Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation |
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| Authors: | GE Gen WANG Hongli XU Jia |
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| Institution: | School of Mechanical Engineering, Tianjin University, Tianjin 300072, China |
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| Abstract: | A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under 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. |
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| Keywords: | rectangular thin plate stochastic stability stochastic Hopf bifurcation |
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