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

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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.