Global Dynamics of a Parametrically and Externally Excited Thin Plate

Both the local and global bifurcations of a parametrically and externally excited simply supported rectangular thin plate are analyzed. The formulas of the thin plate are derived from the von Kármán equation and Galerkin’s method. The method of multiple scales is used to find the averaged equations. The numerical simulation of local bifurcation is given. The theory of normal form, based on the averaged equations, is used to obtain the explicit expressions of normal form associated with a double zero and a pair of purely imaginary eigenvalues from the Maple program. On the basis of the normal form, global bifurcation analysis of a parametrically and externally excited rectangular thin plate is given by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of the thin plate is found by numerical simulation.