Free vibration analysis of single- and double-walled carbon nanotubes based on nonlocal elastic shell models

Abstract

In the present study, the free vibration characteristics of single- and double-walled carbon nanotubes (SWCNTs and DWCNTs) are investigated on the basis of a nonlocal elastic shell model. Eringen’s nonlocal elasticity equations are applied to the classical Donnell shell theory to incorporate the size-effects into the vibration analysis of carbon nanotubes (CNTs). An exact solution is developed for the governing equations of the nonlocal elastic shell model with the inclusion of size effects. Molecular dynamics (MD) simulations are performed to obtain fundamental frequencies of SWCNTs and DWCNTs with different values of aspect ratio and types of chirality. To derive the appropriate values of a nonlocal parameter for vibrations of SWCNTs and DWCNTs, the results of the continuum model are matched with those of MD simulations. This study shows that the small scale effects in the nonlocal model make nanotubes more flexible.