Motions induced by asymmetric vibrations

Abstract.

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 γ(t) imposed by the plate is unsymmetrical, the coin can move macroscopically with a certain drift velocity $\bar{V}$. We analyse here: (a) the vibration threshold below which $\bar{V}=0$, and the generic behavior expected just above threshold; (b) the limiting behavior at very high amplitudes, where $\bar{V}$ should become independent of the amplitude; (c) the complications due to small, macroscopic inhomogeneities on the supporting plate.