Nonlinear Vibration With Primary And 1/3 Subharmonic Resonance Of Circular Sandwich Plate With Initial Deflection

Nonlinear vibration of circular sandwithplate with large initial deflection has been researched mainly in this paper.The basic theory of nonlinear vibration of circular sandwithplate with uniform load is introduced particularly. The basic equation and four kinds of boundary conditions are got by means of Hamilton principle. Secondly, on the base of this equation, the hypothesis of the time mode and the method of calculus of variations, kinetic equation of circular sandwithplate under quiet deflection and floating deflection is educed by use of Galerkin's methods.The stability of nonlinear vibration of circular sandwithplate with initial deflection has been researched. According as stability theorem, stability of every singularity is estimated in the neighboring area and the chart of trajectory with differentξ0 is protractd under four kinds of boundary conditions.The periodical solutions of nonlinear primary resonance for circular sandwithplate are obtained by use of Lindstedt-Poincare perturbation methods .A demonstrative example was discussed through phase portrait,time history and amplitude-frequency curve by use of Runge-Kutta methods.The changing of initial deflection,K and a harmonic force which can affect kinetic characteristic of configuration was researched.The 1/3 subharmonic solution and stability are obtained by the method of multiple scales and the Calerkin Principle.