Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation

The global bifurcations in mode interaction of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation are investigated with the case of the 1:1 internal resonance, the average equations representing the evolution of the amplitudes and phases of the interacting normal modes exhibiting complex dynamics. A global perturbation method, i.e., the higher-dimensional Melnikov method and its extensions proposed by Kova?i? and Wiggins, is utilized to analyze the global bifurcations for the rectangular metallic plate. A sufficient condition for the existence of a Silnikov-type homoclinic orbit is obtained, which implies that chaotic motions may occur for this class of rectangular metallic plates. Finally, numerical results are presented to confirm these analytical predictions.