Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study

In the present work, the vibration characteristics of single- and double-walled carbon nanotubes under various layerwise boundary conditions at different lengths are investigated. This is accomplished by the use of molecular dynamics simulations based on the Tersoff-Brenner and Lennard-Jones potential energy functions. The effects of initial tensile and compressive strains on the resonant frequency of carbon nanotubes are also taken into consideration. From the results generated, it is observed that the natural frequency of carbon nanotubes is strongly dependent on their boundary conditions especially when tubes are shorter in length. The natural frequency and its dependence on tube end conditions reduce by increasing the tube length. The natural frequency of DWCNTs lies between those of the constituent inner and outer SWCNTs and is nearer to those of the outer one. It is further observed that the natural frequency is highly sensitive to tensile and compressive strains. The frequency shift occurring in the presence of small initial strains is positive for tensile strains and negative for compressive strains. The results obtained provide valuable information for calibrating the small scaling parameter of the nonlocal models for the vibration problem of carbon nanotubes.