Hydroelastic vibration of the bottom plate of the cylindrical tank coupled with sloshing

This study is concerned with the hydroelastic vibration of the flexible bottom plate of a cylindrical tank coupled with sloshing. The cylindrical tank is assumed to be placed vertically with the rigid wall. The matrix equations of motion describing the free-surface elevation coupled with the hydroelastic vibration of the bottom plate was derived by using the Lagrangian equation. The so-called non-dimensionalized added virtual increment factors were also calculated and compared to the previous results, and showed exact agreement. The numerical results show that only when the water is shallow and the bottom plate is very flexible, strong coupling exists in the bulging modes and asymmetric modes having one nodal diameter. However, if the fundamental frequency of the plate in contact with fluid is much higher than the fundamental frequency of the sloshing, the coupling between sloshing and the hydroelastic vibration of the bottom plate can be ignored.