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Research Papers

Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

[+] Author and Article Information
R. Ansari

e-mail: r_ansari@guilan.ac.ir

S. Ajori

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

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received December 5, 2011; final manuscript received February 20, 2013; published online June 18, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 135(5), 051016 (Jun 18, 2013) (6 pages) Paper No: VIB-11-1293; doi: 10.1115/1.4024208 History: Received December 05, 2011; Revised February 20, 2013

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

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Figures

Grahic Jump Location
Fig. 1

Schematic view of an armchair SWCNT with C-F boundary conditions (a) before torsional deformation and (b) after torsional deformation

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Fig. 2

Effect of aspect ratio on the torsional vibrations of a C-C (6, 6) SWCNT for different dimensionless length scale parameters l/h

Grahic Jump Location
Fig. 3

Comparison of torsional vibration frequencies from the strain gradient model for C-C and C-F (6,6) SWCNTs with those of MD simulations (l/h = 0.43)

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