Serbia-China bilateral Project [337-00-125/2015-09/12

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Serbia-China bilateral Project [337-00-125/2015-09/12

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Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles

Cajić, Milan; Lazarević, Mihailo; Karličić, Danilo; Sun, HongGuang; Liu, Xiaoting

(Springer Wien, Wien, 2018)

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 . .
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