Authors: Cajić, Milan 
Lazarević, Mihailo
Karličić, Danilo 
Sun, Hong Guang
Liu, Xiaoting
Title: Fractional-order model for the vibration of a nanobeam influenced by an axial magnetic field and attached nanoparticles
Journal: Acta Mechanica
Volume: 229
Issue: 12
First page: 4791
Last page: 4815
Issue Date: 1-Dec-2018
Rank: M22
ISSN: 0001-5970
DOI: 10.1007/s00707-018-2263-7
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.
Keywords: Damping | Fractional viscoelasticity | Magnetic field | Mass nanosensor | Nanobeams | Nonlocal elasticity
Publisher: Springer Link
Project: Dynamics of hybrid systems with complex structures. Mechanics of materials. 
Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design 
Development of methods and techniques for early diagnostic of cervical, colon, oral cavity cancer and melanoma based on a digital image and excitation-emission spectrum in visible and infrared domain 
Serbia-China bilateral Project No. 337-00-125/2015-09/12

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