Free vibration analysis of functionally graded porous plates in contact with bounded fluid

This study investigates the free vibrations of functionally graded porous (FGP) plates in contact with fluid. As an illustrative problem, a rectangular FGP plate is considered as the vertical wall of a rigid tank containing liquid. The plate displacement field is approximated based on the first-order shear deformation theory (FSDT). Thus, the expressions of its strain and kinetic energy are obtained. The fluid is assumed to be incompressible, inviscid, and irrotational. Its velocity potential functions are obtained by applying suitable boundary and compatibility conditions. By using the Rayleigh–Ritz method with two-variable orthogonal polynomials series expansion, the natural frequencies of the FGP plate in contact with fluid are calculated. To validate the method, the results obtained for the natural frequencies are compared with those available in the literature for FGP plates without fluid and isotropic plates with fluid. Then, three different types of porosity distribution are considered to evaluate their effects on the natural frequencies of the plate. Besides, the effect are investigated of different parameters, such as the fluid depth, side-to-thickness ratio, length-to-width (aspect) ratio.