Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles
Само за регистроване кориснике
2018
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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 t...o 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.
Кључне речи:
Nonlocal elasticity / Nanobeams / Mass nanosensor / Magnetic field / Fractional viscoelasticity / DampingИзвор:
Acta Mechanica, 2018, 229, 12, 4791-4815Издавач:
- Springer Wien, Wien
Финансирање / пројекти:
- Serbia-China bilateral Project [337-00-125/2015-09/12
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
- Одрживост и унапређење машинских система у енергетици и транспорту применом форензичког инжењерства, еко и робуст дизајна (RS-MESTD-Technological Development (TD or TR)-35006)
- Развој нових метода и техника за рану дијагностику канцера грлића материце, дебелог црева, усне дупље и меланома на бази дигиталне слике и ексцитационо-емисионих спектара у видљивом и инфрацрвеном домену (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-41006)
DOI: 10.1007/s00707-018-2263-7
ISSN: 0001-5970
WoS: 000450983800004
Scopus: 2-s2.0-85053840078
Колекције
Институција/група
Mašinski fakultetTY - 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 . .