Nonlocal elasticity theory for free vibration of single-walled carbon nanotubes
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Publication Details
Author list: Thongyothee C., Chucheepsakul S., Li T.
Publisher: Trans Tech Publications
Publication year: 2013
Volume number: 747
Start page: 257
End page: 260
Number of pages: 4
ISBN: 9783037857717
ISSN: 1022-6680
eISSN: 1662-8985
Languages: English-Great Britain (EN-GB)
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Abstract
This paper concerns with free vibration analysis of single-walled carbon nanotubes including the effect of small length scale based on the nonlocal elasticity theory. The governing equation of nanotube is derived from Euler beam theory including a nonlocal parameter in the function of masses. Classical solutions are obtained and then compared with the numerical solutions provided by finite element models. Effect of tube chirality and various geometrically boundary conditions are considered. The finite element models of nanotubes are assumed as the virtually analogous frame structures. In the numerical technique, the atomic masses existing on the both ends of beams are assigned by physical and chemical properties of carbon element. The results show that the natural frequencies significantly increase when the nonlocal parameters decrease. The numerical results are in good agreement with the classical solutions for the nanotubes with low aspect ratios and are acceptable for high aspect ratios. Furthermore, the first-ten mode shapes are demonstrated for various aspect ratios and boundary conditions, and the repeated natural frequencies are also highlighted in this study. ฉ (2013) Trans Tech Publications, Switzerland.
Keywords
Finite element model, Free vibration, Mode shape, Single-walled carbon nanotubes
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