Motions induced by asymmetric vibrations : The solid/solid case

We discuss theoretically the motions of a coin on a horizontally vibrating plate, with dry friction between the coin and the plate. As first noticed by Daniel and Chaudhury in a different situation (droplets on a plate), when the periodic acceleration gamma(t) imposed by the plate is unsymmetrical, the coin can move macroscopically with a certain drift velocity V. We analyse here: (a) the vibration threshold below which V=0, and the generic behavior expected just above threshold; (b) the limiting behavior at very high amplitudes, where V should become independent of the amplitude; (c) the complications due to small, macroscopic inhomogeneities on the supporting plate.