Department of Chemistry,Sabzevar Tarbiat moallem University
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.
)