Wave-like deformations for oscillating carbon nanotubes

Carbon nanostructures such as nanotubes and fullerenes, represent future materials because of their remarkable mechanical, electrical and thermal properties. Double-walled carbon nanotubes are widely studied as possible gigahertz oscillators, where the inner tube oscillates within the outer tube. These oscillators are believed to generate frequencies in the gigahertz range and typically of the order of 1–74 GHz. They are also known to generate wave-like formations on the outer surface. In this paper, we study such induced deformations on the surface of the outer tube, as generated by the moving inner tube. Following previous authors we assume that double-walled carbon nanotubes can be modelled as transversely isotropic linearly elastic materials. Using a previously derived approximate force distribution for the resultant van der Waals forces arising from the interatomic interactions, we solve a dynamic linearly elastic problem, and show that the resulting solution exhibits wave-like behaviour.