A variation equation for the wave forcing of floating thin plates

Abstract

A variational equation is derived for a floating thin plate subject to wave forcing. This variational equation is derived from the thin plate equations of motion by including the forcing due to the wave through the integral equation derived using the free surface Green’s function. This equation combines the optimum method forsolving the motion of a thin plate (the variational equation) with the optimum method for solving the wave forcing of a floating body (the Green’s function method). Solutions of the variational equation are presented for some simple thin plate geometries using polynomial basis functions. The variational equation is extended to the case of plates of variable properties and to multiple plates and example solutions are presented.