Dynamic analysis of wave propagation and buckling phenomena in carbon nanotubes(CNTs)

Abstract

The present study focuses on analysing the behaviour of wave propagation in carbon nanotubes along with the characterization of the buckling phenomenon. The carbon nanotubes are modelled as continuum shells that utilize the nonlocal theory of elasticity as these consider the small effects of the nano structures. The expression for the dispersion relation of the wave propagation in single-walled carbon nanotube (SWCNT) and the double-walled carbon nanotubes (DWCNTs) are achieved using a suitable mathematical treatment. For the case of SWCNT, a combined effect of uniform external lateral pressure, uniform axial pressure, stretching of middle surface, the shearing force due to the torque applied, scaling effect are considered, which presents a new concept. The van der Waals (vdW) interaction, additionally, is regarded for the case of DWCNTs. Moreover, the expression for the buckling phenomenon of the DWCNTs and the triple-walled carbon nanotubes (TWCNTS) taking account of the effect of stretching of middle surface, the shearing force due to torque applied, scaling effect, vdW interaction, and net pressure due to vdW interaction has been established. As a special case of the problem, the deduced results of the present study are found to be well-matched with the pre-existing results, hence, validates the undertaken study. The phase velocity and buckling load curves are manifested graphically using numerical data of two distinct kinds of DWCNTs and TWCNTs depending on the armchair configuration. The influence of various affecting parameters the phase velocity and buckling load curves are noted and are illustrated in tabular form. The study may find its potential application for some engineering problems dealing with the characterization of CNTs and wave propagation through them under the combined effect.