Effect of Hydrostatic Pressure on Vibrating Rectangular Plates Coupled with Fluid

Abstract

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