Research on multi-pulse chaotic dynamics of six-dimensional nonautonomous rectangular thin plate

Abstract

The global bifurcations and multi-pulse chaotic dynamics of the four-edge simply supported rectangular thin plate under in-plane excitation are investigated. Based on the von Karman theory and the Reddy's high-order shear deformation theory, the formulas of motion for the four-edge simply supported rectangular thin plate subjected to the in-plane excitation are derived. Then the Galerkin method is employed to discrete the partial differential equations. The non-autonomous ordinary differential equations with three-degree-of-freedom are derived by using this method. The extended Melnikov method is improved to investigate the six-dimensional nonautonomous nonlinear dynamical system in mixed coordinate. The multi-pulse chaotic dynamics of the six-dimensional nonautonomous rectangular thin plate, which is buckled in the first-order mode, meanwhile it is not buckled in the second-order mode and the third-order mode, are studied directly by using this method. The three-order normal forms of the six-dimensional nonautonomous nonlinear dynamical equations are obtained by using the theory of normal form. Then making use of the residue theory, the Melnikov functions can be established. The multi-pulse chaotic motions of the four-edge simply supported rectangular thin plate are found from the numerical simulation which further verifies the result of theoretical analysis.