AXISYMMETRICAL FREE HYDROELASTIC VIBRATION OF A FLEXURAL BOTTOM PLATE IN A CYLINDRICAL TANK SUPPORTED ON AN ELASTIC-FOUNDATION

Theoretical analysis has been carried out on the linear free axisymmetric vibration of an elastic bottom plate of liquid-filled cylindrical tank supported on an elastic foundation. In the analysis, in-plane forces in the plate due to the static liquid pressure were taken into account. Numerical calculations were carried out for various kinds of system parameters: i.e., the radius to thickness ratio, the liquid-plate density ratio, plate material parameters, and the stiffness of the elastic foundation. It was found that the influence of an in-plane force, due to the static deflection of the bottom plate, is prominent for a thin-bottomed plate. In this case, the natural frequencies higher than the second mode initially decrease due to the added mass effect of the contained liquid, and then increase with the liquid height due to the growth of the in-plane force. In the first mode, the influence is small and there seems to be no increase in the natural frequency with liquid height. The calculated results are represented in some graphs, which should provide convenient data for the design of a cylindrical container with a flexible bottom. © 1994 Academic Press Limited.