Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles
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2018
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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.
Ključne reči:
Nonlocal elasticity / Nanobeams / Mass nanosensor / Magnetic field / Fractional viscoelasticity / DampingIzvor:
Acta Mechanica, 2018, 229, 12, 4791-4815Izdavač:
- Springer Wien, Wien
Finansiranje / projekti:
- Serbia-China bilateral Project [337-00-125/2015-09/12
- Dinamika hibridnih sistema složenih struktura. Mehanika materijala (RS-MESTD-Basic Research (BR or ON)-174001)
- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
- Razvoj novih metoda i tehnika za ranu dijagnostiku kancera grlića materice, debelog creva, usne duplje i melanoma na bazi digitalne slike i ekscitaciono-emisionih spektara u vidljivom i infracrvenom domenu (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
Kolekcije
Institucija/grupa
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 . .