Research on the reliability of friction system under combined additive and multiplicative random excitations

•The stochastic averaging method is generalized to the study of the reliability of non-linearly damped friction system.•The reliability of friction system can be improved by Coulomb friction and reduced by random excitations.•When the amplitude of friction is fixed, the effect of the external random excitation on the reliability of system is dominant.•The theoretical analyses are verified by the numerical results.

In this paper, the reliability of a non-linearly damped friction oscillator under combined additive and multiplicative Gaussian white noise excitations is investigated. The stochastic averaging method, which is usually applied to the research of smooth system, has been extended to the study of the reliability of non-smooth friction system. The results indicate that the reliability of friction system can be improved by Coulomb friction and reduced by random excitations. In particular, the effect of the external random excitation on the reliability is larger than the effect of the parametric random excitation. The validity of the analytical results is verified by the numerical results.