GLOBAL AND CHAOTIC DYNAMICS FOR A PARAMETRICALLY EXCITED THIN PLATE

The global bifurcations and chaotic dynamics of a parametrically excited, simply supported rectangular thin plate are analyzed. The formulas of the thin plate are derived by von Karman-type equation and Galerkinʹs approach. The method of multiple scales is used to obtain the averaged equations. Based on the averaged equations, theory of normal form is used to give the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program. On the basis of the normal form, global bifurcation analysis of the parametrically excited rectangular thin plate is given by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is found by numerical simulation.