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On the wave dispersion in microstructured solids

On the wave dispersion in microstructured solids Continuum Mech. Thermodyn. https://doi.org/10.1007/s00161-018-0683-1 ORIGINAL ARTICLE Arkadi Berezovski · M. Erden Yildizdag · Daria Scerrato Received: 19 March 2018 / Accepted: 14 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. Keywords Micromorphic media · Wave propagation · Internal variables 1 Introduction Elastic wave dispersion is very often an indicator of the presence of a microstructure in a solid. The study of the wave dispersion in bodies with regular microstructures goes back to Newton and Euler (see [15]for the historical background). This line of research resulted in crystal lattice theory [13], and is come back in fashion in recent years due to the possibility of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Continuum Mechanics and Thermodynamics Springer Journals

On the wave dispersion in microstructured solids

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Classical and Continuum Physics; Engineering Thermodynamics, Heat and Mass Transfer; Theoretical and Applied Mechanics; Structural Materials
ISSN
0935-1175
eISSN
1432-0959
DOI
10.1007/s00161-018-0683-1
Publisher site
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Abstract

Continuum Mech. Thermodyn. https://doi.org/10.1007/s00161-018-0683-1 ORIGINAL ARTICLE Arkadi Berezovski · M. Erden Yildizdag · Daria Scerrato Received: 19 March 2018 / Accepted: 14 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. Keywords Micromorphic media · Wave propagation · Internal variables 1 Introduction Elastic wave dispersion is very often an indicator of the presence of a microstructure in a solid. The study of the wave dispersion in bodies with regular microstructures goes back to Newton and Euler (see [15]for the historical background). This line of research resulted in crystal lattice theory [13], and is come back in fashion in recent years due to the possibility of

Journal

Continuum Mechanics and Thermodynamics – Springer Journals

Published: May 29, 2018

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