Chaotic Dynamics of a Six-Dimensional Nonautonomous Rectangular Thin Plate under In-Plane Excitation

Chaotic dynamics of a four-edge simply supported rectangular thin plate under in-plane excitation are studied using the multi-degree-of-freedom Melnikov method. Based on the von Karman type equations for the geometric nonlinearity, the governing equations of motion for the four-edge simply supported rectangular thin plate under in-plane excitation are derived. The Galerkin method is employed to discretize the partial differential equations of motion to a three-degree-of-freedom nonlinear system. The three-order normal form is used to analyze the six-dimensional nonautonomous nonlinear system. Some nonlinear terms in this system have less effect than other terms. So these terms are considered as perturbation terms. The chaotic motions of the four-edge simply supported rectangular buckled thin plate under in-plane excitation are found by using numerical simulation, which further verifies the result of theoretical analysis.