Waves in elastic bodies with discrete and continuous dynamic microstructure.



Mishuris, Gennady S, Movchan, Alexander B and Slepyan, Leonid I
(2020) Waves in elastic bodies with discrete and continuous dynamic microstructure. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 378 (2162). 20190313-.

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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)'.

Item Type: Article
Uncontrolled Keywords: wave equations, Green's functions, integral transforms, dispersion relations, dynamic microstructure, mathematical modeling, materials science
Depositing User: Symplectic Admin
Date Deposited: 09 Mar 2020 11:25
Last Modified: 18 Jan 2023 23:58
DOI: 10.1098/rsta.2019.0313
Open Access URL: https://doi.org/10.1098/rsta.2019.0313
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3078317