Exact solution for free vibration of thick rectangular plates made of porous materials

Abstract Free vibration analysis for thick rectangular porous plate saturated by inviscid fluid is presented. Material properties of the plate are assumed to vary through the thickness according to a simple cosine law in term of a coefficient related to plate’s porosity. Based on Reddy’s third-order shear deformation plate theory and considering the effect of fluid in pore network of the porous medium, the equations of motion are obtained. The plate is assumed to be simply supported on two opposite edges and the rest of edges are free, clamped or simply supported. For the sake of analytical solution, a unique approach is employed to decouple the equations of system. Exact frequencies rising from the solution are obtained for a rectangular porous plate made of Berea sandstone. The roles played by mechanical constraints on edges, fluid, geometrical dimensions of plate as well as the effect of the coefficient of plate porosity are investigated. It is found that porosity function affects significantly on the fundamental frequency of the system. Also, the effect of fluid on the dynamic response of plate is studied in detail.