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Elastic wave propagation in weakly nonlinear media and metamaterials: a review of recent developments

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Abstract

In this paper we review recent progress on the analysis, experimental exploration, and application of elastic wave propagation in weakly nonlinear media and metamaterials. We provide a detailed technical discussion overviewing two broad areas of active research: (1) discrete nonlinear periodic systems and metamaterials, and (2) continuous nonlinear systems with a focus on nonlinear guided waves. The specific intent is to introduce the reader to asymptotic analysis methods currently being employed in the field of study, to highlight their results to date, and to motivate follow-on studies. Where appropriate, we include details on experimental explorations and envisioned applications, both of which have received relatively sparse attention to date.

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Acknowledgements

P.P. acknowledges support from the National Science Centre in Poland through Grant No. 2018/31/B/ST8/00753 and partial support through ’Excellence initiative—research university’ program for AGH University of Science and Technology. M.J.L. acknowledges support from the U.S. National Science Foundation under award numbers 1741565 and 1929849.

Funding

The authors list their funding sources in the Acknowledgements.

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Authors and Affiliations

  1. Physics Department, United States Naval Academy, Annapolis, MD, USA

    Matthew D. Fronk

  2. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Lezheng Fang

  3. Department of Robotics and Mechatronics, AGH - University of Science and Technology, Kraków, Poland

    Pawel Packo

  4. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

Authors
  1. Matthew D. Fronk
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  2. Lezheng Fang
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  3. Pawel Packo
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  4. Michael J. Leamy
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Correspondence to Michael J. Leamy.

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Fronk, M.D., Fang, L., Packo, P. et al. Elastic wave propagation in weakly nonlinear media and metamaterials: a review of recent developments. Nonlinear Dyn 111, 10709–10741 (2023). https://doi.org/10.1007/s11071-023-08399-6

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  • DOI: https://doi.org/10.1007/s11071-023-08399-6

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