Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

Abstract

The behaviour of carbon nanotubes in a magnetic field has attracted considerable attention in the scientific community. This paper reports the effects of a longitudinal magnetic field on the vibration of a magnetically sensitive double single-walled carbon nanotube system (DSWNTS). The two nanotubes of the DSWNTS are coupled by an elastic medium. The dynamical equations of the DSWNTS are derived using nonlocal elasticity theory. The two nanotubes are defined as an equivalent nonlocal double-Euler-Bernoulli beam system. Governing equations for nonlocal bending-vibration of the DSWNTS under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell’s relation. An analytical method is proposed to obtain nonlocal natural frequencies of the DSWNTS. The influence of (i) nanoscale effects and (ii) strength of longitudinal magnetic field on the synchronous and asynchronous vibration phase of the DSWNTS is examined. Nonlocal effects with and without the effect of magnetic field are illustrated. Results reveal the difference (quantitatively) by which the longitudinal magnetic field affects the nonlocal frequency in the synchronous and asynchronous vibration modes of a DSWNTS.