On the basis of the dynamic equations of the Jeffcott rotor–stator model with imbalance, the reliabilitysensitivity of the rotor–stator systems with rubbing is examined. A statistical fourth moment method is developed to determine the first four moments of system response and state function. The distribution function of the system state function is approximatelydetermined by the standard normal distribution functions using the Edgeworth series technique. The reliabilityand reliabilitysensitivityare obtained and the effect on reliabilityand reliabilitysensitivity of shaft stiffness and damping, stator stiffness and damping, radial clearance and stator radial stiffness is studied. Numerical results are also presented and discussed.

The first passage of uncertain single degree-of-freedom nonlinear oscillators subjected to random excitation is examined. Statistical fourthmoment method is developed to determine first four moments of system response and state function. Distribution function of the systemstate function is approximately determined by the standard normal distribution functions using Edgeworth series technique and the reliabilityis obtained

This paper presents the dynamics problems of stochastic vibratory machine systems. The random responses of the vibratory machine systems with stochastic parameters subjected to random excitation are researched using a stochastic perturbation method. The numerical results ,are obtained. The dynamic characteristics of nonlinear stochastic vibratory machine are analyzed.

This paper extends the probabilistic finite element method (PFEM) to vector-valued and matrix-valued functions using techniques from matrix calculus and Kronecker algebra, and presents the PFEM in Kronecker notation for linear mad nonlinear continua. The results derived are easily amenable to computa-tional procedures.

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.