Traveling waves in 2D hexagonal granular crystal lattices

Abstract

This study describes the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. The dynamics of the system are modeled using the Hertzian normal contact law. 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 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 directional power law decay of the wave velocity for various angles of impact. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates.