Vibrational analysis of thermal oscillations of single-walled carbon nanotubes under axial strain

The first four flexural vibrational modes of single-walled carbon nanotubes (SWCNTs) of various lengths under different axial strains were studied using atomistic molecular dynamics within the framework of the Brenner interatomic potential and Fourier analysis. The simulated results are in excellent agreement with the Timoshenko beam model, which includes the effect of both rotary inertia and of shearing deformation. From the crossing points of the simulation data with the expected resonance frequencies of the unstrained tubes an upper limit for the effective SWCNT thickness is found (≤0.1 nm), with no adjustable parameters. This partially resolves Yakobson's paradox concerning scattered estimates for nanotube width.