TY  - JOUR
AU  - Nešić, Nikola
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
AU  - Adhikari, Sondipon
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7064
AB  - This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory.
PB  - University of Niš
T2  - FACTA UNIVERSITATIS Series: Mechanical Engineering
T1  - VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION
DO  - 10.22190/FUME230419022N
ER  - 

@article{
author = "Nešić, Nikola and Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo and Adhikari, Sondipon",
year = "2023",
abstract = "This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory.",
publisher = "University of Niš",
journal = "FACTA UNIVERSITATIS Series: Mechanical Engineering",
title = "VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION",
doi = "10.22190/FUME230419022N"
}

Nešić, N., Cajić, M., Karličić, D., Lazarević, M.,& Adhikari, S.. (2023). VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION. in FACTA UNIVERSITATIS Series: Mechanical Engineering
University of Niš..
https://doi.org/10.22190/FUME230419022N

Nešić N, Cajić M, Karličić D, Lazarević M, Adhikari S. VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION. in FACTA UNIVERSITATIS Series: Mechanical Engineering. 2023;.
doi:10.22190/FUME230419022N .

Nešić, Nikola, Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, Adhikari, Sondipon, "VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION" in FACTA UNIVERSITATIS Series: Mechanical Engineering (2023),
https://doi.org/10.22190/FUME230419022N . .

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  - Rosić, Nevena
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
PY  - 2023
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/7234
AB  - Here, the transfer matrix method along with the Bloch theorem are employed to study the frequency spectra in various cases of Timoshenko’s beam periodicity, such as structural, material and boundary periodicity. We additionally compare the location and size of band gaps, and the shape of the band structure in general for different types of foundation layers and relevant parameter values.
PB  - Belgrade: Serbian Society of Mechanics
C3  - 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
T1  - WAVE PROPAGATION IN PERIODIC TIMOSHENKO BEAMS ON DIFFERENT ELASTIC FOUNDATION TYPES
EP  - 219
SP  - 217
UR  - https://hdl.handle.net/21.15107/rcub_machinery_7234
ER  - 

@conference{
author = "Rosić, Nevena and Karličić, Danilo and Cajić, Milan and Lazarević, Mihailo",
year = "2023",
abstract = "Here, the transfer matrix method along with the Bloch theorem are employed to study the frequency spectra in various cases of Timoshenko’s beam periodicity, such as structural, material and boundary periodicity. We additionally compare the location and size of band gaps, and the shape of the band structure in general for different types of foundation layers and relevant parameter values.",
publisher = "Belgrade: Serbian Society of Mechanics",
journal = "9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023",
title = "WAVE PROPAGATION IN PERIODIC TIMOSHENKO BEAMS ON DIFFERENT ELASTIC FOUNDATION TYPES",
pages = "219-217",
url = "https://hdl.handle.net/21.15107/rcub_machinery_7234"
}

Rosić, N., Karličić, D., Cajić, M.,& Lazarević, M.. (2023). WAVE PROPAGATION IN PERIODIC TIMOSHENKO BEAMS ON DIFFERENT ELASTIC FOUNDATION TYPES. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023
Belgrade: Serbian Society of Mechanics., 217-219.
https://hdl.handle.net/21.15107/rcub_machinery_7234

Rosić N, Karličić D, Cajić M, Lazarević M. WAVE PROPAGATION IN PERIODIC TIMOSHENKO BEAMS ON DIFFERENT ELASTIC FOUNDATION TYPES. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023. 2023;:217-219.
https://hdl.handle.net/21.15107/rcub_machinery_7234 .

Rosić, Nevena, Karličić, Danilo, Cajić, Milan, Lazarević, Mihailo, "WAVE PROPAGATION IN PERIODIC TIMOSHENKO BEAMS ON DIFFERENT ELASTIC FOUNDATION TYPES" in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 (2023):217-219,
https://hdl.handle.net/21.15107/rcub_machinery_7234 .

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 . .

TY  - CONF
AU  - Rosić, Nevena
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4078
AB  - In this paper we will investigate non-reciprocal wave propagation in Timoshenko beams,
due to space and time modulation of its elastic properties. To that end, an analytical approach
is used: the Bloch theorem is applied when choosing the solution form for displacement
components and the angle of rotation, which figure in the equations of motion along with the
elastic properties. Also, the Fourier expansion is used to express the periodic nature of the
modulation. By solving the eigenvalue problem for different modulation parameters, we obtain
the band diagrams which can be used to analyze the directionality of wave propagation. These
diagrams clearly represent the breakage of symmetry as a consequence of modulation. Thus, a
modulated beam behaves as a kind of metamaterial, in which one-way propagation of elastic
waves is possible. When shear and rotational effects are neglected, these results converge to
the results for the Euler-Bernoulli beam, which are already present in scientific literature.
PB  - Univerzitet u Beogradu, Mašinski fakultet
C3  - Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.
T1  - Non-reciprocal wave propagation in periodically structured Timoshenko beams
EP  - 125
SP  - 125
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4078
ER  - 

@conference{
author = "Rosić, Nevena and Karličić, Danilo and Cajić, Milan and Lazarević, Mihailo",
year = "2022",
abstract = "In this paper we will investigate non-reciprocal wave propagation in Timoshenko beams,
due to space and time modulation of its elastic properties. To that end, an analytical approach
is used: the Bloch theorem is applied when choosing the solution form for displacement
components and the angle of rotation, which figure in the equations of motion along with the
elastic properties. Also, the Fourier expansion is used to express the periodic nature of the
modulation. By solving the eigenvalue problem for different modulation parameters, we obtain
the band diagrams which can be used to analyze the directionality of wave propagation. These
diagrams clearly represent the breakage of symmetry as a consequence of modulation. Thus, a
modulated beam behaves as a kind of metamaterial, in which one-way propagation of elastic
waves is possible. When shear and rotational effects are neglected, these results converge to
the results for the Euler-Bernoulli beam, which are already present in scientific literature.",
publisher = "Univerzitet u Beogradu, Mašinski fakultet",
journal = "Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.",
title = "Non-reciprocal wave propagation in periodically structured Timoshenko beams",
pages = "125-125",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4078"
}

Rosić, N., Karličić, D., Cajić, M.,& Lazarević, M.. (2022). Non-reciprocal wave propagation in periodically structured Timoshenko beams. in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.
Univerzitet u Beogradu, Mašinski fakultet., 125-125.
https://hdl.handle.net/21.15107/rcub_machinery_4078

Rosić N, Karličić D, Cajić M, Lazarević M. Non-reciprocal wave propagation in periodically structured Timoshenko beams. in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.. 2022;:125-125.
https://hdl.handle.net/21.15107/rcub_machinery_4078 .

Rosić, Nevena, Karličić, Danilo, Cajić, Milan, Lazarević, Mihailo, "Non-reciprocal wave propagation in periodically structured Timoshenko beams" in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022. (2022):125-125,
https://hdl.handle.net/21.15107/rcub_machinery_4078 .

TY  - JOUR
AU  - Rosić, Nevena
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
PY  - 2022
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4073
AB  - Wave attenuation, filtering and guiding is an ongoing topic of scientific
research, as there are many opportunities for improvement of existing
solutions in modern industry. One of the recent advancements has been made
with the use of non-reciprocal metamaterials.Certain properties of metamaterials
have made them suitable for use in various engineering fields. In this study,
we investigate non-reciprocal wave propagation behavior in coupled thin beams
phononics, due to time-modulation of material properties and axial loads. We
compare the results for the beams which are interconnected with Winkler’s
type of elastic layers and elastic or viscoelastic Pasternak layers. An analytic
approach is used to discover directional band gaps and investigate wave propagation
through these systems of beams, at relevant excitation frequencies. The
proposed framework can be exploited in further analysis of phononic systems
based on multiple beams coupled through different mediums and structural
elements modeled with higher-order beam theories.
PB  - Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
PB  - Serbian Society of Mechanics
T2  - Theoretical and applied mechanics
T1  - Parametrically excited unidirectional wave propagation in thin beam phononics
EP  - 155
IS  - 2
SP  - 137
VL  - 49
DO  - https://doi.org/10.2298/TAM221030010R
ER  - 

@article{
author = "Rosić, Nevena and Karličić, Danilo and Cajić, Milan and Lazarević, Mihailo",
year = "2022",
abstract = "Wave attenuation, filtering and guiding is an ongoing topic of scientific
research, as there are many opportunities for improvement of existing
solutions in modern industry. One of the recent advancements has been made
with the use of non-reciprocal metamaterials.Certain properties of metamaterials
have made them suitable for use in various engineering fields. In this study,
we investigate non-reciprocal wave propagation behavior in coupled thin beams
phononics, due to time-modulation of material properties and axial loads. We
compare the results for the beams which are interconnected with Winkler’s
type of elastic layers and elastic or viscoelastic Pasternak layers. An analytic
approach is used to discover directional band gaps and investigate wave propagation
through these systems of beams, at relevant excitation frequencies. The
proposed framework can be exploited in further analysis of phononic systems
based on multiple beams coupled through different mediums and structural
elements modeled with higher-order beam theories.",
publisher = "Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbian Society of Mechanics",
journal = "Theoretical and applied mechanics",
title = "Parametrically excited unidirectional wave propagation in thin beam phononics",
pages = "155-137",
number = "2",
volume = "49",
doi = "https://doi.org/10.2298/TAM221030010R"
}

Rosić, N., Karličić, D., Cajić, M.,& Lazarević, M.. (2022). Parametrically excited unidirectional wave propagation in thin beam phononics. in Theoretical and applied mechanics
Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade., 49(2), 137-155.
https://doi.org/https://doi.org/10.2298/TAM221030010R

Rosić N, Karličić D, Cajić M, Lazarević M. Parametrically excited unidirectional wave propagation in thin beam phononics. in Theoretical and applied mechanics. 2022;49(2):137-155.
doi:https://doi.org/10.2298/TAM221030010R .

Rosić, Nevena, Karličić, Danilo, Cajić, Milan, Lazarević, Mihailo, "Parametrically excited unidirectional wave propagation in thin beam phononics" in Theoretical and applied mechanics, 49, no. 2 (2022):137-155,
https://doi.org/https://doi.org/10.2298/TAM221030010R . .

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 .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Cajić, Milan
AU  - Cvetković, Boško
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6451
AB  - The investigation into the dynamics of robotic and complex mechanical systems has been an active topic of research for many years. The modelling complex rigid multibody systems (RBS) using symbolic equations can provide many advantages over the more widely-used numerical methods of modeling these systems. In this contribution, we propose using procedure for recursive symbolic form computation of the complete dynamics  of robotic systems with the open kinematic chain structures using Rodriquez approach for matrices of coordinate transformations. Dynamic equations are given as Lagrange equations of the second kind in the covariant form with external generalized forces of the gravity, motor-torque, viscous and  spring. On the other side, the use of adaptive (hereditary/actuator: viscoelastic element with an actuator, piezo-viscoelastic,thermo-viscoelastic and magneto-rheologic) elements in complex RBS can be significant for the additional control of these systems and for reducing  undesirable  vibrations. Recently, fractional calculus (FC) has attracted an increased attention of scientific society. The fractional integro-differential operators are a generalization of integration and derivation to fractional operators where fractional derivatives (FD) are often used to describe viscoelastic, rheological properties of advanced materials and dissipative forces in structural dynamics. Here, modeling of dynamics of multibody systems involving generalized forces of a spring/spring-pot/actuator (SSPA) and MR elements modeled with fractional order derivatives, including recently new obtained definitions of FD, is studied. The system is defined as a discrete material system where in the force–displacement relation, mass of the element is neglected. Generalized forces of an element are derived by using the principle of virtual work and force–displacement relation of the fractional order Kelvin–Voigt/Zener model. Finally, the results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model.
PB  - The Hellenic Society of Theoretical & Applied Mechanics (HSTAM)
C3  - Book of abstracts 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  - Modelling of Advanced Robotic Systems with  Fractional order  hereditary/actuator elements
EP  - 39
SP  - 38
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6451
ER  - 

@conference{
author = "Lazarević, Mihailo and Cajić, Milan and Cvetković, Boško",
year = "2019",
abstract = "The investigation into the dynamics of robotic and complex mechanical systems has been an active topic of research for many years. The modelling complex rigid multibody systems (RBS) using symbolic equations can provide many advantages over the more widely-used numerical methods of modeling these systems. In this contribution, we propose using procedure for recursive symbolic form computation of the complete dynamics  of robotic systems with the open kinematic chain structures using Rodriquez approach for matrices of coordinate transformations. Dynamic equations are given as Lagrange equations of the second kind in the covariant form with external generalized forces of the gravity, motor-torque, viscous and  spring. On the other side, the use of adaptive (hereditary/actuator: viscoelastic element with an actuator, piezo-viscoelastic,thermo-viscoelastic and magneto-rheologic) elements in complex RBS can be significant for the additional control of these systems and for reducing  undesirable  vibrations. Recently, fractional calculus (FC) has attracted an increased attention of scientific society. The fractional integro-differential operators are a generalization of integration and derivation to fractional operators where fractional derivatives (FD) are often used to describe viscoelastic, rheological properties of advanced materials and dissipative forces in structural dynamics. Here, modeling of dynamics of multibody systems involving generalized forces of a spring/spring-pot/actuator (SSPA) and MR elements modeled with fractional order derivatives, including recently new obtained definitions of FD, is studied. The system is defined as a discrete material system where in the force–displacement relation, mass of the element is neglected. Generalized forces of an element are derived by using the principle of virtual work and force–displacement relation of the fractional order Kelvin–Voigt/Zener model. Finally, the results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model.",
publisher = "The Hellenic Society of Theoretical & Applied Mechanics (HSTAM)",
journal = "Book of abstracts 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 = "Modelling of Advanced Robotic Systems with  Fractional order  hereditary/actuator elements",
pages = "39-38",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6451"
}

Lazarević, M., Cajić, M.,& Cvetković, B.. (2019). Modelling of Advanced Robotic Systems with  Fractional order  hereditary/actuator elements. in Book of abstracts 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)., 38-39.
https://hdl.handle.net/21.15107/rcub_machinery_6451

Lazarević M, Cajić M, Cvetković B. Modelling of Advanced Robotic Systems with  Fractional order  hereditary/actuator elements. in Book of abstracts 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;:38-39.
https://hdl.handle.net/21.15107/rcub_machinery_6451 .

Lazarević, Mihailo, Cajić, Milan, Cvetković, Boško, "Modelling of Advanced Robotic Systems with  Fractional order  hereditary/actuator elements" in Book of abstracts 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):38-39,
https://hdl.handle.net/21.15107/rcub_machinery_6451 .

TY  - JOUR
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
AU  - Karličić, Danilo
AU  - Sun, HongGuang
AU  - Liu, Xiaoting
PY  - 2018
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2886
AB  - In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation together with the fractional Kelvin-Voigt model. The governing equation for the free vibration of a nanobeam is derived, where Maxwell's equations are used in order to represent the effect of the longitudinal magnetic field. We propose an analytical solution of the problem based on the Laplace transform, Mellin-Fourier transforms, and residue theory. From the validation study, it is shown that the obtained complex roots of the characteristic equation, where the imaginary part is the damped frequency and the real part is the damping ratio, are approximated eigenvalues of the system. In the parametric study, several numerical examples are given to investigate the influence of different parameters on complex roots as well as different masses and numbers of nanoparticles on the damped vibration behavior of a nanobeam system.
PB  - Springer Wien, Wien
T2  - Acta Mechanica
T1  - Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles
EP  - 4815
IS  - 12
SP  - 4791
VL  - 229
DO  - 10.1007/s00707-018-2263-7
ER  - 

@article{
author = "Cajić, Milan and Lazarević, Mihailo and Karličić, Danilo and Sun, HongGuang and Liu, Xiaoting",
year = "2018",
abstract = "In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation together with the fractional Kelvin-Voigt model. The governing equation for the free vibration of a nanobeam is derived, where Maxwell's equations are used in order to represent the effect of the longitudinal magnetic field. We propose an analytical solution of the problem based on the Laplace transform, Mellin-Fourier transforms, and residue theory. From the validation study, it is shown that the obtained complex roots of the characteristic equation, where the imaginary part is the damped frequency and the real part is the damping ratio, are approximated eigenvalues of the system. In the parametric study, several numerical examples are given to investigate the influence of different parameters on complex roots as well as different masses and numbers of nanoparticles on the damped vibration behavior of a nanobeam system.",
publisher = "Springer Wien, Wien",
journal = "Acta Mechanica",
title = "Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles",
pages = "4815-4791",
number = "12",
volume = "229",
doi = "10.1007/s00707-018-2263-7"
}

Cajić, M., Lazarević, M., Karličić, D., Sun, H.,& Liu, X.. (2018). Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles. in Acta Mechanica
Springer Wien, Wien., 229(12), 4791-4815.
https://doi.org/10.1007/s00707-018-2263-7

Cajić M, Lazarević M, Karličić D, Sun H, Liu X. Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles. in Acta Mechanica. 2018;229(12):4791-4815.
doi:10.1007/s00707-018-2263-7 .

Cajić, Milan, Lazarević, Mihailo, Karličić, Danilo, Sun, HongGuang, Liu, Xiaoting, "Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles" in Acta Mechanica, 229, no. 12 (2018):4791-4815,
https://doi.org/10.1007/s00707-018-2263-7 . .

TY  - JOUR
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2527
AB  - In this paper, we investigate the free damped vibration of a nanobeam resting on viscoelastic foundation. Nanobeam and viscoelastic foundation are modeled using nonlocal elasticity and fractional order viscoelasticity theories. Motion equation is derived using D'Alambert's principle and involves two retardation times and fractional order derivative parameters regarding to a nanobeam and viscoelastic foundation. The analytical solution is obtained using the Laplace transform method and it is given as a sum of two terms. First term denoting the drift of the system's equilibrium position is given as an improper integral taken along two sides of the cut of complex plane. Two complex conjugate roots located in the left half-plane of the complex plane determine the second term describing the damped vibration around equilibrium position. Results for complex roots of characteristic equation obtained for a single nanobeam without viscoelastic foundation, where imaginary parts represent damped frequencies, are validated with the results found in the literature for natural frequencies of a single-walled carbon nanotube obtained from molecular dynamics simulations. In order to examine the effects of nonlocal parameter, fractional order parameters and retardation times on the behavior of characteristic equation roots in the complex plane and the time-response of nanobeam, several numerical examples are given.
PB  - Springer, Dordrecht
T2  - Meccanica
T1  - Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters
EP  - 382
IS  - 1-2
SP  - 363
VL  - 52
DO  - 10.1007/s11012-016-0417-z
ER  - 

@article{
author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo",
year = "2017",
abstract = "In this paper, we investigate the free damped vibration of a nanobeam resting on viscoelastic foundation. Nanobeam and viscoelastic foundation are modeled using nonlocal elasticity and fractional order viscoelasticity theories. Motion equation is derived using D'Alambert's principle and involves two retardation times and fractional order derivative parameters regarding to a nanobeam and viscoelastic foundation. The analytical solution is obtained using the Laplace transform method and it is given as a sum of two terms. First term denoting the drift of the system's equilibrium position is given as an improper integral taken along two sides of the cut of complex plane. Two complex conjugate roots located in the left half-plane of the complex plane determine the second term describing the damped vibration around equilibrium position. Results for complex roots of characteristic equation obtained for a single nanobeam without viscoelastic foundation, where imaginary parts represent damped frequencies, are validated with the results found in the literature for natural frequencies of a single-walled carbon nanotube obtained from molecular dynamics simulations. In order to examine the effects of nonlocal parameter, fractional order parameters and retardation times on the behavior of characteristic equation roots in the complex plane and the time-response of nanobeam, several numerical examples are given.",
publisher = "Springer, Dordrecht",
journal = "Meccanica",
title = "Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters",
pages = "382-363",
number = "1-2",
volume = "52",
doi = "10.1007/s11012-016-0417-z"
}

Cajić, M., Karličić, D.,& Lazarević, M.. (2017). Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters. in Meccanica
Springer, Dordrecht., 52(1-2), 363-382.
https://doi.org/10.1007/s11012-016-0417-z

Cajić M, Karličić D, Lazarević M. Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters. in Meccanica. 2017;52(1-2):363-382.
doi:10.1007/s11012-016-0417-z .

Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, "Damped vibration of a nonlocal nanobeam resting on viscoelastic foundation: fractional derivative model with two retardation times and fractional parameters" in Meccanica, 52, no. 1-2 (2017):363-382,
https://doi.org/10.1007/s11012-016-0417-z . .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Bučanović, Ljubiša
AU  - Dragović, Mladen
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6449
AB  - Nanostructures with similar shapes as macro structures such as beams, plates or shells are grown using various technological processes. Nano-scale structures mechanical behaviour is similar to macro structures with the main difference that influences of various size-effects cannot be neglected. Particulary, dynamic behaviour of nanostructures is significant for the development of new types of devices such as nanoactuators, nanosensors or resonators. Nonlinear oscillations and dissipation effects from different sources are important for the investigation of nano-scale resonators. Application of experimental and atomistic methods is limited only to specific and less complex nanostructure systems. Modified continuum based theoretical models have attracted a great attention of researchers in recent years. Here, we observe combined parametric and external resonance of a geometrically nonlinear nanobeam resting on a fractional visco-Pasternak type foundation. Euler-Bernoulli beam theory, nonlinear strain-displacement relation and nonlocal elasticity constitutive equation are  employed to obtained fractional order governing equation for the transverse vibration of a systems, accounting size effects and dissipation effects from external medium. Under the assumption of small fractional damping, we used the perturbation multiple-scales method to obtain an approximated analytical solution for the frequency-amplitude response in combined parametric and external resonance case for variable axial and transverse loads. Influences of different system parameters on frequency-amplitude response are examined on several numerical examples.
PB  - Nanotechnology
C3  - Book of abstracts 14th International Conference on Nanosciences and Nanotechnologies NN17, 4-7 July 2017 Thessaloniki Greece
T1  - Combined resonance of magnetically influenced nanobeam  on fractional visco-Pasternak type foundation
EP  - 103
SP  - 103
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6449
ER  - 

@conference{
author = "Lazarević, Mihailo and Cajić, Milan and Karličić, Danilo and Bučanović, Ljubiša and Dragović, Mladen",
year = "2017",
abstract = "Nanostructures with similar shapes as macro structures such as beams, plates or shells are grown using various technological processes. Nano-scale structures mechanical behaviour is similar to macro structures with the main difference that influences of various size-effects cannot be neglected. Particulary, dynamic behaviour of nanostructures is significant for the development of new types of devices such as nanoactuators, nanosensors or resonators. Nonlinear oscillations and dissipation effects from different sources are important for the investigation of nano-scale resonators. Application of experimental and atomistic methods is limited only to specific and less complex nanostructure systems. Modified continuum based theoretical models have attracted a great attention of researchers in recent years. Here, we observe combined parametric and external resonance of a geometrically nonlinear nanobeam resting on a fractional visco-Pasternak type foundation. Euler-Bernoulli beam theory, nonlinear strain-displacement relation and nonlocal elasticity constitutive equation are  employed to obtained fractional order governing equation for the transverse vibration of a systems, accounting size effects and dissipation effects from external medium. Under the assumption of small fractional damping, we used the perturbation multiple-scales method to obtain an approximated analytical solution for the frequency-amplitude response in combined parametric and external resonance case for variable axial and transverse loads. Influences of different system parameters on frequency-amplitude response are examined on several numerical examples.",
publisher = "Nanotechnology",
journal = "Book of abstracts 14th International Conference on Nanosciences and Nanotechnologies NN17, 4-7 July 2017 Thessaloniki Greece",
title = "Combined resonance of magnetically influenced nanobeam  on fractional visco-Pasternak type foundation",
pages = "103-103",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6449"
}

Lazarević, M., Cajić, M., Karličić, D., Bučanović, L.,& Dragović, M.. (2017). Combined resonance of magnetically influenced nanobeam  on fractional visco-Pasternak type foundation. in Book of abstracts 14th International Conference on Nanosciences and Nanotechnologies NN17, 4-7 July 2017 Thessaloniki Greece
Nanotechnology., 103-103.
https://hdl.handle.net/21.15107/rcub_machinery_6449

Lazarević M, Cajić M, Karličić D, Bučanović L, Dragović M. Combined resonance of magnetically influenced nanobeam  on fractional visco-Pasternak type foundation. in Book of abstracts 14th International Conference on Nanosciences and Nanotechnologies NN17, 4-7 July 2017 Thessaloniki Greece. 2017;:103-103.
https://hdl.handle.net/21.15107/rcub_machinery_6449 .

Lazarević, Mihailo, Cajić, Milan, Karličić, Danilo, Bučanović, Ljubiša, Dragović, Mladen, "Combined resonance of magnetically influenced nanobeam  on fractional visco-Pasternak type foundation" in Book of abstracts 14th International Conference on Nanosciences and Nanotechnologies NN17, 4-7 July 2017 Thessaloniki Greece (2017):103-103,
https://hdl.handle.net/21.15107/rcub_machinery_6449 .

TY  - CONF
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
AU  - Wen, Chen
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4154
AB  - In this communication, we observe the interaction of fundamental parametric resonances with subharmonic resonances of order one-half of a geometrically nonlinear nonlocal nanobeam model resting on a fractional Pasternak-type viscoelastic foundation. Euler-Bernoulli beam theory and nonlinear von Karman strain-displacement relation are employed to obtained fractional order governing equation for the transverse vibration of a system. Under the assumption of small fractional damping, we used the perturbation multiple-scales method to obtain an approximated analytical solution for the frequency-amplitude response. Combined parametric resonance from axial load and subharmonic resonance under external excitation are examined for different parameters of the model. Validation of the multiple scales solution against numerical solution in the phase plane and Poincare map will be provided
PB  - Budapest : CongressLIne Ltd.
C3  - Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.
T1  - Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation
EP  - 2
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4154
ER  - 

@conference{
author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo and Wen, Chen",
year = "2017",
abstract = "In this communication, we observe the interaction of fundamental parametric resonances with subharmonic resonances of order one-half of a geometrically nonlinear nonlocal nanobeam model resting on a fractional Pasternak-type viscoelastic foundation. Euler-Bernoulli beam theory and nonlinear von Karman strain-displacement relation are employed to obtained fractional order governing equation for the transverse vibration of a system. Under the assumption of small fractional damping, we used the perturbation multiple-scales method to obtain an approximated analytical solution for the frequency-amplitude response. Combined parametric resonance from axial load and subharmonic resonance under external excitation are examined for different parameters of the model. Validation of the multiple scales solution against numerical solution in the phase plane and Poincare map will be provided",
publisher = "Budapest : CongressLIne Ltd.",
journal = "Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.",
title = "Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation",
pages = "2-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4154"
}

Cajić, M., Karličić, D., Lazarević, M.,& Wen, C.. (2017). Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.
Budapest : CongressLIne Ltd.., 1-2.
https://hdl.handle.net/21.15107/rcub_machinery_4154

Cajić M, Karličić D, Lazarević M, Wen C. Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.. 2017;:1-2.
https://hdl.handle.net/21.15107/rcub_machinery_4154 .

Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, Wen, Chen, "Combined resonance of a nonlocal nanobeam on fractional Pasternak-type viscoelastic foundation" in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017. (2017):1-2,
https://hdl.handle.net/21.15107/rcub_machinery_4154 .

TY  - CONF
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4150
AB  - In this work, we observe combined parametric and external sub-harmonic resonances of order
one-third of a geometrically nonlinear nonlocal nanobeam model resting on a fractional visco-
Pasternak type foundation. Euler-Bernoulli beam theory, nonlinear strain-displacement relation
and nonlocal elasticity constitutive equation are employed to obtained fractional order governing
equation for the transverse vibration of a system. Under the assumption of small fractional
damping, we used the perturbation multiple-scales method to obtain an approximated analytical
solution for the frequency-amplitude response for variable axial and transverse external loads.
Several numerical examples are given to show the effects of different parameters on frequencyamplitude
response.
PB  - Beograd : Srpsko društvo za mehaniku
C3  - 6th International Congress of Serbian Society  of Mechanics, Tara, Serbia, June 19-21, 2017
T1  - Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation
EP  - 4
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4150
ER  - 

@conference{
author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo",
year = "2017",
abstract = "In this work, we observe combined parametric and external sub-harmonic resonances of order
one-third of a geometrically nonlinear nonlocal nanobeam model resting on a fractional visco-
Pasternak type foundation. Euler-Bernoulli beam theory, nonlinear strain-displacement relation
and nonlocal elasticity constitutive equation are employed to obtained fractional order governing
equation for the transverse vibration of a system. Under the assumption of small fractional
damping, we used the perturbation multiple-scales method to obtain an approximated analytical
solution for the frequency-amplitude response for variable axial and transverse external loads.
Several numerical examples are given to show the effects of different parameters on frequencyamplitude
response.",
publisher = "Beograd : Srpsko društvo za mehaniku",
journal = "6th International Congress of Serbian Society  of Mechanics, Tara, Serbia, June 19-21, 2017",
title = "Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation",
pages = "4-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4150"
}

Cajić, M., Karličić, D.,& Lazarević, M.. (2017). Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation. in 6th International Congress of Serbian Society  of Mechanics, Tara, Serbia, June 19-21, 2017
Beograd : Srpsko društvo za mehaniku., 1-4.
https://hdl.handle.net/21.15107/rcub_machinery_4150

Cajić M, Karličić D, Lazarević M. Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation. in 6th International Congress of Serbian Society  of Mechanics, Tara, Serbia, June 19-21, 2017. 2017;:1-4.
https://hdl.handle.net/21.15107/rcub_machinery_4150 .

Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, "Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation" in 6th International Congress of Serbian Society  of Mechanics, Tara, Serbia, June 19-21, 2017 (2017):1-4,
https://hdl.handle.net/21.15107/rcub_machinery_4150 .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Cajić, Milan
AU  - Mandić, Petar
AU  - Sekara, Tomislav B.
AU  - Sun, HongGuang
AU  - Karličić, Danilo
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2702
AB  - In this paper, we suggest a robust non-square MIMO (4x8) PID controller for the multi-mode active vibration damping of a nanobeam. Nanobeam is modeled by using the nonlocal continuum theory of Eringen to consider the small-scale effects and Euler-Bernoulli beam theory. The problem is analyzed for the free vibration case with Heaviside type disturbance of a nanobeam with and without the controller. The proposed system has four inputs and eight outputs, where by using the static decoupling method, decoupled system of four transfer functions is obtained. The controller parameters dependig on one tuning parmeter are designed to suppress the step disturbance on the input without overshooting. All theoretical results are verified with several numerical examples.
PB  - Institute of Electrical and Electronics Engineers Inc.
C3  - Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
T1  - Multi-mode Active Vibration Control of a Nanobeam using a non-square MIMO PID controller
EP  - 62
SP  - 57
DO  - 10.1109/CCDC.2017.7978066
ER  - 

@conference{
author = "Lazarević, Mihailo and Cajić, Milan and Mandić, Petar and Sekara, Tomislav B. and Sun, HongGuang and Karličić, Danilo",
year = "2017",
abstract = "In this paper, we suggest a robust non-square MIMO (4x8) PID controller for the multi-mode active vibration damping of a nanobeam. Nanobeam is modeled by using the nonlocal continuum theory of Eringen to consider the small-scale effects and Euler-Bernoulli beam theory. The problem is analyzed for the free vibration case with Heaviside type disturbance of a nanobeam with and without the controller. The proposed system has four inputs and eight outputs, where by using the static decoupling method, decoupled system of four transfer functions is obtained. The controller parameters dependig on one tuning parmeter are designed to suppress the step disturbance on the input without overshooting. All theoretical results are verified with several numerical examples.",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
journal = "Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017",
title = "Multi-mode Active Vibration Control of a Nanobeam using a non-square MIMO PID controller",
pages = "62-57",
doi = "10.1109/CCDC.2017.7978066"
}

Lazarević, M., Cajić, M., Mandić, P., Sekara, T. B., Sun, H.,& Karličić, D.. (2017). Multi-mode Active Vibration Control of a Nanobeam using a non-square MIMO PID controller. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
Institute of Electrical and Electronics Engineers Inc.., 57-62.
https://doi.org/10.1109/CCDC.2017.7978066

Lazarević M, Cajić M, Mandić P, Sekara TB, Sun H, Karličić D. Multi-mode Active Vibration Control of a Nanobeam using a non-square MIMO PID controller. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017. 2017;:57-62.
doi:10.1109/CCDC.2017.7978066 .

Lazarević, Mihailo, Cajić, Milan, Mandić, Petar, Sekara, Tomislav B., Sun, HongGuang, Karličić, Danilo, "Multi-mode Active Vibration Control of a Nanobeam using a non-square MIMO PID controller" in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 (2017):57-62,
https://doi.org/10.1109/CCDC.2017.7978066 . .

TY  - CONF
AU  - Mandić, Petar
AU  - Lazarević, Mihailo
AU  - Sekara, Tomislav B.
AU  - Cajić, Milan
AU  - Bučanović, Ljubiša
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2693
AB  - In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.
PB  - Institute of Electrical and Electronics Engineers Inc.
C3  - Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
T1  - Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator
EP  - 1916
SP  - 1911
DO  - 10.1109/CCDC.2017.7978829
ER  - 

@conference{
author = "Mandić, Petar and Lazarević, Mihailo and Sekara, Tomislav B. and Cajić, Milan and Bučanović, Ljubiša",
year = "2017",
abstract = "In this paper stability problem of double inverted pendulum controlled by a fractional differential compensator is investigated. Pendubot is an underactuated mechanical system, i.e. it has only one control input and two degrees of freedom. Detailed mathematical model of Pendubot is derived using the Rodriguez method and then fractional order lead compensator is introduced in order to stabilize it around unstable upright position. D-decomposition method is used to solve the problem of asymptotic stability of closed loop system. Stability regions in control parameters space are calculated using this technique, which allows tuning of the fractional differential compensator to be carried out.",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
journal = "Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017",
title = "Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator",
pages = "1916-1911",
doi = "10.1109/CCDC.2017.7978829"
}

Mandić, P., Lazarević, M., Sekara, T. B., Cajić, M.,& Bučanović, L.. (2017). Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
Institute of Electrical and Electronics Engineers Inc.., 1911-1916.
https://doi.org/10.1109/CCDC.2017.7978829

Mandić P, Lazarević M, Sekara TB, Cajić M, Bučanović L. Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017. 2017;:1911-1916.
doi:10.1109/CCDC.2017.7978829 .

Mandić, Petar, Lazarević, Mihailo, Sekara, Tomislav B., Cajić, Milan, Bučanović, Ljubiša, "Stabilization of Double Inverted Pendulum System by Using a Fractional Differential Compensator" in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 (2017):1911-1916,
https://doi.org/10.1109/CCDC.2017.7978829 . .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Durović, N.
AU  - Cvetković, Boško
AU  - Mandić, Petar
AU  - Cajić, Milan
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2691
AB  - In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order singular time-delay system is considered. In particular, we discuss fractional order linear singular timed-delay systems in state space form. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.
PB  - Institute of Electrical and Electronics Engineers Inc.
C3  - Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
T1  - PDα-type iterative learning control for fractional-order singular time-delay system
EP  - 1910
SP  - 1905
DO  - 10.1109/CCDC.2017.7978828
ER  - 

@conference{
author = "Lazarević, Mihailo and Durović, N. and Cvetković, Boško and Mandić, Petar and Cajić, Milan",
year = "2017",
abstract = "In this paper a closed-loop PDα - type iterative learning control (ILC) of fractional order singular time-delay system is considered. In particular, we discuss fractional order linear singular timed-delay systems in state space form. The sufficient conditions for the convergence in time domain of the proposed PD-alpha type ILC for a class of fractional order singular system are given by the corresponding theorem together with its proof. Finally, the validity of the proposed PDα ILC scheme for a class of fractional order singular time-delay system is verified by a numerical example.",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
journal = "Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017",
title = "PDα-type iterative learning control for fractional-order singular time-delay system",
pages = "1910-1905",
doi = "10.1109/CCDC.2017.7978828"
}

Lazarević, M., Durović, N., Cvetković, B., Mandić, P.,& Cajić, M.. (2017). PDα-type iterative learning control for fractional-order singular time-delay system. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017
Institute of Electrical and Electronics Engineers Inc.., 1905-1910.
https://doi.org/10.1109/CCDC.2017.7978828

Lazarević M, Durović N, Cvetković B, Mandić P, Cajić M. PDα-type iterative learning control for fractional-order singular time-delay system. in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017. 2017;:1905-1910.
doi:10.1109/CCDC.2017.7978828 .

Lazarević, Mihailo, Durović, N., Cvetković, Boško, Mandić, Petar, Cajić, Milan, "PDα-type iterative learning control for fractional-order singular time-delay system" in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017 (2017):1905-1910,
https://doi.org/10.1109/CCDC.2017.7978828 . .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Đurović, Nikola
AU  - Cajić, Milan
AU  - Cvetković, Boško
AU  - Mandić, Petar
AU  - Bučanović, Ljubiša
PY  - 2017
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4153
AB  - This paper addresses the problem of application of fractional order Iterative learning control (FOILC) for complex human arm-support system which can be modelled as nonlinear singular system of fractional order. An algorithm of a new strategy for the FOILC implementation is proposed.Sufficient conditions for the convergence in the time domain of a proposed ILC schemes
are given by the corresponding theorems and proved. Finally, a numerical simulations show the feasibility and effectiveness of the proposed approach.
PB  - Budapest : CongressLIne Ltd.
C3  - Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.
T1  - Feedback PDα type Iterative Learning Control for Fractional-Order Human Arm- Support Nonlinear System
EP  - 2
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4153
ER  - 

@conference{
author = "Lazarević, Mihailo and Đurović, Nikola and Cajić, Milan and Cvetković, Boško and Mandić, Petar and Bučanović, Ljubiša",
year = "2017",
abstract = "This paper addresses the problem of application of fractional order Iterative learning control (FOILC) for complex human arm-support system which can be modelled as nonlinear singular system of fractional order. An algorithm of a new strategy for the FOILC implementation is proposed.Sufficient conditions for the convergence in the time domain of a proposed ILC schemes
are given by the corresponding theorems and proved. Finally, a numerical simulations show the feasibility and effectiveness of the proposed approach.",
publisher = "Budapest : CongressLIne Ltd.",
journal = "Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.",
title = "Feedback PDα type Iterative Learning Control for Fractional-Order Human Arm- Support Nonlinear System",
pages = "2-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4153"
}

Lazarević, M., Đurović, N., Cajić, M., Cvetković, B., Mandić, P.,& Bučanović, L.. (2017). Feedback PDα type Iterative Learning Control for Fractional-Order Human Arm- Support Nonlinear System. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.
Budapest : CongressLIne Ltd.., 1-2.
https://hdl.handle.net/21.15107/rcub_machinery_4153

Lazarević M, Đurović N, Cajić M, Cvetković B, Mandić P, Bučanović L. Feedback PDα type Iterative Learning Control for Fractional-Order Human Arm- Support Nonlinear System. in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017.. 2017;:1-2.
https://hdl.handle.net/21.15107/rcub_machinery_4153 .

Lazarević, Mihailo, Đurović, Nikola, Cajić, Milan, Cvetković, Boško, Mandić, Petar, Bučanović, Ljubiša, "Feedback PDα type Iterative Learning Control for Fractional-Order Human Arm- Support Nonlinear System" in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC2017), edited by Gábor Stépán, Gábor Csernák. Budapest, 2017. (2017):1-2,
https://hdl.handle.net/21.15107/rcub_machinery_4153 .

TY  - CONF
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
AU  - Karličić, Danilo
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6568
AB  - It is well known that nonlocal elasticity models are successfully applied to various nanostructure based systems to study their stability or vibration behavior [1]. Such modified continuum approach shows to be reliable and much more efficient way to study complex nano-scale systems and structures compared to atomistic methods based on discrete nature of nanostructures. Nonlocal elasticity introduces the scale effects into the model via single material parameter also called nonlocal parameter. Dissipation of mechanical energy in nanostructures is important feature of nano-scale system that significantly affects their dynamic or stability behavior. Various
rheological models can be applied to describe such effects. However, well known comparison of fractional derivative rheological models compared to classical integer order one, candidates them for this application [2]. Finally, combination of nonlocal elasticity and fractional order viscoelasticity constitutive relations yield hybrid models that due to their nonlocal nature can describe nonlocality in space domain as well as relaxation/retardation processes in time domain. Here, we apply nonlocal elastic and fractional viscoelastic models to study vibration behavior of nanoplate and nanobeam like structures [3]. Euler-Bernoulli beam theory and Kirchhoff-Love plate theory are used for nanobeams and nanoplates, respectively. Several fractional derivative rheological models are shown and some of them applied to given nanostructure models. Governing equations are derived using D’Alambert’s principle and solutions for the simply supported boundary conditions
are found using separation of variables, Laplace transform and Mellin-Fourier inverse transform methods as well as residue theory. Complex poles of unknown functions are determined by finding the roots of the characteristic equation using technique that is available in the literature. In order to show the effects of fractional derivative parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped frequencies and damping ratios as well as on transient response of the systems, several numerical examples are given.
PB  - Faculty of Mechanical Engineering, Belgrade
PB  - University of Belgrade Mathematical Institute, Serbian Academy of Sciences and Arts
C3  - Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016
T1  - Nonlocal elasticity and fractional viscoelasticity models of nanobeams and nanoplates
EP  - 18
SP  - 18
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6568
ER  - 

@conference{
author = "Cajić, Milan and Lazarević, Mihailo and Karličić, Danilo",
year = "2016",
abstract = "It is well known that nonlocal elasticity models are successfully applied to various nanostructure based systems to study their stability or vibration behavior [1]. Such modified continuum approach shows to be reliable and much more efficient way to study complex nano-scale systems and structures compared to atomistic methods based on discrete nature of nanostructures. Nonlocal elasticity introduces the scale effects into the model via single material parameter also called nonlocal parameter. Dissipation of mechanical energy in nanostructures is important feature of nano-scale system that significantly affects their dynamic or stability behavior. Various
rheological models can be applied to describe such effects. However, well known comparison of fractional derivative rheological models compared to classical integer order one, candidates them for this application [2]. Finally, combination of nonlocal elasticity and fractional order viscoelasticity constitutive relations yield hybrid models that due to their nonlocal nature can describe nonlocality in space domain as well as relaxation/retardation processes in time domain. Here, we apply nonlocal elastic and fractional viscoelastic models to study vibration behavior of nanoplate and nanobeam like structures [3]. Euler-Bernoulli beam theory and Kirchhoff-Love plate theory are used for nanobeams and nanoplates, respectively. Several fractional derivative rheological models are shown and some of them applied to given nanostructure models. Governing equations are derived using D’Alambert’s principle and solutions for the simply supported boundary conditions
are found using separation of variables, Laplace transform and Mellin-Fourier inverse transform methods as well as residue theory. Complex poles of unknown functions are determined by finding the roots of the characteristic equation using technique that is available in the literature. In order to show the effects of fractional derivative parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped frequencies and damping ratios as well as on transient response of the systems, several numerical examples are given.",
publisher = "Faculty of Mechanical Engineering, Belgrade, University of Belgrade Mathematical Institute, Serbian Academy of Sciences and Arts",
journal = "Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016",
title = "Nonlocal elasticity and fractional viscoelasticity models of nanobeams and nanoplates",
pages = "18-18",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6568"
}

Cajić, M., Lazarević, M.,& Karličić, D.. (2016). Nonlocal elasticity and fractional viscoelasticity models of nanobeams and nanoplates. in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016
Faculty of Mechanical Engineering, Belgrade., 18-18.
https://hdl.handle.net/21.15107/rcub_machinery_6568

Cajić M, Lazarević M, Karličić D. Nonlocal elasticity and fractional viscoelasticity models of nanobeams and nanoplates. in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016. 2016;:18-18.
https://hdl.handle.net/21.15107/rcub_machinery_6568 .

Cajić, Milan, Lazarević, Mihailo, Karličić, Danilo, "Nonlocal elasticity and fractional viscoelasticity models of nanobeams and nanoplates" in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016 (2016):18-18,
https://hdl.handle.net/21.15107/rcub_machinery_6568 .

TY  - CONF
AU  - Karličić, Danilo
AU  - Cajić, Milan
AU  - Kozić, Predrag
AU  - Lazarević, Mihailo
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6567
AB  - In recent years, nonlinear and damping effects have become more important in the study of the dynamic behavior of micro- and nano- systems and devices. Therefore, investigators direct special attention to the  mathematical modeling of the dynamic behavior of nano-structures such as carbon nanotubes, ZnO nanotubes and functionally graded beams.
The functionally graded materials (FGM) are types of structures that are composed of at last two-phase inhomogeneous particulate composite and synthesized in such manner that the volume fractions of constituents vary continuously along any desired spatial direction. This results in smooth variation of mechanical properties along desired direction. Nazemnezhad et al. [1] have analyzed the free nonlinear vibration of FG nanobeam based on the von Karman deformation, Euler-Bernoulli beam theory and nonlocal elasticity. They obtained approximated analytical solution for the nonlinear natural frequency by applying the multiple scales perturbation
method. Ansari et al. [2] proposed nonlinear dynamic model to analyze the nonlinear forced vibration of FG nanobeam in thermal environment based on the surface elasticity theory.
Some authors describe dissipation effects in viscoelastic structures and nanostructures using fractional derivative models [3]. Ansari et al. [4] investigated the nonlinear vibration of a nonlocal fractional viscoelastic nanobeam using numerical methods.
By browsing the literature, the authors found a small number of studies focused on the vibration analysis of FG nanobeams embedded in certain type of medium. In this report, we investigated the dynamical model of a functionally graded (FG) beam modeled as a nanobeam with geometric nonlinearity embedded in a fractional Kelvin-Voigt viscoelastic medium by using the nonlocal continuum theory. The material properties of FG nanobeam vary continuously through thickness direction, which is based on the power-low distribution. We assume that the FG nanobeam has simply-supported boundary conditions and vibrates under the influence of the transversal periodic load. Based on the nonlocal Euler-Bernoulli beam theory, von Karman nonlinear  strain-displacements relation, we obtain the nonlinear fractional partial differential equations of transversal motion of the embedded FG nanobeam. By using the assumption of small fractional damping we employed the perturbation method of multiple-scales to obtain the approximated analytical solution of the governing equation of motion. The relationships between frequency-amplitude and force-amplitude in the presence of fractional damping are derived by using the multiple scales method. It is shown that the nonlocal parameter, fractional damping and material property gradient index have significant effects on the vibration behavior of FG nanobeam
and therefore receive substantial attention.
PB  - Faculty of Mechanical Engineering, Belgrade
PB  - University of Belgrade Mathematical Institute, Serbian Academy of Sciences and Arts
C3  - Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016
T1  - Nonlinear forced vibration of a functionally graded nonlocal nanobeam embedded in a fractional viscoelastic medium
EP  - 26
SP  - 26
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6567
ER  - 

@conference{
author = "Karličić, Danilo and Cajić, Milan and Kozić, Predrag and Lazarević, Mihailo",
year = "2016",
abstract = "In recent years, nonlinear and damping effects have become more important in the study of the dynamic behavior of micro- and nano- systems and devices. Therefore, investigators direct special attention to the  mathematical modeling of the dynamic behavior of nano-structures such as carbon nanotubes, ZnO nanotubes and functionally graded beams.
The functionally graded materials (FGM) are types of structures that are composed of at last two-phase inhomogeneous particulate composite and synthesized in such manner that the volume fractions of constituents vary continuously along any desired spatial direction. This results in smooth variation of mechanical properties along desired direction. Nazemnezhad et al. [1] have analyzed the free nonlinear vibration of FG nanobeam based on the von Karman deformation, Euler-Bernoulli beam theory and nonlocal elasticity. They obtained approximated analytical solution for the nonlinear natural frequency by applying the multiple scales perturbation
method. Ansari et al. [2] proposed nonlinear dynamic model to analyze the nonlinear forced vibration of FG nanobeam in thermal environment based on the surface elasticity theory.
Some authors describe dissipation effects in viscoelastic structures and nanostructures using fractional derivative models [3]. Ansari et al. [4] investigated the nonlinear vibration of a nonlocal fractional viscoelastic nanobeam using numerical methods.
By browsing the literature, the authors found a small number of studies focused on the vibration analysis of FG nanobeams embedded in certain type of medium. In this report, we investigated the dynamical model of a functionally graded (FG) beam modeled as a nanobeam with geometric nonlinearity embedded in a fractional Kelvin-Voigt viscoelastic medium by using the nonlocal continuum theory. The material properties of FG nanobeam vary continuously through thickness direction, which is based on the power-low distribution. We assume that the FG nanobeam has simply-supported boundary conditions and vibrates under the influence of the transversal periodic load. Based on the nonlocal Euler-Bernoulli beam theory, von Karman nonlinear  strain-displacements relation, we obtain the nonlinear fractional partial differential equations of transversal motion of the embedded FG nanobeam. By using the assumption of small fractional damping we employed the perturbation method of multiple-scales to obtain the approximated analytical solution of the governing equation of motion. The relationships between frequency-amplitude and force-amplitude in the presence of fractional damping are derived by using the multiple scales method. It is shown that the nonlocal parameter, fractional damping and material property gradient index have significant effects on the vibration behavior of FG nanobeam
and therefore receive substantial attention.",
publisher = "Faculty of Mechanical Engineering, Belgrade, University of Belgrade Mathematical Institute, Serbian Academy of Sciences and Arts",
journal = "Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016",
title = "Nonlinear forced vibration of a functionally graded nonlocal nanobeam embedded in a fractional viscoelastic medium",
pages = "26-26",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6567"
}

Karličić, D., Cajić, M., Kozić, P.,& Lazarević, M.. (2016). Nonlinear forced vibration of a functionally graded nonlocal nanobeam embedded in a fractional viscoelastic medium. in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016
Faculty of Mechanical Engineering, Belgrade., 26-26.
https://hdl.handle.net/21.15107/rcub_machinery_6567

Karličić D, Cajić M, Kozić P, Lazarević M. Nonlinear forced vibration of a functionally graded nonlocal nanobeam embedded in a fractional viscoelastic medium. in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016. 2016;:26-26.
https://hdl.handle.net/21.15107/rcub_machinery_6567 .

Karličić, Danilo, Cajić, Milan, Kozić, Predrag, Lazarević, Mihailo, "Nonlinear forced vibration of a functionally graded nonlocal nanobeam embedded in a fractional viscoelastic medium" in Booklet of Abstracts Mini-symposium “ Fractional Calculus with applications in problems of diffusion, control and dynamics of complex systems”,  July 13, 2016 (2016):26-26,
https://hdl.handle.net/21.15107/rcub_machinery_6567 .

TY  - CONF
AU  - Lazarević, Mihailo
AU  - Cajić, Milan
AU  - Nešić, Nikola
AU  - Karličić, Danilo
AU  - Djurović, Nikola
AU  - Bučanović, Ljubiša
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6448
AB  - Recent advances in the field of nano-science are increasing the number of theoretical studies investigating the mechanical behavior of nanostructures and nanocomposites using nonlocal continuum models. Such models show to be an efficient tool to describe the vibration or stability behavior of nanoplate, nanobeam or complex nanostructure systems without any specific demands for computational resources. Using this theory, nonlocal effects such as long range interactions and forces between atoms are included via single material parameter also called nonlocal parameter whose values are usually calibrated with molecular dynamics simulations or using dispersion curves of atomic models. Nonlocal theory is convenient to include into a model various external field effects such as magnetic or temperature field on the mechanical behavior of nanostructures. In this paper, we analyze the free transverse vibration of a nanoplate model representing the graphene sheet nanostructure that is subjected to the influence of in-plane magnetic field. Governing equation of a nanoplate is derived employing the nonlocal elasticity theory of Eringen, Kirchhoff–Love plate theory and Maxwell classical equations. Finite element formulation for the magnetically influenced nanoplate is proposed to find the solution for natural frequencies of the system for different boundary conditions. Results obtained via finite element method are confirmed with other results from the literature. Influences of nonlocal parameter and the magnitude of magnetic field on natural frequencies are investigated through several numerical examples of graphene sheet nanostructure. This study can be useful for future research of more complex nanoplate based systems
PB  - Nanotechnology
C3  - Book of abstracts 13th International Conference on Nanosciences and Nanotechnologies NN16, 5-8 July 2016 Thessaloniki Greece
T1  - Nonlocal vibration of a nanoplate  influenced by in-plane magnetic field using finite element method
EP  - 283
SP  - 283
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6448
ER  - 

@conference{
author = "Lazarević, Mihailo and Cajić, Milan and Nešić, Nikola and Karličić, Danilo and Djurović, Nikola and Bučanović, Ljubiša",
year = "2016",
abstract = "Recent advances in the field of nano-science are increasing the number of theoretical studies investigating the mechanical behavior of nanostructures and nanocomposites using nonlocal continuum models. Such models show to be an efficient tool to describe the vibration or stability behavior of nanoplate, nanobeam or complex nanostructure systems without any specific demands for computational resources. Using this theory, nonlocal effects such as long range interactions and forces between atoms are included via single material parameter also called nonlocal parameter whose values are usually calibrated with molecular dynamics simulations or using dispersion curves of atomic models. Nonlocal theory is convenient to include into a model various external field effects such as magnetic or temperature field on the mechanical behavior of nanostructures. In this paper, we analyze the free transverse vibration of a nanoplate model representing the graphene sheet nanostructure that is subjected to the influence of in-plane magnetic field. Governing equation of a nanoplate is derived employing the nonlocal elasticity theory of Eringen, Kirchhoff–Love plate theory and Maxwell classical equations. Finite element formulation for the magnetically influenced nanoplate is proposed to find the solution for natural frequencies of the system for different boundary conditions. Results obtained via finite element method are confirmed with other results from the literature. Influences of nonlocal parameter and the magnitude of magnetic field on natural frequencies are investigated through several numerical examples of graphene sheet nanostructure. This study can be useful for future research of more complex nanoplate based systems",
publisher = "Nanotechnology",
journal = "Book of abstracts 13th International Conference on Nanosciences and Nanotechnologies NN16, 5-8 July 2016 Thessaloniki Greece",
title = "Nonlocal vibration of a nanoplate  influenced by in-plane magnetic field using finite element method",
pages = "283-283",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6448"
}

Lazarević, M., Cajić, M., Nešić, N., Karličić, D., Djurović, N.,& Bučanović, L.. (2016). Nonlocal vibration of a nanoplate  influenced by in-plane magnetic field using finite element method. in Book of abstracts 13th International Conference on Nanosciences and Nanotechnologies NN16, 5-8 July 2016 Thessaloniki Greece
Nanotechnology., 283-283.
https://hdl.handle.net/21.15107/rcub_machinery_6448

Lazarević M, Cajić M, Nešić N, Karličić D, Djurović N, Bučanović L. Nonlocal vibration of a nanoplate  influenced by in-plane magnetic field using finite element method. in Book of abstracts 13th International Conference on Nanosciences and Nanotechnologies NN16, 5-8 July 2016 Thessaloniki Greece. 2016;:283-283.
https://hdl.handle.net/21.15107/rcub_machinery_6448 .

Lazarević, Mihailo, Cajić, Milan, Nešić, Nikola, Karličić, Danilo, Djurović, Nikola, Bučanović, Ljubiša, "Nonlocal vibration of a nanoplate  influenced by in-plane magnetic field using finite element method" in Book of abstracts 13th International Conference on Nanosciences and Nanotechnologies NN16, 5-8 July 2016 Thessaloniki Greece (2016):283-283,
https://hdl.handle.net/21.15107/rcub_machinery_6448 .

TY  - CONF
AU  - Cajić, Milan
AU  - Lazarević, Mihailo
AU  - Sun, HongGuang
AU  - Karličić, Danilo
AU  - Chen, Wen
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4186
AB  - Here, we investigate the free vibration behavior of a nanoplate resting on a foundation
with viscoelastic properties using nonlocal elasticity and fractional viscoelasticity
approach. Nanoplate is modeled using nonlocal and fractional viscoelastic constitutive
equation and orthotropic Kirchhoff-Love plate theory. Viscoelastic foundation is
represented by the viscoelastic model with fractional derivative operator. Governing
equation is derived using D’Alambert’s principle and solution is assumed in terms of
Fourier series using separation of variables method and satisfying the simply supported
boundary conditions for nanoplate. Fractional differential equation is solved using the
Laplace and Mellin-Fourier transforms and residue theory. Complex poles of unknown
function are determined by finding the roots of the characteristic equation using technique
that is available in the literature. In order to show the effect of fractional derivative
parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped
frequency and damping ratio as well as on nanoplate’s displacement, few numerical
examples are given.
PB  - Belgrade: Serbian Society of Mechanics
PB  - Faculty of Technical Sciences Novi Sad
C3  - Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia
T1  - Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach
EP  - 500
SP  - 491
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4186
ER  - 

@conference{
author = "Cajić, Milan and Lazarević, Mihailo and Sun, HongGuang and Karličić, Danilo and Chen, Wen",
year = "2016",
abstract = "Here, we investigate the free vibration behavior of a nanoplate resting on a foundation
with viscoelastic properties using nonlocal elasticity and fractional viscoelasticity
approach. Nanoplate is modeled using nonlocal and fractional viscoelastic constitutive
equation and orthotropic Kirchhoff-Love plate theory. Viscoelastic foundation is
represented by the viscoelastic model with fractional derivative operator. Governing
equation is derived using D’Alambert’s principle and solution is assumed in terms of
Fourier series using separation of variables method and satisfying the simply supported
boundary conditions for nanoplate. Fractional differential equation is solved using the
Laplace and Mellin-Fourier transforms and residue theory. Complex poles of unknown
function are determined by finding the roots of the characteristic equation using technique
that is available in the literature. In order to show the effect of fractional derivative
parameters, damping coefficients and nonlocal parameter on complex roots i.e. damped
frequency and damping ratio as well as on nanoplate’s displacement, few numerical
examples are given.",
publisher = "Belgrade: Serbian Society of Mechanics, Faculty of Technical Sciences Novi Sad",
journal = "Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia",
title = "Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach",
pages = "500-491",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4186"
}

Cajić, M., Lazarević, M., Sun, H., Karličić, D.,& Chen, W.. (2016). Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia
Belgrade: Serbian Society of Mechanics., 491-500.
https://hdl.handle.net/21.15107/rcub_machinery_4186

Cajić M, Lazarević M, Sun H, Karličić D, Chen W. Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach. in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia. 2016;:491-500.
https://hdl.handle.net/21.15107/rcub_machinery_4186 .

Cajić, Milan, Lazarević, Mihailo, Sun, HongGuang, Karličić, Danilo, Chen, Wen, "Vibration of an orthotropic nanoplate resting on a viscoelastic foundation: nonlocal and fractional derivative viscoelasticity approach" in Proceedings of International Conference on Fractional Differentiation and its Application ICFDA16, 18-20 July 2016, Novi Sad, Serbia (2016):491-500,
https://hdl.handle.net/21.15107/rcub_machinery_4186 .

TY  - JOUR
AU  - Cajić, Milan S.
AU  - Lazarević, Mihailo
PY  - 2016
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/2358
AB  - U ovom radu su prikazane dve različite metode za određivanje sila i momenata reakcija idealnih veza u zglobovima. Razmatrani sistem više tela ima strukturu otvorenog kinematskog lanca. Prva metoda se odnosi na određivanje glavnih vektora i momenata reakcija veza u simboličkoj formi koja se zasniva na Rodrigezovom pristupu i pogodna je za simboličko računanje. Druga prikazana metoda je vektorska metoda koja je bazirana na vektorima momenata masa i vektorima rotatorima vezanih za pol i usmerenu osu. Oba primera su prikazana i diskutovana na sistemu tri kruta tela.
AB  - In this paper two different methods for determination of frictionless joint reaction forces and moments are presented. The considered multibody system has an open kinematic chain structure. The first method refers to the determination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic form. The second method presented is the method based on the so-called vectors of the body mass moments and vector rotators coupled for a pole and oriented axes. Both approaches are presented and discussed on the three- like rigid multibody system.
PB  - Univerzitet u Beogradu - Mašinski fakultet, Beograd
T2  - FME Transactions
T1  - Određivanje reakcija zgloba u sistemu više krutih tela, dva različita pristupa
T1  - Determination of joint reactions in a rigid multibody system, two different approaches
EP  - 173
IS  - 2
SP  - 165
VL  - 44
DO  - 10.5937/fmet1602165C
ER  - 

@article{
author = "Cajić, Milan S. and Lazarević, Mihailo",
year = "2016",
abstract = "U ovom radu su prikazane dve različite metode za određivanje sila i momenata reakcija idealnih veza u zglobovima. Razmatrani sistem više tela ima strukturu otvorenog kinematskog lanca. Prva metoda se odnosi na određivanje glavnih vektora i momenata reakcija veza u simboličkoj formi koja se zasniva na Rodrigezovom pristupu i pogodna je za simboličko računanje. Druga prikazana metoda je vektorska metoda koja je bazirana na vektorima momenata masa i vektorima rotatorima vezanih za pol i usmerenu osu. Oba primera su prikazana i diskutovana na sistemu tri kruta tela., In this paper two different methods for determination of frictionless joint reaction forces and moments are presented. The considered multibody system has an open kinematic chain structure. The first method refers to the determination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic form. The second method presented is the method based on the so-called vectors of the body mass moments and vector rotators coupled for a pole and oriented axes. Both approaches are presented and discussed on the three- like rigid multibody system.",
publisher = "Univerzitet u Beogradu - Mašinski fakultet, Beograd",
journal = "FME Transactions",
title = "Određivanje reakcija zgloba u sistemu više krutih tela, dva različita pristupa, Determination of joint reactions in a rigid multibody system, two different approaches",
pages = "173-165",
number = "2",
volume = "44",
doi = "10.5937/fmet1602165C"
}

Cajić, M. S.,& Lazarević, M.. (2016). Određivanje reakcija zgloba u sistemu više krutih tela, dva različita pristupa. in FME Transactions
Univerzitet u Beogradu - Mašinski fakultet, Beograd., 44(2), 165-173.
https://doi.org/10.5937/fmet1602165C

Cajić MS, Lazarević M. Određivanje reakcija zgloba u sistemu više krutih tela, dva različita pristupa. in FME Transactions. 2016;44(2):165-173.
doi:10.5937/fmet1602165C .

Cajić, Milan S., Lazarević, Mihailo, "Određivanje reakcija zgloba u sistemu više krutih tela, dva različita pristupa" in FME Transactions, 44, no. 2 (2016):165-173,
https://doi.org/10.5937/fmet1602165C . .

TY  - CONF
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/6453
AB  - In this paper, we analyze the free transverse vibration of a nanobeam model representing the carbon nanotube that is subjected to the influence of longitudinal magnetic field. Governing equation of a nanobeam is derived employing the nonlocal elasticity theory of Eringen, Euler-Bernoulli beam theory and Maxwell classical equations. Solution for natural frequencies of a nanobeam is proposed by using the finite element method. Influences of nonlocal parameter and the magnitude of magnetic field on dimensionless natural frequencies are investigated through several numerical examples.
PB  - University of Thessaly Press
C3  - Proceedings of 8th GRACM International Congress on Computational Mechanics,Volos,Greece,12 July – 15 July 2015, University of Thessaly Press 2015
T1  - Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method
EP  - 7
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_6453
ER  - 

@conference{
author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo",
year = "2015",
abstract = "In this paper, we analyze the free transverse vibration of a nanobeam model representing the carbon nanotube that is subjected to the influence of longitudinal magnetic field. Governing equation of a nanobeam is derived employing the nonlocal elasticity theory of Eringen, Euler-Bernoulli beam theory and Maxwell classical equations. Solution for natural frequencies of a nanobeam is proposed by using the finite element method. Influences of nonlocal parameter and the magnitude of magnetic field on dimensionless natural frequencies are investigated through several numerical examples.",
publisher = "University of Thessaly Press",
journal = "Proceedings of 8th GRACM International Congress on Computational Mechanics,Volos,Greece,12 July – 15 July 2015, University of Thessaly Press 2015",
title = "Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method",
pages = "7-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_6453"
}

Cajić, M., Karličić, D.,& Lazarević, M.. (2015). Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method. in Proceedings of 8th GRACM International Congress on Computational Mechanics,Volos,Greece,12 July – 15 July 2015, University of Thessaly Press 2015
University of Thessaly Press., 1-7.
https://hdl.handle.net/21.15107/rcub_machinery_6453

Cajić M, Karličić D, Lazarević M. Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method. in Proceedings of 8th GRACM International Congress on Computational Mechanics,Volos,Greece,12 July – 15 July 2015, University of Thessaly Press 2015. 2015;:1-7.
https://hdl.handle.net/21.15107/rcub_machinery_6453 .

Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, "Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method" in Proceedings of 8th GRACM International Congress on Computational Mechanics,Volos,Greece,12 July – 15 July 2015, University of Thessaly Press 2015 (2015):1-7,
https://hdl.handle.net/21.15107/rcub_machinery_6453 .

TY  - CONF
AU  - Cajić, Milan
AU  - Karličić, Danilo
AU  - Lazarević, Mihailo
PY  - 2015
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/4248
AB  - We propose a mathematical framework to examine the free damped transverse vibration of
nanobeams with attached nanoparticles by using the nonlocal theory of Eringen and fractional
calculus. Governing equation of nanobeam with arbitrary attached nanoparticle is derived by
considering the viscoelastic constitutive equation involving fractional order derivative and
nonlocal Euler-Bernoulli beam theory. The solution is proposed by using the method of
separation of variables. Eigenvalues and mode shapes are determined for two typical boundary
conditions. The solution of fractional order differential equation in terms of a time function is
found via Laplace transform method. The time dependent behavior is examined by observing the
time function for different values of fractional order parameter and different ratios of other
parameters in the model.
PB  - Belgrade: Serbian Society of Mechanics
PB  - Novi Sad: Faculty of Technical Sciences
C3  - Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c
T1  - Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle
EP  - 10
SP  - 1
UR  - https://hdl.handle.net/21.15107/rcub_machinery_4248
ER  - 

@conference{
author = "Cajić, Milan and Karličić, Danilo and Lazarević, Mihailo",
year = "2015",
abstract = "We propose a mathematical framework to examine the free damped transverse vibration of
nanobeams with attached nanoparticles by using the nonlocal theory of Eringen and fractional
calculus. Governing equation of nanobeam with arbitrary attached nanoparticle is derived by
considering the viscoelastic constitutive equation involving fractional order derivative and
nonlocal Euler-Bernoulli beam theory. The solution is proposed by using the method of
separation of variables. Eigenvalues and mode shapes are determined for two typical boundary
conditions. The solution of fractional order differential equation in terms of a time function is
found via Laplace transform method. The time dependent behavior is examined by observing the
time function for different values of fractional order parameter and different ratios of other
parameters in the model.",
publisher = "Belgrade: Serbian Society of Mechanics, Novi Sad: Faculty of Technical Sciences",
journal = "Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c",
title = "Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle",
pages = "10-1",
url = "https://hdl.handle.net/21.15107/rcub_machinery_4248"
}

Cajić, M., Karličić, D.,& Lazarević, M.. (2015). Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c
Belgrade: Serbian Society of Mechanics., 1-10.
https://hdl.handle.net/21.15107/rcub_machinery_4248

Cajić M, Karličić D, Lazarević M. Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle. in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c. 2015;:1-10.
https://hdl.handle.net/21.15107/rcub_machinery_4248 .

Cajić, Milan, Karličić, Danilo, Lazarević, Mihailo, "Nonlocal vibration of fractional order viscoelastic nanobeam with attached nanoparticle" in Proceedings of the 5th International Congress of Serbian Society of Mechanics, Arandjelovac, June 15-17, 2015, I1c (2015):1-10,
https://hdl.handle.net/21.15107/rcub_machinery_4248 .