Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation*

Abstract：A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate un-der axial inplane excitation considering the influence of random environment factors. Firstly, the model is simplified by applying the stochastic averaging method of quasi-nonintegrable Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process are utilized to analyze the stochastic stability of the trivial solution of the system. Thirdly, the stochastic Hopf bifurcation of the vibration model is explored according to the qualitative changes in stationary probability density of system response, showing that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simple way on the potential applications of stochastic stability and bifurcation analysis. Keywords：rectangular thin plate; stochastic stability; stochastic Hopf bifurcation The nonlinear oscillation of thin plates has been paid much attention in the case of large deformation. With the application of thin plates in shuttles and large space sta-tions, nonlinear dynamics, bifurcation, and the chaos of thin plates have become more and more important. In the past decade, a number of investigations have been mad