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Non-reciprocal wave propagation in time-modulated elastic lattices with inerters

Danilo Karličić, Milan Cajic, Stepa Paunović, Aleksandar Obradović, Sondipon Adhikari, Johan Christensen

Applied Mathematical Modelling, Volume: 117, Pages: 316 - 335

Swansea University Author: Milan Cajic

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DOI (Published version): 10.1016/j.apm.2022.12.029

Abstract

Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the li...

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Published in: Applied Mathematical Modelling
ISSN: 0307-904X
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62200
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A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. 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spelling v2 62200 2022-12-22 Non-reciprocal wave propagation in time-modulated elastic lattices with inerters 08b3d2d27daffae99331d905f63a6697 Milan Cajic Milan Cajic true false 2022-12-22 ACEM Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices. Journal Article Applied Mathematical Modelling 117 316 335 Elsevier BV 0307-904X Non-reciprocial wave propagation; Mechancial metamaterials; Phononic lattices; Inerters; Time-modulated properties; Coupled beams system 1 5 2023 2023-05-01 10.1016/j.apm.2022.12.029 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University DK and SP acknowledge the support by the Serbian Ministry of Education, Science and Technological Development through the Mathematical Institute of the Serbian Academy of Sciences and Arts. MC and SA acknowledge funding from European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 896942 (METASINK). JC acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (Grant No. RYC-2015-17156). JC also acknowledges the support from the Comunidad de Madrid (Spain) - multiannual agreement with UC3M (“Excelencia para el Profesorado Universitario” - EPUC3M14) - Fifth regional research plan 2016–2020. 2024-07-25T15:36:00.4956726 2022-12-22T10:50:43.6608841 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Danilo Karličić 1 Milan Cajic 2 Stepa Paunović 3 Aleksandar Obradović 4 Sondipon Adhikari 5 Johan Christensen 6 62200__26249__4694df882d2745b8b7dc718dcc155446.pdf Non-reciprocal wave propagation in time-modulated elastic lattices.pdf 2023-01-11T12:19:09.9092632 Output 4838166 application/pdf Accepted Manuscript true 2023-12-20T00:00:00.0000000 ©2022 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
spellingShingle Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
Milan Cajic
title_short Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
title_full Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
title_fullStr Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
title_full_unstemmed Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
title_sort Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
author_id_str_mv 08b3d2d27daffae99331d905f63a6697
author_id_fullname_str_mv 08b3d2d27daffae99331d905f63a6697_***_Milan Cajic
author Milan Cajic
author2 Danilo Karličić
Milan Cajic
Stepa Paunović
Aleksandar Obradović
Sondipon Adhikari
Johan Christensen
format Journal article
container_title Applied Mathematical Modelling
container_volume 117
container_start_page 316
publishDate 2023
institution Swansea University
issn 0307-904X
doi_str_mv 10.1016/j.apm.2022.12.029
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
active_str 0
description Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.
published_date 2023-05-01T15:35:59Z
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