Wave interaction with a floating finite elastic plate of arbitrary shape

Wave interaction with a floating finite elastic plate is considered, based on the linearized velocity potential theory for fluid flow, and the thin elastic plate model for plate deflection. The shape of the plate can be arbitrary, and free edge conditions are imposed at its edge. The solution procedure is established by dividing the domain into two subdomains-one below free surface and the other below the plate. The velocity potential in each subdomain is expanded into a series of eigenfunctions in the vertical directions based on separation of variables. This avoids numerical difficulty in computation of the fifth derivatives in the plate covered subdomain. Then the three-dimensional problem is decomposed into an infinite number of coupled two-dimensional problems in the horizontal plane. Each two-dimensional problem is transformed into an integral equation along the plate edge. On the artificial vertical interface between two subdomains, an orthogonal inner product is introduced for the eigenfunctions, through which the edge conditions, together with continuous conditions of pressure and velocity, are satisfied. The boundary integral equations and the derivatives along the plate edge are solved numerically through the boundary element method and the finite difference scheme. Extensive results are provided and analyzed for plates with various thicknesses and shapes, including the plate displacement, average curvature, disturbed far-field amplitude, scattering cross section, and the wave exciting force.