A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials

Cajic, Milan; Karlicic, Danilo; Paunovic, Stepa; Adhikari, Sondipon

doi:10.2298/tam200117003c

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A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials

Milan Cajic, Danilo Karlicic

, Stepa Paunovic, Sondipon Adhikari

Theoretical and Applied Mechanics, Volume: 47, Issue: 1, Pages: 81 - 97

Swansea University Authors: Danilo Karlicic , Sondipon Adhikari

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DOI (Published version): 10.2298/tam200117003c

Abstract

Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or t...

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Published in:	Theoretical and Applied Mechanics
ISSN:	1450-5584 2406-0925
Published:	National Library of Serbia 2020
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa54988
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first_indexed	2020-08-17T08:59:55Z
last_indexed	2020-09-17T03:19:01Z
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spelling	2020-09-16T17:00:11.8542766 v2 54988 2020-08-17 A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials d99ee591771c238aab350833247c8eb9 0000-0002-7547-9293 Danilo Karlicic Danilo Karlicic true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2020-08-17 EEN Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin–Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter. Journal Article Theoretical and Applied Mechanics 47 1 81 97 National Library of Serbia 1450-5584 2406-0925 phononic crystals, acoustic metamaterials, dissipation, fractional viscoelasticity, dispersion relations 25 5 2020 2020-05-25 10.2298/tam200117003c COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2020-09-16T17:00:11.8542766 2020-08-17T09:57:43.6900613 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Milan Cajic 1 Danilo Karlicic 0000-0002-7547-9293 2 Stepa Paunovic 3 Sondipon Adhikari 4 54988__17941__a15d9cd22d4141dcb8889399af3d63d9.pdf 54988.pdf 2020-08-17T09:59:41.8023566 Output 891369 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true English
title	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
spellingShingle	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials Danilo Karlicic Sondipon Adhikari
title_short	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
title_full	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
title_fullStr	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
title_full_unstemmed	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
title_sort	A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
author_id_str_mv	d99ee591771c238aab350833247c8eb9 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv	d99ee591771c238aab350833247c8eb9_*_Danilo Karlicic 4ea84d67c4e414f5ccbd7593a40f04d3_*_Sondipon Adhikari
author	Danilo Karlicic Sondipon Adhikari
author2	Milan Cajic Danilo Karlicic Stepa Paunovic Sondipon Adhikari
format	Journal article
container_title	Theoretical and Applied Mechanics
container_volume	47
container_issue	1
container_start_page	81
publishDate	2020
institution	Swansea University
issn	1450-5584 2406-0925
doi_str_mv	10.2298/tam200117003c
publisher	National Library of Serbia
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str	1
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description	Research on phononic and acoustic materials and structures emerged in the recent decade as a result of switching from theoretical physics to applications in various engineering fields. Periodicity is the main characteristic of the phononic medium stemming from periodic material phases, geometry or the boundary condition with wave propagation properties analysed through frequency band structure. To obtain these characteristics, the generalized Bloch theorem is usually applied to obtain the dispersion relations of viscously damped resonant metamaterials. Here we develop a novel analytical approach to analyse the fractionally damped model of phononic crystals and acoustic metamaterials introduced through the fractional-order Kelvin–Voigt and Maxwell damping models. In the numerical study, the results obtained using the proposed models are compared against the elastic cases of the phononic crystal and locally resonant acoustic metamaterial, where significant differences in dispersion curves are identified. We show that the fractional-order Maxwell model is more suitable for describing the dissipation effect throughout the spectrum due to the possibility of fitting both, the order of fractional derivative and the damping parameter.
published_date	2020-05-25T04:08:53Z
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score	11.036706

A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials

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