Open Access

ARTICLE

Elastic Vibration Behaviors Oof Carbon Nanotubes Based on Micropolar Mechanics

G. Q. Xie^1,2, S. Y. Long^1,3

1 Department of Engineering Mechanics, Hunan University, Changsha 410082, P.R. China
2 The Key Laboratory of Advanced Technology for Vehicle Body Design & Manufacture of Ministry of Education, Hunan University, Changsha 410082, P.R. China
3 Corresponding author

Computers, Materials & Continua 2006, 4(1), 11-20. https://doi.org/10.3970/cmc.2006.004.011

Abstract

The concept of the micropolar theory is employed to investigate vibration behaviors of carbon nanotubes. The constitutive relation has been deduced from the two-dimensional analysis of the microstructure of the carbon nanotube. Van der Waals interactions are simulated by a weak spring model. Hamilton's principle is employed to obtain dynamics equations of the multi-walled carbon nanotube. Numerical examples for both single-walled and double-walled carbon nanotubes are presented and the significant difference in vibration behaviors between them has been distinguished. Numerical results show that fundamental frequencies for the cantilever single-walled carbon nanotube decreases with increase of the aspect ratio of them, and the fundamental frequencies of the double-walled carbon nanotube are lower than those of the single-walled carbon nanotube with the same inner diameter and length. The first four natural frequencies for the double-walled carbon are coaxial.

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Keywords

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