Hydro-Elastic Oscillations of the Bottom Membrane of a Rectangular Container Filled with Fluid

The analysis of the hydro-elastic interactions of the covering membrane of fluid-filled cavities or containers has a main importance due to the solution of practical problems founded in engineering applications. In this paper the dynamic behaviour of the bottom membrane of a rectangular container filled with a non-viscous and incompressible fluid is analyzed. The fluid velocity potential 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 deformation equation for the membrane in contact with the fluid and by applying a discretization procedure to the associated generalized work equation, a system is obtained, for the calculus of the membrane frequencies of vibration. The influence of different geometrical parameters such as dimension, aspect ratio, container relative height, relative thickness as well as the fluid density on these frequencies is analysed. Validation of the method is made by comparing the results with those obtained by other authors and theories.