Vol. 11, No. 3, 2016

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Nonlocal forced vibration of a double single-walled carbon nanotube system under the influence of an axial magnetic field

Marija B. Stamenković, Danilo Karličić, Goran Janevski and Predrag Kozić

Vol. 11 (2016), No. 3, 279–307

The influence of various physical phenomena on the dynamic behavior of nanostructures has been attracting more and more attention of the scientific community. This paper discusses the effects of the axial magnetic field on the externally excited double single-walled carbon nanotube (DSWCNT) coupled by a Winkler elastic medium. It is assumed that both carbon nanotubes are identical and under the influence of compressive axial load with simply supported ends. Based on the Eringen nonlocal elasticity and Euler–Bernoulli beam theory, the system of two coupled nonhomogeneous partial differential equations of motion is derived, where the effects of the Lorentz magnetic force are obtained via a Maxwell relation. The dynamic responses of the DSWCNT system for four different cases of external transversal load are considered. The closed form solutions for the transversal displacements are obtained by applying the Bernoulli–Fourier method of particular integrals on the system of nonhomogeneous partial differential equations of motion. Also, analytical expressions of the amplitude ratio for forced vibration are derived and then validated with existing results. Moreover, the obtained analytical results for fundamental natural frequency are validated with results obtained by molecular dynamics (MD) simulation and show fine agreements. The effects of compressive axial load, nonlocal parameter, axial magnetic field and stiffness coefficient of the elastic medium on the forced dynamic behavior of DSWCNT are considered through numerical examples. From numerical results we can conclude that the dynamical behavior of DSWCNT is greatly influenced by the magnetic field and nonlocal parameter. Furthermore, by selecting the intensity of the axial magnetic field in a certain range, it is possible to adjust the stiffness of the system without changing the material and geometric parameters. This effect implies a change in the natural frequencies of the system.

forced vibration, nonlocal elasticity, axial magnetic field, analytical solution, carbon nanotubes
Received: 25 May 2015
Revised: 30 September 2015
Accepted: 1 January 2016
Published: 26 July 2016
Marija B. Stamenković
Mathematical Institute of the Serbian Academy of Science and Arts
Kneza Mihaila 36
11001 Belgrade
Danilo Karličić
Faculty of Mechanical Engineering
University of Niš
A. Medvedeva 14
18000 Niš
Goran Janevski
Department of Mechanical Engineering
University of Niš
A. Medvedeva 14
18000 Niš
Predrag Kozić
Faculty of Mechanical Engineering
University of Niš
A. Medvedeva 14
18000 Niš