Short carbon nanotubes of smaller aspect ratio (say, between 10 and 50) are finding significant application in nanotechnology. This paper studies vibration of such short carbon nanotubes whose higher-order resonant frequencies fall within terahertz range. Because rotary inertia and shear deformation are significant for higher-order modes of shorter elastic beams, the carbon nanotubes studied here are modeled as Timoshenko beams instead of classical Euler beams. Detailed results are demonstrated for double-wall carbon nanotubes of aspect ratio 10, 20, or 50 based on the Timoshenko-beam model and the Euler-beam model, respectively. Comparisons between different single-beam or double-beam models indicate that rotary inertia and shear deformation, accounted for by the Timoshenko-beam model, have a substantial effect on higher-order resonant frequencies and modes of double-wall carbon nanotubes of small aspect ratio (between 10 and 20). In particular, Timoshenoko-beam effects are significant for both large-diameter and small-diameter double-wall carbon nanotubes, while double-beam effects characterized by noncoaxial deflections of the inner and outer tubes are more significant for small-diameter than large-diameter double-wall carbon nanotubes. This suggests that the Timoshenko-beam model, rather than the Euler-beam model, is relevant for terahertz vibration of short carbon nanotubes.
Terahertz Vibration of Short Carbon Nanotubes Modeled as Timoshenko Beams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, April 16, 2003; final revision; May 15, 2004. Associate Editor: A. A. Ferri. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Yoon , J., Ru, C. Q., and Mioduchowski, A. (February 1, 2005). "Terahertz Vibration of Short Carbon Nanotubes Modeled as Timoshenko Beams ." ASME. J. Appl. Mech. January 2005; 72(1): 10–17. https://doi.org/10.1115/1.1795814
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