Wave characteristics in aligned forests of single-walled carbon nanotubes using nonlocal discrete and continuous theories

Abstract

Elastic waves within forests of single-walled carbon nanotubes (SWCNTs) have been of particular interest to researchers of nanotechnology and applied physics. To date, wave motion in individual single-, double-, and multi- walled carbon nanotubes has been extensively investigated, however, characteristics of the transverse waves in three-dimensional clusters of SWCNTs have not been revealed. In this paper, using nonlocal Rayleigh, Timoshenko, and higher-order beam theories, shear and flexural frequencies as well as their corresponding phase and group velocities of transverse waves within such nanostructures are studied via discrete and continuous models. Using continuous models, the explicit expressions of the above-mentioned characteristics of waves are obtained. The efficacy of the proposed continuous models is proved by comparing their results with those of the nonlocal discrete models. The roles of wavenumber, radius of the constitutive SWCNTs, slenderness ratio, small-scale parameter, intertube distance, and population of the ensemble on the characteristics of transverse waves are comprehensively examined.