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Published April 1, 2009 | Submitted
Journal Article Open

Highly nonlinear solitary waves in heterogeneous periodic granular media


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, brass, 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 good agreement between experiments and numerical simulations. We also find 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.

Additional Information

© 2009 Elsevier. Received 20 December 2007; revised 22 October 2008; accepted 17 December 2008. Communicated by R.P. Behringer. Available online 3 January 2009. M.A.P. acknowledges support from the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information (where he was a postdoc during much of this research) and the Graduate Aerospace Laboratories at Caltech (GALCIT) for hosting one of his visits. C.D. acknowledges support from ARO and NSF (CMMI), and P.G.K. acknowledges support from NSF-DMS and CAREER. We thank Devvrath Khatri, Vitali F. Nesterenko, and two anonymous referees for useful suggestions.

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