Eur. Phys. J. Plus (2018) 133: 219
https://doi.org/10.1140/epjp/i2018-12039-5

Regular Article

Vibration of initially stressed carbon nanotubes under magneto-thermal environment for nanoparticle delivery via higher-order nonlocal strain gradient theory

¹ Borjavaran Center of Applied Science and Technology, University of Applied Sciences and Technology, Tehran, Iran
² Department of Mechanical Engineering, Isfahan University of Technology, 8415683111, Isfahan, Iran
³ Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

^* e-mail: ariobarzan.oderj@gmail.com

Received: 18 December 2017
Accepted: 1 May 2018
Published online: 11 June 2018

Abstract

In this paper, the forced vibration of a single-walled carbon nanotube (SWCNT) under a moving nanoparticle is investigated based on the higher-order nonlocal strain gradient theory. The SWCNT is subjected to thermo-mechanical stresses and an external longitudinal magnetic field. The influences of higher-order stress gradients in conjunction with the strain gradient nonlocality are taken into account. Using Hamilton’s principle and Maxwell’s equations, the higher-order differential equations of motion are derived. An analytical solution is obtained for the dynamic deflection of SWCNTs using the Galerkin method. Furthermore, the governing differential equation is solved numerically using the precise integration method. The results of the two solution procedures are compared and an excellent agreement is found between them. Finally, the influences of various scale parameters, the velocity of the moving nanoparticle, the initial axial stress, the temperature change and longitudinal magnetic field on the dynamic response of SWCNTs are investigated.