Abstract
We experimentally investigate the dynamics of two particles driven vertically and free to collide in a nearly one-dimensional channel. Both spherical particles are Delrin with a diameter of d = 5.0 mm. We obtained data for driving frequencies, f, ranging from 26.06 to 29.52 HZ and acceleration magnitudes, Γ, from 1.79 to 2.42 g. High speed digital imaging is used to extract the positions of the two particles from experiment, with digital imaging analysis used to extract velocities and accelerations from sequential images. The total energy and the velocity of the particles before and after collisions are studied in both the lab frame and centre of mass frame. Most of the experimental results suggest a linear dependence for the relative velocity after collision on the relative velocity before collision with the coefficient of restitution approximately constant at 0.8. However, some data in the low impact velocity regime indicates the possibility of an occasional energy transfer between the rotational and translational degrees of freedom.
Highlights
A bouncing ball driven vertically on a vibrating platform under gravity has received a lot of attentions since the pioneering work of Luck and Mehta [1]
Since only the translational energy is used to calculate the coefficient of restitution, the relative velocity after collision may be greater than the relative velocity before collision due to the gaining of translational energy at the expense of the rotational energy
We studied the dynamics of two Delrin particles driven vertically in a nearly one-dimensional channel
Summary
A bouncing ball driven vertically on a vibrating platform under gravity has received a lot of attentions since the pioneering work of Luck and Mehta [1]. Despite the simplicity of this dynamical system, a rich variety of behaviours may occur including periodic motion, period-doubling cascade and chaos [2]. Understanding these behaviours requires a precise knowledge of the inelasticity characterized by the coefficient of restitution, e [3], which is defined as the ratio between the rebound velocity and the impact velocity: e = vout/vin (1). The coefficient of restitution is defined in the range of 0 ≤ e ≤ 1, but in some special cases like oblique collisions [5] and nanoparticle collisions [6], the coefficient of restitution may exceed unity Such behavior can be described as the super-elastic collisions. Numerous investigations have been developed to experimentally and numerically study single particle dynamics including using aspherical and grain-filled particles [8-
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