Highly Nonlinear Solitary Waves in Heterogeneous Periodic Granular Media

TL;DR

This study investigates how highly nonlinear solitary waves propagate in one-dimensional granular chains with heterogeneous periodic structures, using experiments, simulations, and theory to understand the effects of material composition on wave behavior.

Contribution

The paper introduces a comprehensive analysis of nonlinear wave propagation in heterogeneous granular media, combining experimental, numerical, and theoretical approaches for the first time.

Findings

Excellent agreement between experiments and simulations.

Theoretical model accurately predicts wave properties in heterogeneous chains.

Heterogeneity significantly influences wave width and speed.

Abstract

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, bronze, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find very good agreement between experiments and numerical simulations. We find equally good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system.