Vibration of simply supported plates in contact with liquid by using membrane curvilinear elements

This paper concerns the free vibrations of a simply supported plate in contact with liquid on one side. The plate is placed into a hole of an infinite rigid wall. The analysed problem is a coupled problem of the fluid-structure type. It is assumed that the fluid is inviscid and incompressible. The boundary integral equation is used for describing the hydrodynamic pressure. The plate equation is formulated in the form of two harmonic equations. The surface of the plate is discretized using triangular curvilinear 6-node elements of the membrane type. These elements are simultaneously the finite elements for the plate and the boundary elements for the liquid. Numerical examples of the free vibrations of circular and rectangular plates are considered and are compared with analytical and analytical-numerical solutions.