Effect of Hydrostatic Pressure on Vibrating Rectangular Plates Coupled with Fluid

This study is focused on the hydrostatic vibration analysis of a rectangular plate in partial contact with a bounded fluid in bottom and vertical directions. A set of admissible trial functions is required to satisfy the clamped and simply supported geometric boundary conditions. The fluid velocity potential satisfying fluid boundary conditions is derived, and the wet dynamic modal functions of the plate are expanded, in terms of the finite Fourier series, for a compatibility requirement along the contacting surface between the plate and the fluid. The natural frequencies of the plate coupled with sloshing fluid modes are calculated using the Rayleigh-Ritz method, based on minimizing the Rayleigh quotient. The proposed analytical method is verified by comparing the presented results with the results obtained by three-dimensional finite element analysis. Finally, the influence of boundary conditions, plate and tank dimensions, fluid depth and hydrostatic pressure on, natural frequencies is examined and discussed in detail.