The vibration behavior of double-walled carbon nanotube (DWCNT) is investigated based on Donnell shell theory with van der Waals interaction taken into consideration. In addition, new results are obtained for the natural frequencies of a DWCNT based on a simplified version of Donnell shell theory by neglecting the tangential inertia terms. The resulting reduced characteristic equation for the natural frequency represents the radial mode of vibration. The factor of neglecting tangential inertia relative to the values of frequencies obtained by full Donnell shell theory is also obtained with attendant interesting results. Further possible simplifications of Donnell shell theory are introduced. For the first time in the literature, the effect of neglect of tangential inertia terms in DWCNTs is investigated. Accurate approximate analytical formulas are uncovered for the fundamental natural frequencies and compared with the exact values.
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e-mail: demetris.pentaras@cut.ac.cy
e-mail: elishako@fau.edu
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Effective Approximations for Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory
Demetris Pentaras,
Demetris Pentaras
Department of Mechanical Engineering and Materials Science and Engineering,
e-mail: demetris.pentaras@cut.ac.cy
Cyprus University of Technology
, 3041 Limassol, Cyprus; Department of Ocean and Mechanical Engineering, Florida Atlantic University
, Boca Raton, FL 33431-0991
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Isaac Elishakoff
Isaac Elishakoff
Department of Ocean and Mechanical Engineering,
e-mail: elishako@fau.edu
Florida Atlantic University
, Boca Raton, FL 33431-0991
Search for other works by this author on:
Demetris Pentaras
Department of Mechanical Engineering and Materials Science and Engineering,
Cyprus University of Technology
, 3041 Limassol, Cyprus; Department of Ocean and Mechanical Engineering, Florida Atlantic University
, Boca Raton, FL 33431-0991e-mail: demetris.pentaras@cut.ac.cy
Isaac Elishakoff
Department of Ocean and Mechanical Engineering,
Florida Atlantic University
, Boca Raton, FL 33431-0991e-mail: elishako@fau.edu
J. Nanotechnol. Eng. Med. May 2011, 2(2): 021013 (4 pages)
Published Online: May 17, 2011
Article history
Received:
December 22, 2010
Revised:
February 3, 2011
Online:
May 17, 2011
Published:
May 17, 2011
Citation
Pentaras, D., and Elishakoff, I. (May 17, 2011). "Effective Approximations for Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory." ASME. J. Nanotechnol. Eng. Med. May 2011; 2(2): 021013. https://doi.org/10.1115/1.4003601
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