Thermal buckling of double-walled carbon nanotubes

The thermal buckling of an armchair double-walled carbon nanotube (DWCNT), which is subjected to axial compression due to temperature rise, is derived and analyzed based on Timoshenko beam model, including transverse shear deformation and rotary inertia. According to the analysis, the effect of van der Waals force between the nanotubes on the critical buckling temperature of mode 1 of armchair DWCNT is significant, especially for smaller diameter nanotubes. The van der Waals force makes the DWCNT stiffer and increases the buckling temperature. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The critical buckling temperature ratio of a Timoshenko beam to a Euler beam for the armchair DWCNT significantly decreases with increasing the diameter and mode number. Therefore, for the higher-order modes, the Timoshenko beam model is able to predict the critical buckling temperature of larger diameter DWCNT.