A Theory for Transverse Deflection of Poroelastic Plates

A theory is presented for the bending of fluid-saturated poroelastic plates. The governing equations, based on linear consolidation theory, reduce to a single fourth-order integro-partial-differential equation to be solved for the transverse displacement of the middle surface. This equation resembles the classical plate equation but has an added convolution integral, which represents the viscous losses due to the flow of fluid relative to the solid. Laplace transform and perturbation solution methods are presented. The Laplace-transformed poroelastic plate equation and the first-order equation of the perturbation expansion have the forms of the standard plate equation. Results are given for a simply-supported rectangular plate with a time-dependent surface pressure.