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Research Papers

Analytical Treatment of the Free Vibration of Single-Walled Carbon Nanotubes Based on the Nonlocal Flugge Shell Theory

[+] Author and Article Information
R. Ansari1

Department of Mechanical Engineering,  University of Guilan, P.O. Box 3756, Rasht, Iranr_ansari@guilan.ac.ir

H. Rouhi

Department of Mechanical Engineering,  University of Guilan, P.O. Box 3756, Rasht, Iran

1

Corresponding author.

J. Eng. Mater. Technol 134(1), 011008 (Dec 08, 2011) (8 pages) doi:10.1115/1.4005347 History: Received February 24, 2011; Revised July 28, 2011; Published December 08, 2011; Online December 08, 2011

In the current work, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) under different boundary conditions are investigated. A nonlocal elastic shell model is utilized, which accounts for the small scale effects and encompasses its classical continuum counterpart as a particular case. The variational form of the Flugge type equations is constructed to which the analytical Rayleigh–Ritz method is applied. Comprehensive results are attained for the resonant frequencies of vibrating SWCNTs. The significance of the small size effects on the resonant frequencies of SWCNTs is shown to be dependent on the geometric parameters of nanotubes. The effectiveness of the present analytical solution is assessed by the molecular dynamics simulations as a benchmark of good accuracy. It is found that, in contrast to the chirality, the boundary conditions have a significant effect on the appropriate values of nonlocal parameter.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 3

Atomic structures of simulated (a) (8,8) armchair and (b) (14,0) zigzag CNTs

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Figure 4

Fundamental resonant frequencies from continuum shell model and MD simulation for (8,8) armchair SWCNT with SS boundary conditions

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Figure 5

Fundamental resonant frequencies from continuum shell model and MD simulation for (8,8) armchair SWCNT with CC boundary conditions

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Figure 9

Fundamental resonant frequencies from nonlocal shell model and MD simulation for (8,8) armchair SWCNTs with CC boundary conditions for different values of E and h

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Figure 10

Vibration mode shapes of a SWCNT with SS boundary conditions in the fifth circumferential mode number (R=8.5nm, L/R=5): (a) first axial mode, (b) second axial mode, (c) third axial mode, and (d) fourth axial mode.

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Figure 8

Variation of resonant frequencies with circumferential mode number for a SWCNT with SS boundary conditions (R=8.5nm, L/R=5)

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Figure 1

Schematic of a SWCNT treated as an elastic shell

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Figure 2

Schematic of SWCNTs. (a) One atomic layer at both ends is held fixed to simulate simply supported-simply supported boundary conditions. (b) Four atomic layers at both ends are held fixed to simulate clamped-clamped boundary conditions. (c) One atomic layer at one end and four atomic layers at another one are held fixed to simulate clamped-simply supported boundary conditions. (d) Four atomic layers at one end are held fixed to simulate clamped-free boundary conditions.

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Figure 6

Fundamental resonant frequencies from continuum shell model and MD simulation for (8,8) armchair SWCNT with CS boundary conditions

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Figure 7

Fundamental resonant frequencies from continuum shell model and MD simulation for (8,8) armchair SWCNT with CF boundary conditions

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