The research of nonlinear vibration of damped circular sandwich plate with initial deflection

摘要

The forced vibration of damped circular sandwich plate with initial deflection is studied in this paper. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the loosely clamped boundary condition, got the standard Duffing equation with square and cubic minor items by dimensionless process, and gaind the quadratic analytical solution of the principal resonance problem of circular sandwich plate by means of the multi-scale method, the frequency response equation when the principal resonance is excitated, and the necessary and sufficient condition on stability of the vibration is are obtained synchronously. Discussed the infection to the amplitude while the correlative physical and geometric parameters are changing, drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.