Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
825328 | International Journal of Engineering Science | 2011 | 14 Pages |
Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e0), (ii) e0 is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e0 is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e0 in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit.