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A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom.Subsequently a one-dimensional It(o) stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems.The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically.Finally,a stochastic optimal control model is proposed and solved.The numerical results show the effectiveness of this method.