Vibrations of Poroelastic Plates: Mixed Displacement-Pressure Modelisation and Experiments

This paper presents the equations of motion of air saturated rectangular poroelastic plates. The model is based on a mixed displacement-pressure formulation of Biot's theory. Two equations of motion are obtained and solved with the Galerkin method for any boundary conditions. These equations take into account the solid-fluid coupling effects. Simulations of the bending vibrations of a rectangular water saturated sandstone and air saturated acoustic foam are performed for studying the influence of the viscous damping through the permeability. Experiments on clamped plates made of low density acoustic materials (fibrous and polyurethane foam) are used to check the limits of this model. On these materials the structural damping is predominant compared to viscous damping.