Comparison of the Two Formulations of w-u-v and w-F in Nonlinear Plate Analysis

Abstract

In a moderately large deflection plate theory of von Karman and Chu-Herrmann, one may consider thin-plate equations of either the transverse and in-plane displacements, w-u-v formulation, or the transverse displacement and Airy function, w-F formulation. Under the Galerkin procedure, we examine if the modal equations of two plate formulations preserve the Hamiltonian property which demands energy conservation in the conservative limit of no damping and forcing. In the w-F formulation, we have shown that modal equations are Hamiltonian for the first four symmetric modes of a simply-supported plate. In contrast, the corresponding modal equations of w-u-v formulation do not exhibit the Hamiltonian property when a finite number of sine terms are included in the in-plane displacement expansions.