Evidences of global bifurcations of an imperfect circular plate

The global bifurcations in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of the third-order subharmonic resonance, in which an excitation frequency is near triple natural frequencies, is considered. The equations governing nonlinear oscillations of an imperfect circular plate are reduced to a system of non-autonomous ordinary differential equations via Galerkinʹs procedure. The method of multiple scales is used to obtain a system of autonomous ordinary differential equations, and then Kovačič and Wiggins’ method is used to investigate the global dynamics of the plate. Having found a sufficient condition under which Silnikov-type homoclinic orbit can exist, we failed to observe any numerical evidences of global bifurcation.