Hydroelastic analysis of a floating plate of finite draft

In this paper the diffraction of incident surface water waves by a very large floating structure of finite thickness and draft is under consideration. The floating structure (platform) of finite, but small, draft is modelled by a thin elastic isotropic plate. An analytical and numerical study of the hydroelastic behavior of the plate is presented. The problem is solved for the main case of finite water depth. To simplify the equations involved, the half-plane problem is considered. Recommendations are given for other horizontal planforms of the plate and possible extensions of the method developed. The deflection of the plate is represented as a series of solutions with respect to the plate draft; we present and use first and second terms. Each of these terms can be written as a series of exponential functions multiplied by coefficients. The integro-differential formulation and equation obtained, the dispersion relations in the plate region and open water, the Green’s theorem, the geometrical-optics approach and the Lindstedt method are used to determine reduced wavenumbers of zero and first draft order. Further, sets of equations are derived to find the corresponding wave-mode amplitudes. Results obtained for the plate of finite draft are compared to those for a plate with zero draft.