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Propagation of highly nonlinear solitary waves in a curved granular chain

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Abstract

We assemble granular chains composed of spheres of uniform diameter in different curved configurations. We study the properties of highly nonlinear solitary waves traveling in the curved channels as a function of the curve angle and of the radius of curvature, using experiments and numerical simulations. We observe that solitary waves propagate robustly even under drastic deflection, such as \(90^{\circ }\) and \(180^{\circ }\) turns. When the solitary waves encounter a sharp turn with a radius of curvature as small as one spherical particle’s diameter, we report the formation of secondary solitary waves resulting from the interaction with the guiding rail. We compare experimental results with numerical simulations based on a discrete element model that accounts for nonlinear and dissipative interactions between particles. This study demonstrates that granular chains are efficient wave-guides, even in complex geometrical configurations. Moreover, the findings in this study suggest that solitary waves could be used as novel information and/or energy carriers.

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Acknowledgments

The authors at the University of Pittsburgh acknowledge the support of the Federal Railroad Administration under contract DTFR53-12-C-00014 and the University of Pittsburgh’s Mascaro Center for Sustainable Innovation. JY acknowledges the support of the University of South Carolina and the National Science Foundation (CMMI-1234452). This work was also partially supported by the National Science Foundation [CMMI-0825983 and CMMI-844540 (CAREER)].

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Authors and Affiliations

  1. Laboratory for Nondestructive Evaluation and Structural Health Monitoring Studies, Department of Civil and Environmental Engineering, University of Pittsburgh, 729 Benedum Hall, 3700 O’Hara St., Pittsburgh, PA, 15261, USA

    Luyao Cai, Piervincenzo Rizzo & Xianglei Ni

  2. Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Room A220, Columbia, SC, 29208, USA

    Jinkyu Yang

  3. Engineering and Applied Science, California Institute of Technology, 1200 E California Boulevard, MC 105-50, Pasadena, CA, 91125, USA

    Chiara Daraio

  4. Department of Mechanical and Process Engineering, ETH Zürich, Tannenstrasse 3, 8092 , Zürich, Switzerland

    Chiara Daraio

Authors
  1. Luyao Cai
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  2. Jinkyu Yang
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  3. Piervincenzo Rizzo
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  4. Xianglei Ni
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  5. Chiara Daraio
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Correspondence to Piervincenzo Rizzo.

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Cai, L., Yang, J., Rizzo, P. et al. Propagation of highly nonlinear solitary waves in a curved granular chain. Granular Matter 15, 357–366 (2013). https://doi.org/10.1007/s10035-013-0414-z

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  • DOI: https://doi.org/10.1007/s10035-013-0414-z

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