The linear wave response of a floating thin plate on water of variable depth

Abstract

We present a solution for the linear wave forcing of a floating two-dimensional thin plate on water of variable depth. The solution method is based on reducing the problem to a finite domain, which contains both the region of variable water depth and the floating thin plate. In this finite region, the outward normal derivative of the potential on the boundary is expressed as a function of the potential. This is accomplished by using integral operators for the radiating boundaries and the boundary under the plate. Laplace's equation in the finite domain is solved using the boundary element method and the integral equations are solved by numerical integration. The same discretisation is used for the boundary element method and to integrate the integral equations. The results show that there is a significant region where the solution for a plate with a variable depth differs from the simpler solutions for either variable depth but no plate or a plate with constant depth. Furthermore, the presence of the plate increases the frequency of influence of the variable depth.