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

Milan Cajic, Danilo Karlicic Orcid Logo, Stepa Paunovic, Sondipon Adhikari

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

Swansea University Authors: Danilo Karlicic Orcid Logo, 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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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 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.
Keywords: phononic crystals, acoustic metamaterials, dissipation, fractional viscoelasticity, dispersion relations
College: College of Engineering
Issue: 1
Start Page: 81
End Page: 97