Transverse vibrations of a thin rectangular porous plate saturated by a fluid

A simple model of the transverse vibrations of a thin rectangular porous plate saturated by a fluid is proposed. The model is based on the classical theory of homogeneous plates and on Biot's stress-strain relations in an isotropic porous medium with a uniform porosity. Two coupled dynamic equations of equilibrium relating the plate deflection and the fluid/solid relative displacement are found and their physical interpretation is given. The energy dissipation by viscous friction is included in the model. An approximate calculation of the natural frequencies of vibration is given for rigid plates with various boundary conditions at the edges. The influence of porosity, tortuosity and permeability on the resonances is studied and a condition of maximum damping involving these parameters is given. (C) 2001 Academic Press.