Compressibility Effects on the Hydroelastic Vibration of a Plate at an Off-center Position of a Rectangular Container Filled with Fluid

Abstract

Fluid filled containers are encountered in many technological applications such as in nuclear or aerospace engineering. In this paper the dynamic behaviour of a plate at an off-center position of a rectangular container filled with a compressible and non-viscous fluid is analyzed. The fluid velocity potential that verifies the wave equation is obtained first by applying a method of separation of variables and afterwards the pressure field is calculated with the momentum’s linearized equation. Taking into account the equation of deformation of the plate in contact with the fluid on the lower and upper sides, expressed in series expansion of the associated modes and applying an integration procedure with respect to the functions involved, an analytical expression is obtained for the calculus of the plate frequencies of vibration. The influence of different geometrical parameters such as dimension, aspect ratio, relative thickness as well as the fluid density on these frequencies is analysed for different values of the fluid sound speed regarding the compressibility effects. Also the influence of the off-center position of the plate, density ratio of the two fluid domains and the fluid sound speed on the frequency is analysed. Validation of the method is made by comparing the results with those obtained by other authors and theories.