On the random aspect of intermittent stick/slip motion

Abstract

A stochastic interpretation of the stick/slip mechanism is proposed to model and mitigate the complicated friction interaction that occurs between surfaces, with direct implications on the stability of dynamic mechanical systems involved. Most investigations dealt with the estimation of such stability regions in a deterministic framework. A realistic approach is to consider random aspects in the analysis of complex dynamic behaviors. In the present article, a stick–slip nonlinear model possessing multiple periodic solutions is considered under fluctuating random excitations. The time evolution of the probability density function is studied by employing an adaptive path integration method and then compared through Monte-Carlo simulations. A parametric study is performed on characteristics such as noise intensity and initial distribution. The physical example employed will permit to assume the entrance of noise through a first-order linear filter. Results reveal that the randomness factor extremely affects the probability of occurrence of each solution, justifying the application of such analyses in reliability-related studies and situations where sensitivity to randomness is acute.