By using the stochastic averaging method based on generalized harmonic functions, Pontryagin equation and backward Kolmogorov equation of a 5DOF strongly nonlinear vibration system under Gaussian white noise excitation, were established. The mean first-passage time and the conditional reliability function and the conditional probability density function of the mean first-passage time were obtained after solving the above two higher-dimensional partial differential equations. All theoretical results were verified with Monte Carlo numerical simulation.%利用基于广义谐和函数的随机平均法,建立了高斯白噪声激励下五自由度强非线性随机振动系统的Pon -tryagin方程及后向Kolmogorov方程.求解这两个高维偏微分方程,得到了系统的平均首次穿越时间、条件可靠性函数以及平均首次穿越时间的条件概率密度.用Monte Carlo数值模拟验证了理论方法的有效性.
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