Nonlinear Waves in Disordered Diatomic Granular Chains

TL;DR

This study explores how highly nonlinear waves propagate and scatter in disordered diatomic granular chains, revealing two distinct regimes of wave behavior influenced by disorder levels, with implications for modeling heterogeneity effects.

Contribution

It introduces a novel analogy between disordered granular chains and spin chains, and characterizes the transition between different wave propagation regimes.

Findings

Low-disorder chains support solitary waves with exponential decay.

High-disorder chains exhibit power-law decay of wave amplitude.

Wave transmission becomes insensitive to disorder beyond a critical level.

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.