Traveling Waves in 2D Hexagonal Granular Crystal Lattices

TL;DR

This paper investigates the dynamic wave response in 2D hexagonal granular lattices, combining experiments, simulations, and theoretical models to understand wave decay, velocity scaling, and disorder effects.

Contribution

It extends the binary collision approximation to 2D hexagonal lattices and provides new insights into wave decay and disorder effects in granular systems.

Findings

Wave structures emerge and decay after impact

Predicted decay rates match simulations and experiments

Scaling relations describe wave velocity decay

Abstract

We describe the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. After the initial impact strikes the system, a characteristic wave structure emerges and continuously decays as it propagates through the lattice. Using an extension of the binary collision approximation (BCA) for one-dimensional chains, we predict its decay rate, which compares well with numerical simulations and experimental data. While the hexagonal lattice does not support constant speed traveling waves, we provide scaling relations that characterize the power law decay of the wave velocity. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates.