  We consider a stochastic model for the directed motion of a solid object due
to the rectification of asymmetric surface vibrations with Poissonian
shot-noise statistics. The friction between the object and the surface is given
by a piecewise-linear friction force. This models the combined effect of
dynamic friction and singular dry friction. We derive an exact solution of the
stationary Kolmogorov-Feller (KF) equation in the case of two-sided
exponentially distributed amplitudes. The stationary density of the velocity
exhibits singular features such as a discontinuity and a delta-peak singularity
at zero velocity, and also contains contributions from non-integrable solutions
of the KF equation. The mean velocity in our model generally varies
non-monotonically as the strength of the dry friction is increased, indicating
that transport improves for increased dissipation.
