Energy-conserving Galerkin representation of clamped plates under a moderately large deflection

In the moderately large deflection plate theory of von Karman and Chu–Herrmann, one can formulate dynamic equations of a thin plate by considering either the transverse and in-plane displacements, w–u–v formulation, or the transverse displacement and Airy function, w–F formulation. Previously, for a simply supported plate we have investigated the Hamiltonian property of modal equations obtained by the Galerkin representation under w–u–v and w–F formulations. We extend here such investigations to a rectangular clamped plate with similar conclusions. That is, the modal equations of w–F formulation are Hamiltonian and hence energy conserving at any order of truncation. On the other hand, the corresponding modal equations of w–u–v formulation do not conserve energy when only a small number of sine terms are included in the in-plane displacement expansions.