Subharmonic Motion of Particles in a Vibrating Tube

TL;DR

This paper investigates the subharmonic motion of inelastic particles in a vibrating tube, revealing mode dominance at specific frequency ratios and proposing a new timescale related to pile recompaction.

Contribution

It introduces a molecular dynamics simulation study of particle motion in a vibrating tube, identifying subharmonic modes and a new timescale for pile recompaction.

Findings

Dominant modes at frequency ratios 1/2, 1/3, 1/1.

Motion described by superposition of multiple modes.

Proposes a new timescale τ for pile recompaction.

Abstract

We study the motion of strongly inelastic particles in a narrow vibrating tube using molecular dynamics simulation. At low frequency of the vibration, we observe qualitative changes of the motion, as the depth of the pile increases. The center of mass of the particle cloud can be described by a superposition of modes of different frequencies. For certain values of the depth, a single mode dominates. The frequency of the dominant mode is 1/2, 1/3, or 1/1 of the vibration. We suggest that the behavior can be understood in terms of a new time-scale $\tau$, reflecting the recompaction time for a finite-depth pile.