Geodesic
A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
Theoretical and applied mechanics, Tome 47 (2020) no. 1.

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@article{TAM_2020_47_1_a6,
     author = {Milan Caji\'c and Danilo Karli\v{c}i\'c and Stepa Paunovi\'c and Sondipon Adhikari},
     title = {A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials},
     journal = {Theoretical and applied mechanics},
     pages = {81 - 97},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2020},
     url = {http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a6/}
}
TY  - JOUR
AU  - Milan Cajić
AU  - Danilo Karličić
AU  - Stepa Paunović
AU  - Sondipon Adhikari
TI  - A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
JO  - Theoretical and applied mechanics
PY  - 2020
SP  - 81 
EP  -  97
VL  - 47
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a6/
ID  - TAM_2020_47_1_a6
ER  - 
%0 Journal Article
%A Milan Cajić
%A Danilo Karličić
%A Stepa Paunović
%A Sondipon Adhikari
%T A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials
%J Theoretical and applied mechanics
%D 2020
%P 81 - 97
%V 47
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a6/
%F TAM_2020_47_1_a6
Milan Cajić; Danilo Karličić; Stepa Paunović; Sondipon Adhikari. A fractional calculus approach to metadamping in phononic crystals and acoustic metamaterials. Theoretical and applied mechanics, Tome 47 (2020) no. 1. http://geodesic.mathdoc.fr/item/TAM_2020_47_1_a6/