A variational equation for the wave forcing of floating thin plates

A variational equation is presented for floating thin plates subject to wav e forcing. This equation is derived from the thin plate equation of motion by including the wave forcing using the free-surface Green function. This v ariational 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 pl ate geometries using polynomial basis functions. The variational equation i s extended to the case of plates of variable properties and to multiple pla tes and further solutions are presented. (C) 2001 Elsevier Science Ltd. All rights reserved.