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On the wave dispersion in microstructured solids

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Abstract

In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle. The dispersion relation is obtained and the possibility of the emerging band gaps is shown in such microstructured materials. Some numerical simulations are also performed in order to highlight the dispersive nature of the material under study.

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Authors and Affiliations

  1. Department of Cybernetics, School of Science, Tallinn University of Technology, Tallinn, Estonia

    Arkadi Berezovski

  2. Department of Mechanical Engineering, University of California, Berkeley, CA, 94720, USA

    M. Erden Yildizdag

  3. M&MoCs Research Center, University of L’Aquila, L’Aquila, Italy

    Daria Scerrato

  4. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia

    Daria Scerrato

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  1. Arkadi Berezovski
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  2. M. Erden Yildizdag
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  3. Daria Scerrato
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Correspondence to Daria Scerrato.

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Communicated by Francesco dell’Isola.

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Berezovski, A., Yildizdag, M.E. & Scerrato, D. On the wave dispersion in microstructured solids. Continuum Mech. Thermodyn. 32, 569–588 (2020). https://doi.org/10.1007/s00161-018-0683-1

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