Nonlinear Waves in Disordered Diatomic Granular Chains
Abstract
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.
Cite
@article{arxiv.0904.0426,
title = {Nonlinear Waves in Disordered Diatomic Granular Chains},
author = {Laurent Ponson and Nicholas Boechler and Yi Ming Lai and Mason A. Porter and P. G. Kevrekidis and Chiara Daraio},
journal= {arXiv preprint arXiv:0904.0426},
year = {2015}
}
Comments
10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results)