Solitary wave trains in granular chains: Experiments, theory and simulations

TL;DR

This paper investigates how solitary wave trains form in granular chains due to impacts or geometric changes, revealing exponential force unloading and confirming findings through experiments and simulations.

Contribution

It introduces a simple analytical model explaining solitary wave train formation and force unloading in granular chains, supported by experiments and numerical simulations.

Findings

Force unloading at chain edges is nearly exponential.

Wave train amplitudes decrease with each solitary wave.

Experimental and numerical results agree with analytical predictions.

Abstract

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains' masses and the striker mass. Numerical calculations and experiments corroborate these findings.