Energy of a single bead bouncing on a vibrating plate: Experiments and numerical simulations

Abstract

The energy of a single bead bouncing on a vibrating plate is determined in simulations and experiments by tracking the bead-plate collision times. The plate oscillates sinusoidally along the vertical with the dimensionless peak acceleration [Formula presented] and the bead-plate collisions are characterized by the velocity restitution coefficient [Formula presented] Above the threshold dimensionless peak acceleration [Formula presented] which does not depend on the restitution coefficient, the bead energy is shown to initially increase linearly with the vibration amplitude A, whereas it is found to scale like [Formula presented] where [Formula presented] is the peak velocity of the plate, only in the limit [Formula presented] The threshold [Formula presented] is shown to decrease when the bead is subjected, in simulations, to additional nondissipative collisions occurring with the typical frequency [Formula presented] As a consequence, the bead energy scales like [Formula presented] for all vibration strengths in the limit [Formula presented] From the experimental and numerical findings, an analytical expression of the bead energy as a function of the experimental parameters is proposed. © 2003 The American Physical Society.