Application of nonlocal beam models for carbon nanotubes

Abstract

Investigations of wave and vibration properties of single-or multi-walled carbon nanotubes based on nonlocal beam models have been reported recently. However, there are numerous inconsistencies in the handling of the governing equations, applied forces, and boundary conditions based on some of the reported nonlocal beam models. In this paper, the consistent equations of motion for the nonlocal Euler and Timoshenko beam models are provided, and some issues on the nonlocal beam theories are discussed. The models are then applied to the studies of wave properties of single-and double-walled nanotubes. The wave and vibration properties of the nanotubes based on the presented nonlocal beam equations are studied, and scale effects are discussed.

Vibration of Single-Walled Carbon Nanotubes by Using Nonlocal Theory

“…Carbon nanotubes and underlying research are connected with Iijima and his famous paper [7]. Carbon nanotubes are closed graphene sheets of cylindrical shape with interesting mechanical properties.…”

Wave propagation in carbon nanotubes: nonlocal elasticity-induced stiffness and velocity enhancement effects

“…With such consideration, the nonlocal forces at long-range between molecules and lattice lead to the nonlocal stress-strain equation with higherorder strain gradients. Because of its simplicity and superiority, the analysis of wave propagation in CNTs using the nonlocal stress approach was recently reported [Wang and Hu 2005;Wang et al 2006c;Lu et al 2007;Heireche et al 2008;. In particular, [Lu et al 2007] derived the equation of motion for a nonlocal Timoshenko beam to investigate the wave propagation characteristics in single-walled and double-walled CNTs.…”

“…Because of its simplicity and superiority, the analysis of wave propagation in CNTs using the nonlocal stress approach was recently reported [Wang and Hu 2005;Wang et al 2006c;Lu et al 2007;Heireche et al 2008;. In particular, [Lu et al 2007] derived the equation of motion for a nonlocal Timoshenko beam to investigate the wave propagation characteristics in single-walled and double-walled CNTs. Other nonlocal shell models were also employed for further research in a number of studies Wang et al 2006b;Wang and Varadan 2007;Xie et al 2007a;Xie et al 2007b;.…”

Virus sensor based on single-walled carbon nanotube: improved theory incorporating surface effects

“…Note that the model of Lu et al [6] or Lu et al [7] is valid for a surface elasticity loading modelled as a conservative loading. The reader is referred also to the recent study of Challamel & Elishakoff [12] for a discussion on conservative versus non-conservative modelling of surface elasticity effects.…”