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Research Papers

Effective Approximations for Natural Frequencies of Double-Walled Carbon Nanotubes Based on Donnell Shell Theory

[+] Author and Article Information
Demetris Pentaras1

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 33431-0991demetris.pentaras@cut.ac.cy

Isaac Elishakoff

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991elishako@fau.edu

1

Corresponding author.

J. Nanotechnol. Eng. Med 2(2), 021013 (May 17, 2011) (4 pages) doi:10.1115/1.4003601 History: Received December 22, 2010; Revised February 03, 2011; Published May 17, 2011; Online May 17, 2011

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.

Copyright © 2011 by American Society of Mechanical Engineers
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