Free vibration of an elastic bottom plate of a partially fluid-filled cylindrical container with an internal body

An analytical method is developed to consider the free vibration of an elastic bottom plate of a partially fluid-filled cylindrical rigid container with an internal body. The internal body is a rigid cylindrical block that is concentrically and partially submerged inside the container. The developed method captured the analytical features of the velocity potential in a non-convex, continuous, and simply connected fluid domain including the interaction between the fluid and the structure. The interaction between the fluid and the bottom plate is included. The Galerkin method is used for matching the velocity potentials appropriate to two distinct fluid regions across the common horizontal boundary (artificial horizontal boundary). Then, the Rayleigh–Ritz method is also used to calculate the natural frequencies and modes of the bottom plate of the container. The results obtained for the problem without internal body are in close agreement with both experimental and numerical results available in the articles. A finite element analysis is also used to check the validity of the present method in the presence of the internal body. Furthermore, the influences of various variables such as fluid level, internal body radius, internal body length, and the number of nodal diameters and circles on the dynamic behaviour of the coupled system are investigated.