@article{55246f9892d54c2488461fca91cdcccd,
title = "Waves in elastic bodies with discrete and continuous dynamic microstructure",
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",
keywords = "dynamic microstructure, wave equations, Green's functions, integral transforms, dispersion relations, Dispersion relations, Dynamic microstructure, Green{\textquoteright}s functions, Wave equations, Integral transforms",
author = "Gennady Mishuris and Movchan, {Alexander B.} and Slepyan, {Leonid I.}",
note = "Funding Information: Data accessibility. This article does not contain any additional data. Competing interests. We declare we have no competing interests. Funding. A.B.M. would like to acknowledge the support of the EPSRC Program (grant no. EP/L024926/1). G.S.M. acknowledges financial support from the ERC Advanced Grant {\textquoteleft}Instabilities and nonlocal multiscale modelling of materials{\textquoteright} (grant no. ERC-2013-ADG-340561-INSTABILITIES) and the British Council UK– Israel Science Lectureships Programme enabling his visit to Tel Aviv University. He is also thankful to the Royal Society for the Wolfson Research Merit Award and the Isaac Newton Institute for Mathematical Sciences for Simon{\textquoteright}s Fellowship. L.I.S. is grateful to Prof. Dov Sherman for the support of a grant (under the same name) received by him from the Israel Science Foundation. He is thankful to the Isaac Newton Institute for Mathematical Sciences for Simon{\textquoteright}s Fellowship. This work was supported by EPSRC (grant no. EP/R014604/1). Acknowledgements. A.B.M. is grateful for the invitation and support from Tel Aviv University for an academic visit in October 2018. L.I.S. thanks Prof. Dov Sherman for organizing the seminar {\textquoteleft}Dynamic phenomena in media with microstructure{\textquoteright}, School of Mechanical Engineering, Tel Aviv University, 7–12 October 2018. L.I.S. is also very grateful to all the colleagues who took part in the event in person or online. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme {\textquoteleft}Bringing pure and applied analysis together via the Wiener–Hopf technique, its generalizations and applications{\textquoteright} where work on this paper was completed. Funding Information: Funding. A.B.M. would like to acknowledge the support of the EPSRC Program (grant no. EP/L024926/1). G.S.M. acknowledges financial support from the ERC Advanced Grant ?Instabilities and nonlocal multiscale modelling of materials? (grant no. ERC-2013-ADG-340561-INSTABILITIES) and the British Council UK?Israel Science Lectureships Programme enabling his visit to Tel Aviv University. He is also thankful to the Royal Society for the Wolfson Research Merit Award and the Isaac Newton Institute for Mathematical Sciences for Simon?s Fellowship. L.I.S. is grateful to Prof. Dov Sherman for the support of a grant (under the same name) received by him from the Israel Science Foundation. He is thankful to the Isaac Newton Institute for Mathematical Sciences for Simon?s Fellowship. This work was supported by EPSRC (grant no. EP/R014604/1). Publisher Copyright: {\textcopyright} 2019 The Authors.",
year = "2020",
month = jan,
day = "10",
doi = "10.1098/rsta.2019.0313",
language = "English",
volume = "378",
journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "0962-8428",
publisher = "Royal Society",
number = "2162",
}