On energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation

We study a friction controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in quantities such as displacement, traveled distance, and energy loss due to friction. Assuming that the random excitation is switched off at some time, it is shown that the problem can be treated in an analytic, explicit, manner. Particularly, we derive formulas for the moments of the displacement and distance, and also for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process given by a system of SDEs. This equation is solved by reduction to a parametric Riemann boundary value problem of complex analysis.