Stochastic stability and first passage failure for a thin rectangular plate subject to stochastic parametrical excitation

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (4) : 179-183.

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Stochastic stability and first passage failure for a thin rectangular plate subject to stochastic parametrical excitation

Ge Gen1; Wang Hong-li2 ; Xu jia2

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Abstract

One stochastic two dimensional dynamical model of a thin rectangular plate subject to in-plate stochastic parametrical excitation with control is proposed based on Galerkin’s approach. At first the model is simplified applying the stochastic average theory of quasi-integral Hamilton system. Secondly, the optimal control law is derived from the dynamical programming equations and the control constraints.
Finally, the Backward Kolmogorov equation for reliability function had been established. The dynamical programming equations for maximum reliability problem are finalized and their relationships to the backward Kolmogorov equation for the reliability function are pointed out. The numerical results show that the procedure is effective and efficiency.

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thin rectangular plate / Stochastic optimal control / First passage failure

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Ge Gen; Wang Hong-li;Xu jia. Stochastic stability and first passage failure for a thin rectangular plate subject to stochastic parametrical excitation[J]. Journal of Vibration and Shock, 2012, 31(4): 179-183