Hydro-static effect on free vibration of circular plate in contact with bounded fluid on elastic foundation

This research studies the effect of hydro-static pressure on the free vibration of a circular plate in contact with an inviscid and bounded fluid. The plate is in bottom of rigid cylindrical vessel with clamped boundary condition. At first, the potential energy of the plate on elastic foundation is performed by solving the governing equation on circular plate with clamped boundary condition. Next, the governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The natural frequencies and mode shapes of the plate are determined by applying the Rayleigh-Ritz method on the total energy of the system. The effects of the parameters such as fluid height, fluid density, plate thickness to its radius ratio, and wave numbers on the natural frequencies and mode shapes are investigated. Comparison of analytically outcome of this study is made with results of the experimental modal test.