Influence of Nonlinearities on the Degenerate Vibration Modes of a Square Plate

Abstract

von Karman's nonlinear plate equations are used to investigate the effects of nonlinearities on the degenerate vibration modes of a square plate. Galerkin's procedure is used to reduce the problem to two coupled nonlinear differential equations, and approximate solutions are obtained by the method of harmonic balance. For linear vibrations, the degenerate modes can be superimposed to form an infinite variety of nodal patterns. However, the nonlinear analysis shows that for finite amplitude vibrations the modes combine to give only four distinct nodal patterns. These nodal patterns are oriented along the lines of symmetry of the plate.