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Published December 15, 2007 | Submitted
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Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains


We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer/heavier beads (stainless steel) are alternated with softer/lighter ones (polytetrafluoroethylene beads). We find excellent agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of the dimer lattice on the properties (width and propagation speed) of the obtained highly nonlinear wave solutions.

Additional Information

Author preprint. We acknowledge support from the Caltech Information Science and Technology initiative (M.A.P.), start-up funds from Caltech (C.D.), and NSFDMS and CAREER (P.G.K.). I.S. performed his work as a visiting student of GALCIT at Caltech. We thank A. Molinari and V.F. Nesterenko for useful discussions.

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