A variational equation for the wave forcing of floating thin plates

A variational equation is presented for floating thin plates subject to wave forcing. This equation is derived from the thin plate equation of motion by including the wave forcing using the free-surface Green function. This variational equation combines the standard method for solving the motion of a thin plate (a variational equation) with the standard method for solving the wave forcing of a floating body (the free-surface Green 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 further solutions are presented. (C) 2001 Elsevier Science Ltd. All rights reserved.