期刊
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
卷 49, 期 6, 页码 509-522出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2011.01.002
关键词
Single walled carbon nanotube; Wavenumber; Nonlocal elasticity; Molecular mechanics; Nonlocal small scale parameter
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 (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) 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. (C) 2011 Elsevier Ltd. All rights reserved.
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