Dynamical Stability of Primary Resonance System of a Thin Rectangular Plate on Nonlinear Foundation in Temperature Field

In order to study the dynamical stability of primary resonance system of a thin rectangular plate on nonlinear foundation subject to harmonic excitation in temperature field,the nonlinear dynamical equation of the system is established according to elastic theory.A nonlinear vibration equation is obtained based on Galerkin's method.The type of equilibrium point and the stability of the system are analyzed by means of stability theory.By using the amplitude of excitation F as the control parameter,the results of numerical analysis are as follows: from the analyzing results of history diagram and phase diagram,the stability of the system varies with changing the control parameter of the system;the amplitude of the primary resonance system increases with the control parameter F increasing;and the amplitude of the primary resonance system exists beating phenomenon when the control parameter F is small.