Elastic Vibration Behaviors Oof Carbon Nanotubes Based on Micropolar Mechanics
G. Q. Xie; S. Y. Long

Source CMC: Computers, Materials, & Continua, Vol. 4, No. 1, pp. 11-20, 2006
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Keywords Vibration, Carbon nanotubes, Micropolar mechanics, Hamilton's principle
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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