Role of parameters in the stochastic dynamics of a stick-slip oscillator

Abstract

In this paper a parametric analysis of a sample of responses of a dry-friction oscillator is performed in order to construct a statistical model. The system consists of a simple oscillator moving on a base with a rough surface. Due to this roughness, the mass is subject to a dry-frictional force modeled as a Coulomb friction. It is considered that the base has an imposed stochastic bang-bang motion which excites the system in a stochastic way and, induces stochastic stick-slip oscillations. The base velocity is modeled by a Poisson process for which a probabilistic model is fully specified. The system response is composed by a random sequence alternating stick and slip-modes. With realizations of the system, a statistical model is constructed for this sequence. Statistics and histograms of the random variables which characterize the stick-slip process are estimated. The objective of the paper is to analyze how these estimated statistics and histograms vary with the system parameters, i.e., to make a parametric analysis of the statistical model of the stick-slip process.