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Published in

World Scientific Publishing, International Journal of Computational Methods, 04(08), p. 879-890, 2011

DOI: 10.1142/s0219876211002873

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Free Vibration Analysis of Double-Walled Carbon Nanotubes Using the Smoothed Finite Element Method

Journal article published in 2011 by Lifeng Wang ORCID, Dong Han, G. R. Liu, Xiangyang Cui
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

This paper studies the resonant frequencies and the associated vibration modes of an individual double-walled carbon nanotube, using gradient smoothing technique. The study uses a double-elastic beam based on the Euler beam theory with the consideration of the intertube van der Waals interactions. A gradient smoothed formulation is deployed to deal with the fourth-order differential equation of the Euler beam problems for dynamic analysis of the double-walled carbon nanotubes. In the double-thin beam problems, a set of linear shape functions are adopted to approximate the displacement field. Smoothing domains are then formed for computing the smoothed curvature and bending moment field. Compared with analysis results of multi-beam theory, numerical examples indicate that very accurate results could be yielded when a reasonable number of nodes were used. The results also showed that non-coaxial intertube resonance would be excited at the higher resonant frequencies of double-walled carbon nanotubes. In addition, free vibration of a double-walled carbon nanotube with inner wall simple supported and outer wall one end fixed and the other end free is studied.