HYDROELASTIC VIBRATION OF A CIRCULAR CONTAINER BOTTOM PLATE USING THE GALERKIN METHOD

Abstract

The free vibration of a flexible thin plate placed into a circular hole and elastically connected to the rigid bottom slab of a circular cylindrical container filled with fluid having a free surface is studied. The liquid is assumed to be incompressible, inviscid and irrotational. The effect of the free surface wave is also taken into account in the analysis. First of all, the exact expression of velocity potential of the liquid movement is derived by a combination of the superposition method and the method of separation of variables. With the help of the Fourier–Bessel series expansion, part of the unknown coefficients in the solution is determined by the consistency condition between the liquid movement and the plate vibration, in the form of integrals associated with the dynamic deflection of the plate. Then, the Galerkin method is applied to derive the eigenfrequency equation of the fluid–plate interaction. Finally, the effects of various parameters and the free surface wave on eigenfrequencies of the fluid–plate system are discussed. As a consequence, the accuracy of the nondimensional added virtual mass incremental (NAVMI) factor solution has also been evaluated by comparing with the more accurate Galerkin solution. It is shown that the proposed method is also applicable to the vibration analysis of circular plates in contact with an infinite liquid by only taking a finite but larger size of liquid to replace the infinite liquid in the computation.