Free vibrations of a double-walled carbon nanotube (DWNT) are studied. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting each other by van der Waals forces. An original method is proposed to calculate the first seven order resonant frequencies and relative vibrational modes. Detailed results are demonstrated for DWNTs according to the different boundary conditions between inner and outer tubes, such as fixed-free, cantilever-free, fixed-simple and fixed-fixed (reduced form) supported ends. Our results indicate that there is a special invariable frequency for a DWNT that is not affected by different combinations of boundary conditions. All vibrational modes of the DWNT must be coaxial when the resonant frequency is smaller than this frequency. Some noncoaxial vibrations will occur when their resonant frequencies exceed the frequency. Especially, the first noncoaxial resonant frequency is still invariable for all different boundary conditions. A change of resonant frequency for various lengths of DWNTs is discussed in detail. In addition, our model predicts a new coaxial-noncoaxial vibrational mode in fixed-simple supports for inner and outer tubes of a DWNT.
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March 2008
Research Papers
Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions Between Inner and Outer Tubes
Kai-Yu Xu,
Kai-Yu Xu
Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics,
e-mail: kyxu@staff.shu.edu.cn.
Shanghai University
, 99 Shangda Road, Shanghai 200444, China; College of Engineering, Michigan Technological University
, 1400 Townsend Drive, Houghton, MI 49931
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Elias C. Aifantis,
Elias C. Aifantis
College of Engineering,
Michigan Technological University
, 1400 Townsend Drive, Houghton, MI 49931
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Yong-Hua Yan
Yong-Hua Yan
Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University
, 99 Shangda Road, Shanghai 200444, China
Search for other works by this author on:
Kai-Yu Xu
Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University
, 99 Shangda Road, Shanghai 200444, China; College of Engineering, Michigan Technological University
, 1400 Townsend Drive, Houghton, MI 49931e-mail: kyxu@staff.shu.edu.cn.
Elias C. Aifantis
College of Engineering,
Michigan Technological University
, 1400 Townsend Drive, Houghton, MI 49931
Yong-Hua Yan
Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University
, 99 Shangda Road, Shanghai 200444, ChinaJ. Appl. Mech. Mar 2008, 75(2): 021013 (9 pages)
Published Online: February 26, 2008
Article history
Received:
August 3, 2006
Revised:
May 31, 2007
Published:
February 26, 2008
Citation
Xu, K., Aifantis, E. C., and Yan, Y. (February 26, 2008). "Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions Between Inner and Outer Tubes." ASME. J. Appl. Mech. March 2008; 75(2): 021013. https://doi.org/10.1115/1.2793133
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