Frictional stick-slip oscillation as a first-passage problem

UPMC Université Paris 06, Institut des Systèmes Intelligents et de Robotique - Paris, France, EU

^a yon@zero-th.org

Received: 6 June 2011
Accepted: 8 August 2011

Abstract

We study complex frictional stick-slip oscillations by formulating a novel first-passage time problem whose solutions are used to compute distributions of stick-slip oscillation periods, displacements, and slip durations for a generic family of stochastic friction models. Approximate solutions are developed using a level-crossing expansion due to Rice and Stratonovich. Sample results for a minimal Langevin sliding friction model agree with simulations over a range of system parameters, and reproduce qualitative features of prior experimental studies of stick-slip motion. The analysis also reveals a complex oscillatory regime near the transition from stick-slip to continuous sliding, in which additional transient modes are excited through boundary-noise interactions.