Hydroelasticity of a circular plate on water of finite or infinite depth

Abstract

This paper considers the diffraction of incident surface waves by a floating elastic circular plate. We investigate the hydroelastic response of the plate to a plane incident wave for two cases of water depth. An analytic and numerical study is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as series of Bessel functions is the key idea of the approach. After a brief introduction and formulation of the problem, we derive the main integro-differential equation by the use of the thin plate theory and Green's theorem. The plate deflection, the free-surface elevation and the Green's function are expressed in cylindrical coordinates as series of Bessel functions. For the coefficients, a set of algebraic equations is obtained, yielding the approximate solution for the case of infinite water depth. Then a solution is obtained for the general case of finite water depth analogously. The exact solution is approximated by taking a finite number of roots of the dispersion relation into account. Numerical results for the plate deflection, initiated wave pattern and free-surface elevation are presented for various physical parameters of the problem, together with some remarks on the computation and discussion.