VIBRATIONS OF CIRCULAR PLATES RESTING ON A SLOSHING LIQUID: SOLUTION OF THE FULLY COUPLED PROBLEM

Abstract

Vibrations of circular plates resting on a sloshing liquid free surface are studied. The fully coupled problem between sloshing modes of the free surface and bulging modes of the plate is solved by using the Rayleigh–Ritz method. The sloshing boundary condition is directly inserted into the eigenvalue problem. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. The fluid is considered inviscid and incompressible; it is described by the velocity potential expanded in a series. The present model has as limit cases: (1) circular plates resting on half-infinite liquid domain and (2) circular plates completely covering the liquid in a circular cylindrical tank. The theory is suitable for all axisymmetric plate boundary conditions. The effect of free surface waves on the plate natural frequencies is significant when the fundamental bulging mode of the plate has its natural frequency close to those of the first sloshing modes of the free surface. The present original solution allows the study of plates having a very strong coupling between sloshing and bulging modes to be studied to a high level of accuracy. The convergence of the method is shown. The natural frequencies and mode shapes for different system parameters are given.