Hydroelastic interaction between water waves and a thin elastic plate of arbitrary geometry

An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow. Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system. According to the surface boundary conditions, the fluid domain is divided into two regions, namely, an open water region and a plate-covered region. With the assumption that all the motion is time-harmonic, the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion. The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction. A system of simultaneous equations, including two edge conditions and two matching conditions, is set up for deriving the expansion coefficients. As an example, numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate. The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.