Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes

WANG Bi-rong; DENG Zi-chen; XU Xiao-jian; WANG Yan

doi:10.3879/j.issn.1000-0887.2014.05.002

Volume 35 Issue 5

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WANG Bi-rong, DENG Zi-chen, XU Xiao-jian, WANG Yan. Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes[J]. Applied Mathematics and Mechanics, 2014, 35(5): 478-486. doi: 10.3879/j.issn.1000-0887.2014.05.002

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Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes

doi: 10.3879/j.issn.1000-0887.2014.05.002

¹Department of Engineering Mechanics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024,P.R.China

Funds: The National Basic Research Program of China(973 Program)(2011CB610300)；The National Natural Science Foundation of China(11372252；11172239)

Received Date: 2013-12-19
Rev Recd Date: 2014-02-18
Publish Date: 2014-05-15

Abstract

Abstract

The effects of nonlocal factors on the wave dispersion in the doublewalled carbon nanotube(DWCNT) were analyzed with the modified Timoshenko beam model modified based on the stress gradient theory. Coupling with Van der Waals force, the dispersion characteristics, such as phase velocity, frequency, critical frequency and amplitude ratio of outer tube to inner tube, were studied. The results show that: for a given wave number, both the first 4 modes’phase velocities and frequencies of the DWCNT decrease with rise of the nonlocal shear factor, in which no obvious linear law is found. It is notable that for the 3rd and 4th modes the amplitude ratios do not decrease with the rise of the nonlocal shear factor. Meanwhile, the nonlocal shear factor has prominent effects on the wave dispersion characteristics of the DWCNT especially at relatively higher wave numbers.
- double-walled carbon nanotubes,
- wave propagation,
- stress gradient theory,
- dispersion relation

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References(16)

References

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