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.

This paper extends the stochastic perturbation method to vector-valued and matrix-valued functions. The numerical method for the response and reliability of uncertain structures is formulated using matrix calculus, Kronecker algebra and perturbation theory. Random variables and system derivatives are conveniently arranged into two-dimensional matrices and generalized mathematical formulae are obtained. The results derived are easily amenable to computational procedures.

Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory and the sensitivity analysis approach are employed to present a practical and efficient method for the reliability sensitivity of automobile components with arbitrary distribution parameters. On the condition of first four moments of Original random variables known, the reliability sensitivity theory and case studies are researched. The respective program can be used to obtain the reliability sensitivity of automobile components with arbitrary distribution parameters accurately and quickly.

Techniques from the perturbation method, the second moment and reliability-based design theory are employed to present a practical and effective method for the reliability-based design of automobile components. The theoretical formulae of reliability-based design of automobile compo-nents are obtained. The reliability-based design methods are employed to develop the reliability design of atttomobile axles and springs. The corresponding program can be used to obtain the reliabilit\-based desien parameters of automobile components accurately and quickly,