Nonlinear Superharmonic Resonance of Damped Circular Sandwich Plates with Initial Deflection

Abstract

The nonlinear superharmonic resonance phenomenon of damped circular sandwich plates under uniform load is investigated. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the clamped BC. Using multi-scale method, the periodical solutions were obtained which was of nonlinear the third-order superharmonic resonance. The FRF equation of the superharmonic resonance is obtained, and the necessary and sufficient condition on stability of the vibration are obtained synchronously.The infection to the amplitude while the correlative physical and geometric parameters changing were discussed, Drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.