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

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