On the basis of the rubbing dynamics equation of the Jeffcott rotor stator model with imbalance, the sensitivity of rotor stator systems with rubbing is studied. The effect on sensitivity of shaft stiffness and damping, stator stiffness and damping, radial clearance, and stator radial stiffness is investigated. The numerical results are presented and discussed.

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.

Techniques from the perturbation method, the reliability-baseddesign theory and optimisation techniques are employed to present apractical and effective method for the reliability-based optimisation ofautomobile components. The theoretical formulae for reliability-basedoptimisation are obtained. The most probable point perturbation method(MPPPM) and reliability-based optimisation theory are employed todevelop the reliability-based optimal design of automobile components.Two examples are used to illustrate the reliability-based optimisationformulation and demonstrate the method. The accuracy of the approachproposed is evaluated by comparing their results to that obtained fromMonte Carlo simulations (MCS)

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.

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.