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Research Papers

# Oscillation of C60 Fullerene in Carbon Nanotube Bundles

[+] Author and Article Information
R. Ansari

e-mail: r_ansari@guilan.ac.ir

A. Alipour

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 September 15, 2011; final manuscript received February 20, 2013; published online June 18, 2013. Assoc. Editor: Wei-Hsin Liao.

J. Vib. Acoust 135(5), 051009 (Jun 18, 2013) (10 pages) Paper No: VIB-11-1208; doi: 10.1115/1.4024377 History: Received September 15, 2011; Revised February 20, 2013

## Abstract

This paper aims to present a thorough investigation into the mechanics of a $C60$ fullerene oscillating within the center of a carbon nanotube bundle. To model this nanoscale oscillator, a continuum approximation is used along with a classical Lennard–Jones potential function. Accordingly, new semianalytical expressions are given in terms of single integrals to evaluate van der Waals potential energy and interaction force between the two nanostructures. Neglecting the frictional effects and using the actual van der Waals force distribution, the equation of motion is directly solved. Furthermore, a new semianalytical formula is derived from the energy equation to determine the precise oscillation frequency. This new frequency formula has the advantage of incorporating the effects of initial conditions and geometrical parameters. This enables us to conduct a comprehensive study of the effects of significant system parameters on the oscillatory behavior. Based upon this study, the variation of oscillation frequency with geometrical parameters (length of tubes or number of tubes in bundle) and initial energy (potential energy plus kinetic energy) is shown.

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## Figures

Fig. 1

Geometry of a C60-CNT bundle oscillator: (a) continuum model and (b) discrete model

Fig. 2

Distributions of (a) vdW interaction force and (b) potential energy for different numbers of tubes in the bundle (L = 100A°)

Fig. 3

Distributions of (a) vdW interaction force and (b) potential energy for different ranges of the tubes length (N = 6)

Fig. 4

Variation of minimum potential energy with half length of CNT bundle corresponding to different numbers of tubes in the bundle

Fig. 5

Variation of (a) separation distance and (b) velocity with time (N = 6,L = 100A°)

Fig. 6

Variation of initial separation distance with initial velocity corresponding to different initial energies (N = 6,L = 100A°)

Fig. 7

Variation of (a) vdW interaction force and (b) separation distance with time using continuum and discrete models (N = 4,L = 22.5A°,El = -0.1989  eV)

Fig. 8

Variation of frequency with initial energy corresponding to different lengths of tubes in the bundle (N = 6)

Fig. 9

Variation of (a) critical initial separation distance and (b) maximum frequency with the half length of tubes in the bundle (N = 6)

Fig. 10

Variation of maximum velocity with the amplitude of motion corresponding to various lengths of tubes in the bundle (N = 6)

Fig. 11

Comparison between the oscillation frequency of the present model corresponding to different initial potential energies and one given in [36] (N = 6)

Fig. 12

Variation of oscillation frequency with initial energy corresponding to different numbers of tubes in the bundle (L = 100A°)

Fig. 13

Variation of maximum velocity with the motion amplitude for different numbers of tubes in the bundle (L = 100A°)

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