Vertical vibrations of circular plate in multi-layered poroelastic media

Abstract

This thesis is concerned with vertical vibrations of an elastic circular plate resting on or buried in a poroelastic medium. The poroelastic medium is governed by Biot ‘s poroelastodynamic theory and considered as a homogeneous half-space and a multi-layered half-space. The plate is subjected to axisymmetric time-harmonic vertical loading and its response is governed by the classical thin-plate theory. The contact surface between the plate and the half-space is assumed to be smooth and either fully permeable or impermeable. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Contact stresses and pore pressure jumps are established in terms of generalized coordinates through the solution of flexibility equations based on the influence functions corresponding to vertical and pore pressure loads. The generalized coordinates are obtained by establishing the equations of motion of the plate through the application of Lagrange ‘s equations of motion. Finally, the response of the plate can be obtained by back substituting the generalized coordinates into the assumed displacement function. A computer program based on the above method is developed. The accuracy and numerical stability of the present solution scheme are verified by comparing with the existing studies. Numerical results indicate that the plate response is significantly influence by the depth of embedment, the frequency of excitation and flexibility of the plate. In addition, the poroelastic material properties and the hydraulic boundary condition of the plate influence the plate response at high frequencies. The applied load is mainly carried through the solid skeleton at low frequencies and through both solid and fluid phases at higher frequencies.