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Double Hopf Bifurcation of a Simply Supported Rectangular Thin Plate With Parametrically and Externally Excitations

Zhou Y

Based on the singularity theory, the double Hopf bifurcation problem of a rectangular thin plate with four edges simply supported under the combined actions of the parametric excitation and the external excitation are investigated in the case of the principal parametric resonance and internal resonance. Considering weak damping and weak excitation, the bifurcation equation of the thin plate system is obtained, and the bifurcation diagrams of the thin plate system are given on the parameter plane. Then, the stationary solutions and its stability for the rectangular thin plate are analyzed.