Coupled vibration analysis of liquid-filled rigid cylindrical storage tank with an annular plate cover

An analytical approach is developed to investigate the vibration characteristics of the sloshing and bulging modes for a liquid-filled rigid circular cylindrical storage tank with an elastic annular plate in contact with sloshing surface of liquid. The cylindrical tank is filled with a non-viscous and incompressible liquid having a free surface. The free surface of liquid is partially covered by an annular plate with outer clamped edge and inner free edge. The liquid domain is limited by a rigid cylindrical wall and a rigid flat bottom. As the effect of free surface waves is taken into account in the analysis, the bulging and sloshing modes are studied. The solution for the velocity potential of liquid movement is assumed as a suitable harmonic function that satisfies the Laplace equation and the relevant boundary conditions. The Rayleigh-Ritz method is used to derive the frequency equation of the liquid-filled rigid cylindrical tank with an annular plate on the sloshing surface. The effects of inner-to-outer radius ratio, thickness of annular plate and liquid volume on vibration characteristics of the storage tank are studied. To demonstrate the validity of the present analytical approach, the published results are compared for the rigid cylindrical tank without a plate and the finite element analysis is performed for the tank with a plate.