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

• Published in: Nonlinearity Vol. 24; no. 2; pp. 351 - 372
• Main Authors: Baule, A, Touchette, H, Cohen, E G D
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.02.2011; Institute of Physics
• Subjects: Constants; Discontinuity; Dry friction; Dynamic tests; Exact sciences and technology; Exact solutions; Fluctuation; Global analysis, analysis on manifolds; Inference from stochastic processes; time series analysis; Mathematical analysis; Mathematical methods in physics; Mathematics; Other topics in mathematical methods in physics; Physics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Solid surfaces; Statistics; Stochastic processes; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; External field; Discontinuity; Motion; Fluctuations; Zero; Force; Path integral; Nonlinear analysis; Slip; Velocity distribution; Solid; Surface; Random field; Friction; Friction coefficient; Distribution function; Transition probability; Sign; Dynamic model; Mathematical physics; Random vibration; Stationary distribution
• ISSN: 0951-7715; 1361-6544
• DOI: 10.1088/0951-7715/24/2/001

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 modelled 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.