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．

According to the relationship of forcing frequency to natural frequency, the quasi-failure model and thequasi-failure probability for the random continuous vibration systems are defined, and the frequencyreliability analysis method for avoiding the resonant is Ixesented. By using the vibration theory and thereliability technique, the quasi-failure analysis method for resoramt problem for the random continuousvibration systems is studied.

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.

The dynamic equations of the Jeffcott rotor with imbalance are concerned. The reliabilityof rotor systems with rubbing is examined. A statistical fourth moment method is developedto determine the first four moments of the system response and the state function.The distribution function of the system state function is approximately determined byusing the Edgeworth series technique. Its reliability is obtained. The effect on the reliabilityof the shaft stiffness, the external damping coefficient, the degree of imbalance andthe stator stiffness is studied. Numerical results are also presented and discussed.