Stick-slip motion of solids with dry friction subject to random vibrations and an external field

TL;DR

This paper models the complex dynamics of a solid object experiencing dry friction, random vibrations, and an external force, deriving analytical expressions for velocity transitions, work distribution, and fluctuation relations.

Contribution

It introduces a path integral approach to analytically analyze dry friction dynamics under stochastic vibrations and external forces, including fluctuation relations.

Findings

Derived transition probability for velocity

Obtained stationary distribution of work

Established fluctuation relation for work fluctuations

Abstract

We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being proportional to the sign of the object's velocity relative to the surface, and therefore shows a discontinuity at zero velocity. Using a path integral approach, we derive analytical expressions for the transition probability of the object's velocity and the stationary distribution of the work done on the object due to the external force. From the latter distribution, we also derive a fluctuation relation for the mechanical work fluctuations, which incorporates the effect of the dry friction.