Authors: Cajić, Milan 
Karličić, Danilo 
Paunović, Stepa 
Adhikari, Sondipon
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
Journal: Theoretical and Applied Mechanics
Volume: 47
Issue: 1
First page: 81
Last page: 97
Issue Date: 25-May-2020
Rank: M24
ISSN: 1450-5584
DOI: 10.2298/TAM200117003C
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: Acoustic metamaterials | Dispersion relations | Dissipation | Fractional viscoelasticity | Phononic crystals
Publisher: Serbian Society of Mechanics

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