On the basis of the dynamics equation of Jeffcott rotor stator model with imbal-ance, the random responses of rotor stator systems with rubbing is studied.The method is based on a second order expansion of the governing equations and the matrix calculus, the Kronecker algebra is used in the mathematical development. The random parameters including shaft stiffness and damping, stator stiffness and damp-ing, radial clearance and stator radial stiffness are used to research the random responses of the rotor-stator systems. The numerical results are also presented and discussed.

在一般随机有限元法的基础上，给出了在随机参数的联合概率密度函数未知的情况下，具有相关失效模式的非线性动态随机结构系统可靠性分析的方法．应用四阶矩技术、最大熵理论、边缘概率分布函数的概念和不完全概率信息理论，解决了多自由度非线性随机结构振动系统的首次超限破坏问题．

Based on the generalized probabilistic finite element method, this paper presents anapproximate solution technique for general multi-degree-of-freedom nonlinear random vibrationsystems with random parameters. The fourth-moment technique, maximum entropy theory andincomplete probability information theory are employed to systematically develop a reliabilityanalysis method for dynamic random structural systems with correlation failure modes underunavailable joint probability density functions of basic random variables. The first passage problemof multi-degree-of-freedom nonlinear random vibration systems is solved.

Techniques from perturbation method and reliability-based design theory are employed to present the practical and effective method for the reliability-based design of gear pairs. The theoretical formulae of reliability-based design of gear pairs are obtained. The corresponding program can be used to obtain the reliability-based design parameters of gear pairs accurately and quickly.

将可靠性设计理论与灵敏度分析方法相结合，讨论了具有任意分布参数的机械零件的可靠性灵敏度设计问题，提出了可靠性灵敏度设计的计算方法，给出了可靠性灵敏度的变化规律，研究了设计参数的改变对机械零件的可靠性的影响，为机械零件的可靠性设计提供了理论依据。