Wave diffraction and radiation by a vertical cylinder standing near a floating elastic plate

Wave diffraction and radiation problems by a vertical cylinder standing near a floating elastic plate are considered. The linearized velocity potential theory is used to describe the fluid flow, and the thin elastic plate model is adopted for the elastic plate. The numerical solution procedure starts from dividing the fluid domain into two sub-domains, one below free surface and the other below the elastic plate. In the vertical direction, the velocity potential is expanded into a series of eigenfunctions based on separation of variables, which decomposes the three-dimensional problem into an infinite number of coupled two-dimensional problems in the horizontal plane. In the two sub-domains, each of two-dimensional problem is transformed into an integral equation. On the artificial vertical surface between two subdomains, an orthogonal inner product is applied for the eigenfunctions, and the edge conditions of elastic plate are satisfied. On the vertical surface of cylinder, similar inner product is adopted, and the boundary condition on the cylinder surface is imposed. A combined boundary element method and finite difference scheme is introduced to solve the integral differential equations numerically. Extensive results for the hydrodynamic force are provided and analyzed. It is found that the hydrodynamic force is highly oscillatory due to the complex interactions between cylinder and plate.