Application of Hamilton-Dirichlet's Principle to Analysis of Wave-induced Responses of an Elastic Floating Plate

Many analytical methods have been proposed to calculate hydroelastic responses of a very large pontoon type structure in waves. In relation to the elastic response of such pontoon type structure in waves, Isshiki and Nagata proposed four kinds of variational principles related to motions of the elastic plate floating on a water surface and clarified the mutual relationship of these variational principles. "Modified Hamilton-Dirichlet's Principle 2" which is expressed using the velocity potential is one of four kinds of variational principles and has expressed the motions of the fluid and plate. In this paper, in order to calculate the wave-induced responses of an elastic floating plate in waves, a new method is proposed which uses the "Modified Hamilton-Dirichlet's Principle 2" and the "eigenfunction expansion method for fluid motion". The velocity potentials in regions with and without the plate are expanded by eigenfunctions in vertical mode which satisfy the governing equations and free-surface conditions, taking into account the presence of the plate in the same manner as Kim and Ertekin. In this method, "Modified Hamilton-Dirichlet's Principle 2" is finally reduced to a variational equation which corresponds to boundary conditions on the plate's edge and is applicable to the plate with arbitrary horizontal shape. This proposed method has the expression which can be applied to the floating plate with arbitrary horizontal shape. However, in this paper, as a 1st step, the calculated results of two kinds of rectangular horizontal plates are compared with the experimental results.