Dynamic response of a rigid block resting on a diagonally shaken horizontal substrate

The model inspired by behavior of a rigid block on a diagonally shaken horizontal substrate with harmonically varying dry friction is applied to the analysis of vibration-induced motion. Depending on the vibration angle and dimensionless group parameters, five modes of periodic motion are identified: stick–stick, one-burst and two-burst stick–slip, non-stick, and alternating slip-free flight. Criteria governing the initiation of the motion modes are derived. It is shown that for a given plate acceleration there exists an optimal vibration angle, at which the average velocity of the induced motion reaches maximum. The scaling dependence for the maximum drift velocity is found. Reasonably good agreement has been found between the mean drift velocity measured experimentally and that predicted by the model for one-burst stick-slip motion.