Construction of a statistical model for the dynamics of a base-driven stick-slip oscillator

Abstract

In this paper the dynamics of a dry-friction oscillator driven by a stochastic base motion has been analyzed. The system consists of a simple oscillator (mass-spring) moving on a base with a rough surface. This roughness induces a dry-frictional force between the mass and the base which is 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. The non-smooth behavior of the dry-frictional force associated with the non-smooth stochastic base motion induces in the system stochastic stick-slip oscillations. A statistical model is constructed for the stick-slip dynamics of the system. The objective is to characterize, from a statistical view point, the response of the dry-friction oscillator composed by a sequence of stick and slip-modes. Defined a time interval for analysis, some of the variables which appear in this statistical model are the number of time intervals in which stick and slip occur, the instants at which they begin and their duration. These variables are modeled as stochastic objects. Statistics of them, as mean, variance and entropy, and histograms, are computed by the integration of the dynamics equations of the system using independent samples of the base movement generated with the Monte Carlo method.