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  - JOUR
AU  - Nešić, Nikola
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Obradović, Aleksandar
AU  - Simonović, Julijana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3789
AB  - This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation
EP  - 2026
IS  - 3
SP  - 2003
VL  - 107
DO  - 10.1007/s11071-021-07081-z
ER  - 

@article{
author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Obradović, Aleksandar and Simonović, Julijana",
year = "2022",
abstract = "This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation",
pages = "2026-2003",
number = "3",
volume = "107",
doi = "10.1007/s11071-021-07081-z"
}

Nešić, N., Cajić, M., Karličić, D., Obradović, A.,& Simonović, J.. (2022). Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics
Springer, Dordrecht., 107(3), 2003-2026.
https://doi.org/10.1007/s11071-021-07081-z

Nešić N, Cajić M, Karličić D, Obradović A, Simonović J. Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics. 2022;107(3):2003-2026.
doi:10.1007/s11071-021-07081-z .

Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Obradović, Aleksandar, Simonović, Julijana, "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation" in Nonlinear Dynamics, 107, no. 3 (2022):2003-2026,
https://doi.org/10.1007/s11071-021-07081-z . .

TY  - JOUR
AU  - Nešić, Nikola
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Obradović, Aleksandar
AU  - Simonović, Julijana
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4360
AB  - This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation
EP  - 2026
IS  - 3
SP  - 2003
VL  - 107
DO  - 10.1007/s11071-021-07081-z
ER  - 

@article{
author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Obradović, Aleksandar and Simonović, Julijana",
year = "2022",
abstract = "This paper investigates the nonlinear dynamic behavior of a nonlocal functionally graded Euler-Bernoulli beam resting on a fractional visco-Pasternak foundation and subjected to harmonic loads. The proposed model captures both, nonlocal parameter considering the elastic stress gradient field and a material length scale parameter considering the strain gradient stress field. Additionally, the von Karman strain-displacement relation is used to describe the nonlinear geometrical beam behavior. The power-law model is utilized to represent the material variations across the thickness direction of the functionally graded beam. The following steps are conducted in this research study. At first, the governing equation of motion is derived using Hamilton's principle and then reduced to the nonlinear fractional-order differential equation through the single-mode Galerkin approximation. The methodology to determine steady-state amplitude-frequency responses via incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the perturbation multiple scales method for the weakly nonlinear case and numerical integration Newmark method in the case of strong nonlinearity. It has been shown that the application of the incremental harmonic balance method in the analysis of nonlocal strain gradient theory-based structures can lead to more reliable studies for strongly nonlinear systems. In the parametric study, it is shown that, on the one hand, parameters of the visco-Pasternak foundation and power-law index remarkable affect the amplitudes responses. On the contrary, the nonlocal and the length-scale parameters are having a small influence on the amplitude-frequency response. Finally, the effects of the fractional derivative order on the system's damping are displayed at time response diagrams and subsequently discussed.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation",
pages = "2026-2003",
number = "3",
volume = "107",
doi = "10.1007/s11071-021-07081-z"
}

Nešić, N., Cajić, M., Karličić, D., Obradović, A.,& Simonović, J.. (2022). Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics
Springer, Dordrecht., 107(3), 2003-2026.
https://doi.org/10.1007/s11071-021-07081-z

Nešić N, Cajić M, Karličić D, Obradović A, Simonović J. Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. in Nonlinear Dynamics. 2022;107(3):2003-2026.
doi:10.1007/s11071-021-07081-z .

Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Obradović, Aleksandar, Simonović, Julijana, "Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation" in Nonlinear Dynamics, 107, no. 3 (2022):2003-2026,
https://doi.org/10.1007/s11071-021-07081-z . .