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Published August 2014 | Published
Journal Article Open

Traveling waves in 2D hexagonal granular crystal lattices


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.

Additional Information

© 2014 This article is published with open access at Springerlink.com. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. Received: 11 April 2013; published online: 7 April 2014. This research is supported in part by the Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF), made possible in part by the American Recovery and Reinvestment Act of 2009, administered by ORISE-ORAU under contract no. DE-AC05-06OR23100, and the Army Research OfficeMURI grant US ARO W911NF-09-1-0436. P.G.K. acknowledges support from the US National Science Foundation under Grant No. CMMI-1000337, the US Air Force under Grant No. FA9550-12-1-0332, the Alexander von Humboldt Foundation, and the Alexander S. Onassis Public Benefit Foundation.

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