Granular chains with soft boundaries: Slowing the transition to quasi-equilibrium

TL;DR

This study investigates how soft boundaries in granular chains influence the dynamics, showing that softer walls delay the transition to equilibrium and can localize energy, with potential applications in energy management.

Contribution

It provides a detailed numerical analysis of how soft boundaries affect wave reflection and energy localization in granular chains, introducing a toy model for energy trapping.

Findings

Soft walls slow the reflection of solitary waves.

Softer boundaries delay the transition to quasi-equilibrium.

Soft boundaries promote formation of breather-like energy entities.

Abstract

We present here a detailed numerical study of the dynamical behaviour of `soft' uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the formation of solitary waves (SWs). Here, however, the system response to the material properties of the grains and boundaries is further explored. In particular, we examine the details of the transition of the system from a SW phase to an equilibrium-like (or quasi-equilibrium) phase and for this reason we ignore the effects of dissipation in this study. We find that the soft walls slow the reflection of SWs at the boundaries of the system, which in turn slows the journey to quasi-equilibrium. Moreover, the increased grain-wall compression as the boundaries are softened results in fewer average grain-grain contacts at any given time in the quasi-equilibrium phase. These effects lead to increased kinetic energy fluctuations in the short term in softer systems. We conclude with a toy model which exploits the results of soft-wall systems. This toy model supports the formation of breather-like entities and may therefore be useful for localizing energy in desired places in the granular chain.