Waves in elastic bodies with discrete and continuous dynamic microstructure-Reference-Cited by-同舟云学术

Waves in elastic bodies with discrete and continuous dynamic microstructure

Published:2019-11-25 Issue:2162 Volume:378 Page:20190313
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Mishuris Gennady S.¹^ORCID,Movchan Alexander B.²^ORCID,Slepyan Leonid I.³^ORCID

Affiliation:

1. Department of Mathematics, IMPACS, Aberystwyth University, Aberystwyth SY23 3BZ, UK

2. Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK

3. School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, PO Box 39040, Ramat Aviv, 69978 Tel Aviv, Israel

Abstract

This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green's kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

Funder

EPSRC Program

ERC Advanced

British Council UK–Israel Science Lectureships Programme

Israel Science Foundation

EPSRC

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2019.0313

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3. Kunin IA. 1982 Elastic media with microstructure I: One-dimensional models (eds M Cardona P Fulde H-J Queisser E Kröner). Springer Series in Solid State Sciences No. 26. Berlin Germany: Springer (Nauka 1975 in Russian).

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