [13]. A representation for contact traction is established in terms of generalized coordinates through the solution of a flexibility equation based on a fundamental solution of the half-space based on Biot’s theory [13].
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