Continuous rolling motion of a disk on a vibrating plate

We studied the behavior of the continuous rolling motion (CRM) of a disk placed on a vibrating plate observed in the experiment using numerical simulations. Numerical simulations show that a rolling disk on a vibrating plate abruptly stops in case of pure rolling without slipping, whereas CRM occurs in the case of slipping. CRM occurs in two frequency bands separated by a gap. We use numerical simulations to determine the gap and the frequency domains for different values of the coefficient of sliding friction. The characteristics of rolling motion depend on the coefficient of slip friction and frequency of vibration.