TY  - JOUR
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Paunović, Stepa
AU  - Obradović, Aleksandar
AU  - Adtkihari, Sondipon
AU  - Christensen, Johan
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3972
AB  - Non-reciprocal wave propagation in acoustic and elastic media has received much atten- tion of researchers in recent years. This phenomenon can be achieved by breaking the reci- procity 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 in- vestigate 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 lat- tices 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 multi- ple 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 inves- tigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.
PB  - Elsevier
T2  - Applied Mathematical Modelling
T1  - Non-reciprocal wave propagation in time-modulated elastic lattices with inerters
EP  - 335
SP  - 316
VL  - 117
DO  - 10.1016/j.apm.2022.12.029
ER  - 

@article{
author = "Karličić, Danilo and Cajić, Milan and Paunović, Stepa and Obradović, Aleksandar and Adtkihari, Sondipon and Christensen, Johan",
year = "2023",
abstract = "Non-reciprocal wave propagation in acoustic and elastic media has received much atten- tion of researchers in recent years. This phenomenon can be achieved by breaking the reci- procity 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 in- vestigate 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 lat- tices 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 multi- ple 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 inves- tigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.",
publisher = "Elsevier",
journal = "Applied Mathematical Modelling",
title = "Non-reciprocal wave propagation in time-modulated elastic lattices with inerters",
pages = "335-316",
volume = "117",
doi = "10.1016/j.apm.2022.12.029"
}

Karličić, D., Cajić, M., Paunović, S., Obradović, A., Adtkihari, S.,& Christensen, J.. (2023). Non-reciprocal wave propagation in time-modulated elastic lattices with inerters. in Applied Mathematical Modelling
Elsevier., 117, 316-335.
https://doi.org/10.1016/j.apm.2022.12.029

Karličić D, Cajić M, Paunović S, Obradović A, Adtkihari S, Christensen J. Non-reciprocal wave propagation in time-modulated elastic lattices with inerters. in Applied Mathematical Modelling. 2023;117:316-335.
doi:10.1016/j.apm.2022.12.029 .

Karličić, Danilo, Cajić, Milan, Paunović, Stepa, Obradović, Aleksandar, Adtkihari, Sondipon, Christensen, Johan, "Non-reciprocal wave propagation in time-modulated elastic lattices with inerters" in Applied Mathematical Modelling, 117 (2023):316-335,
https://doi.org/10.1016/j.apm.2022.12.029 . .