Coupled vibratory characteristics of a rectangular container bottom plate

Abstract

The natural frequencies of an elastic thin plate placed into a rectangular hole and connected to the rigid bottom slab of a rectangular container filled with fluid having a free surface are studied. The fluid is assumed to be incompressible, inviscid and irrotational, and the effect of surface waves is neglected. An analytical-Ritz method is developed to study the vibratory characteristics of the plate in contact with the fluid. First of all, the exact expression of the motion of the fluid is obtained, in which the unknown coefficients are determined by using the method of separation of variables and the method of Fourier series expansion. Then, the Ritz approach is used to obtain the frequency equation of the system. The vibrating beam functions are adopted as the admissible functions for the wet-mode expansion of the plate, and the added virtual mass incremental (AVMI) matrices are obtained for plates with arbitrary boundary conditions. Finally, a convergence study is carried out and some numerical results are given. The accuracy of AVMI factor solutions is discussed by comparing with the more accurate analytical-Ritz solutions presented in this paper. Furthermore, It is seen that the present method is also suitable for the vibration analysis of rectangular plates in contact with infinite fluid by taking the finite, but larger size fluid domain as an approximation in the computation. © 2000 Academic Press.