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 . .

TY  - CONF
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
AU  - Paunović, Stepa
AU  - Karličić, Danilo
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6450
AB  - This paper shows the transverse vibration analysis of complex multiple coupled nanobeams system. Observed system is composed of an arbitrary number of aligned nanobeam structures embedded in viscoelastic medium where damping features of nanobeams and viscoelastic medium are represented by the fractional viscoelastic models while small-scale effects are considered using the Eringen’s nonlocal elasticity. In addition, non-homogeneities of the system such as different nanobeams cross-sections or density are observed within the paper. Governing equations are derived using using the d’Alembert’s principle, differential form of nonlocal stress relation and local stress-strain viscoelastic constitutive equation of fractional Kelvin-Voigt type. Semi-analyitical solutions for the transient response of simply supported nanobeams in the system are obtained using the separation of variables method, Laplace and Mellin-Fourier integral transforms, residue theory and modal expansion method. The problem of decoupling the governing equations of a non-homogenous system is solved by adopting the methodology from the literature. Several numerical examples are given to show the effects of different physical parameters on the transient response of such a system. Presented dynamic analysis and results could be used in future theoretical studies with additional physical effects included into the model. There is also a potential for use of this type of analysis in design procedures of modern nanodevices for calculation of their dynamic behavior that is much faster compared to atomistic based models.
PB  - The Hellenic Society of Theoretical & Applied Mechanics (HSTAM)
C3  - Proceedings  of  12th HSTAM International Congress on Mechanics, Hellenic society for theoretical and applied mechanics (HSTAM),The Aristotle University of Thessaloniki, Greece, 22 – 25 September 2019
T1  - Vibration of a coupled fractional viscoelastic multi-nanobeam systems
EP  - 10
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6450
ER  - 

@conference{
author = "Cajić, Milan and Lazarević, Mihailo and Paunović, Stepa and Karličić, Danilo",
year = "2019",
abstract = "This paper shows the transverse vibration analysis of complex multiple coupled nanobeams system. Observed system is composed of an arbitrary number of aligned nanobeam structures embedded in viscoelastic medium where damping features of nanobeams and viscoelastic medium are represented by the fractional viscoelastic models while small-scale effects are considered using the Eringen’s nonlocal elasticity. In addition, non-homogeneities of the system such as different nanobeams cross-sections or density are observed within the paper. Governing equations are derived using using the d’Alembert’s principle, differential form of nonlocal stress relation and local stress-strain viscoelastic constitutive equation of fractional Kelvin-Voigt type. Semi-analyitical solutions for the transient response of simply supported nanobeams in the system are obtained using the separation of variables method, Laplace and Mellin-Fourier integral transforms, residue theory and modal expansion method. The problem of decoupling the governing equations of a non-homogenous system is solved by adopting the methodology from the literature. Several numerical examples are given to show the effects of different physical parameters on the transient response of such a system. Presented dynamic analysis and results could be used in future theoretical studies with additional physical effects included into the model. There is also a potential for use of this type of analysis in design procedures of modern nanodevices for calculation of their dynamic behavior that is much faster compared to atomistic based models.",
publisher = "The Hellenic Society of Theoretical & Applied Mechanics (HSTAM)",
journal = "Proceedings  of  12th HSTAM International Congress on Mechanics, Hellenic society for theoretical and applied mechanics (HSTAM),The Aristotle University of Thessaloniki, Greece, 22 – 25 September 2019",
title = "Vibration of a coupled fractional viscoelastic multi-nanobeam systems",
pages = "10-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6450"
}

Cajić, M., Lazarević, M., Paunović, S.,& Karličić, D.. (2019). Vibration of a coupled fractional viscoelastic multi-nanobeam systems. in Proceedings  of  12th HSTAM International Congress on Mechanics, Hellenic society for theoretical and applied mechanics (HSTAM),The Aristotle University of Thessaloniki, Greece, 22 – 25 September 2019
The Hellenic Society of Theoretical & Applied Mechanics (HSTAM)., 1-10.
https://hdl.handle.net/21.15107/rcub_machinery_6450

Cajić M, Lazarević M, Paunović S, Karličić D. Vibration of a coupled fractional viscoelastic multi-nanobeam systems. in Proceedings  of  12th HSTAM International Congress on Mechanics, Hellenic society for theoretical and applied mechanics (HSTAM),The Aristotle University of Thessaloniki, Greece, 22 – 25 September 2019. 2019;:1-10.
https://hdl.handle.net/21.15107/rcub_machinery_6450 .

Cajić, Milan, Lazarević, Mihailo, Paunović, Stepa, Karličić, Danilo, "Vibration of a coupled fractional viscoelastic multi-nanobeam systems" in Proceedings  of  12th HSTAM International Congress on Mechanics, Hellenic society for theoretical and applied mechanics (HSTAM),The Aristotle University of Thessaloniki, Greece, 22 – 25 September 2019 (2019):1-10,
https://hdl.handle.net/21.15107/rcub_machinery_6450 .