Stochastic optimal control of first-passage failure for rectangular thin plate vibration model under gaussian white-noise excitations

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasi-nonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito 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.