Abstract：One stochastic two dimensional dynamical model of a simple supported thin rectangular plate subject to in-plate stochastic parametrical excitation is proposed based on elastic theory and Galerkin’s approach. At first the model is simplified applying the stochastic average theory of quasi-integral Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively is utilized to analyze the local and global stochastic stability of the trivial solution of system. Finally, it is explored that the stochastic Hopf bifurcation of the model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. And the results of numerical simulation support the theoretical analysis.
2011, Vol. 30 
