Coupled Vibration and Sloshing Analysis of the Circular Plate resting on the Free Surface of a Fluid-Filled Cylindrical Tank

Abstract

This study formulates the energy approach and applies the assumed modes method to the coupled sloshing and vibration of the circular plate resting on the free surface of a cylindrical tank that is placed vertically. The wall is assumed to be rigid. The Lagrangian equation was used to derive the matrix equations of motion describing the free-surface elevation and the vibration of the circular plate, which equations clearly show the coupling effect between the sloshing and the vibration of the circular plate. Considering the limiting cases, the so-called non-dimensionalized added virtual increment factors were also derived. The coupled natural frequencies and mode shapes were calculated to investigate the coupling effect. The numerical results show that the added mass effect becomes larger only when the fluid is shallow, or the surrounding wall is close to the circular plate. The matrix equations of motion derived in this study can be effectively used for both the calculation of the natural frequencies of coupled sloshing and elastic vibration, and the time responses subjected to excitation force.