Effect of Longitudinal Magnetic Field on Vibration Response of Double-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

Abstract

This paper aims to study the effect of externally applied longitudinal magnetic field on the transverse vibration of viscoelastic double-walled carbon nanotubes (visco-DWCNTs) embedded in a viscoelastic medium. The analyses are carried out based on the nonlocal viscoelastic model and Euler–Bernoulli beam theory. Governing equations are derived for the vibration of the embedded visco-DWCNT subjected to a magnetic field, where the Lorentz magnetic force, the surrounding viscoelastic medium, the intertube van der Waals forces and viscoelasticity of the DWCNT are taken into consideration. In this study, the transfer function method is employed to solve the governing equations, which enables one to obtain the natural frequencies and the corresponding mode shapes in closed form for the DWCNTs with arbitrary boundary conditions. Here the developed mechanics model is first compared with the existing techniques available in the literature in a few particular cases, where excellent agreement is achieved. The validation of the model is followed by a detailed parametric study of the effects of longitudinal magnetic field, nonlocal parameter, boundary conditions, structural damping coefficient and aspect ratio of the DWCNTs on their vibration. The study demonstrates the efficiency of the present technique designed for vibration analysis of a complicated multi-physics system comprising DWCNTs, the viscoelastic medium and a magnetic field in longitudinal direction.