Study of two-section composite chain of beads under vertical vibration

Abstract

We investigated the dynamic properties of a two-section composite chain of beads under vertical vibration. By analyzing the chain's motion, including phase-shift, mean dilation, center-of-mass displacement, and energy, we found that with different bead arrangements, the chain behaved in different ways. We believe that interaction existing at the interface between bead sections provides the underlying cause. This interaction causes different energy in different arrangements, which leads to different dynamic characteristics. -6]. For example, if waves propagate from heavy to light beads, most of the energy will be transmitted through the interface; in contrast if waves propagate from light to heavy beads, most of the energy will be reflected. Such single-direction transmission, which can be thought of as an "acoustic-diode" effect, is due to the strong nonlinearity arising from granular materials. The study on granular chain behavior under continuous vertical vibration was initially conducted by Luding et al. [7,8]. They pointed out that for a chain of beads with high coefficient of restitution (i.e. "hard" beads), as the vibrational acceleration increases, it will transite from a condensed phase (where all beads stay in contact with each other and move as a whole with the vibration source) to a fluidized phase (where all beads move independently from one another and away from the source). However, for a chain of beads with low coefficient of restitution (i.e. "soft" beads), one sees a transition from a condensed phase to a clustered phase (where all beads move away from the source but still approximately stay in contact with each other) without fluidization, essentially because the dissipation of energy in "soft" bead collisions is greater than that in "hard" beads. Luding's work was based on a chain consisting of only one type of bead (referred to as "single-section chain"). Although still focused on single-section chains, these studies were extended by others [9][10][11] to include the use of Boltzmann's equation and molecular dynamic simulation [12][13][14] to analyze the motion of the granular materials; few studies report on the behavior of composite chains.In the present paper, we describe the dynamics of composite granular chains under continuous vertical vibration.