摘　要：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Pontryagin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。

Abstract: By using the stochastic averaging method based on the generalized harmonic function, this paper established the Pontryagin equation and backward Kolmogorov equation of 5DOF strongly nonlinear vibration system under Gaussian white noises excitations. The mean first-passage time and conditional reliability function and the conditional probability density function of the mean first-passage time were obtained from solving the above two high-dimensional partial differential equations. All theoretical results are verified by Monte Carlo digital simulation.