Intrinsic vibration of multiwalled carbon nanotubes

This work aims to study intertube mechanical vibration of a freestanding or elastically constrained multiwall carbon nanotube. New intertube resonant frequencies and the non-coaxial vibrational modes are calculated. The first few intertube resonant frequencies are found to fall into a very narrow range and be insensitive to the intertube resonant modes, the length of multiwall nanotubes, and the end conditions. In particular, for a shorter or long but periodically supported multiwall carbon nanotube, the first few intertube resonant frequencies predicted by the present model are comparable to the first few natural frequencies given by the widely used elastic beam model. Although the intertube resonance, first studied in this work, would not substantially affect overall deflection of a multiwall carbon nanotube, it will inevitably cause internal non-concentric distortion and thus significantly affect some important physical (such as electronic and optical) properties of multiwall carbon nanotubes.