Double-mode modeling of chaotic and bifurcation dynamics for a simply supported rectangular plate in large deflection

This paper presents a new approach to characterize the conditions that can possibly lead to chaotic motion for a simply supported large deflection rec tangular plate by utilizing the criteria of the fractal dimension and the m aximum Lyapunov exponent, The governing partial differential equation of th e simply Supported rectangular plate is first derived and simplified to a s et of two ordinary differential equations by the Galerkin method. Several d ifferent features including Fourier spectra. state-space plot, Poincare map and bifurcation diagram are then numerically computed by using a double-mo de approach. These features are used to characterize the dynamic behavior o f the plate subjected to various excitation conditions. Numerical examples are presented to verify the validity of the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. The numeri cal results indicate that large deflection motion of a rectangular plate po ssesses many bifurcation points, two different chaotic motions and some jum p phenomena under various lateral loading. The results of numerical simulat ion indicate that the computed bifurcation points can lead to either a tran scritical bifurcation or a pitchfork bifurcation for the motion of a large deflection rectangular plate. Meanwhile, the points of pitchfork bifurcatio n can gradually lead to chaotic motion in some specific loading conditions. The modeling result thus obtained by using the method proposed in this pap er can be employed to predict the instability induced by the dynamics of a large deflection plate. (C) 2001 Elsevier Science Ltd. All rights reserved.