Research of Nonlinear Primary Resonance of Damped Circular Sandwich Plates with Initial Deflection

The nonlinear forced vibration of damped circular sandwich plates is studied. From the movement equations of circular sandwich plate expressed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. The standard Duffing equation with square and cubic minor items was obtained by dimensionless processed. The quadratic analytical solution of the principal resonance was deduced by multi-scale method. The FRF of primary resonance periodical solutions were obtained, synchronously the necessary and sufficient condition on stability of the vibration are obtained. The infection to the amplitude when the correlative physical and geometric parameters changing was discussed. The trajectories in moving phase planes during the stabilization process, the stabilities and singularities of the solutions are analyzed.