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Research Papers

# On New Aspects of Nested Carbon Nanotubes as Gigahertz Oscillators

[+] Author and Article Information
R. Ansari1

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

B. Motevalli

Department of Mechanical Engineering, University of Guilan, 3756 Rasht, Iran

1

Corresponding author.

J. Vib. Acoust 133(5), 051003 (Jul 26, 2011) (10 pages) doi:10.1115/1.4003933 History: Received November 07, 2009; Revised March 28, 2011; Published July 26, 2011; Online July 26, 2011

## Abstract

Nested carbon nanotubes exhibit telescopic oscillatory motion with frequencies in the gigahertz range. In this paper, our previously proposed semi-analytical expression for the interaction force between two concentric carbon nanotubes is used to solve the equation of motion. That expression also enables a new semi-analytical expression for the precise evaluation of oscillation frequency to be introduced. Alternatively, an algebraic frequency formula derived based on the simplifying assumption of constant van der Waals force is also given. Based on the given formulas, a thorough study on different aspects of operating frequencies under various system parameters is conducted, which permits fresh insight into the problem. Some notable improvements over the previously drawn conclusions are made. The strong dependence of oscillatory frequency on system parameters including the extrusion distance and initial velocity of the core as initial conditions for the motion is shown. Interestingly, our results indicate that there is a special initial velocity at which oscillatory frequency is unique for any arbitrary length of the core. A particular relationship between the escape velocity (the minimum initial velocity beyond which the core will leave the outer nanotube) and this specific initial velocity is also revealed.

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## Figures

Figure 1

Time history of separation distance and velocity of the core (L2=L1=50 Å, RC=3.39 Å,RO=6.784 Å)

Figure 2

Comparison of the vdW interaction force obtained by Eq. 7 with and without nondominant terms (L2=L1=60 Å, RC=1.957 Å, RO=5.423 Å)

Figure 3

A schematic diagram of potential energy

Figure 4

Variations of potential energy with the half length and radius of the core (L2=100 Å)

Figure 5

Comparison of frequency-amplitude curves associated with actual and constant vdW models

Figure 6

Variations of oscillatory frequency with (a) extrusion length and (b) initial velocity, for different length ratios

Figure 7

Representation of amplitudes for similar extrusion length and different lengths of the core

Figure 8

Variation of oscillatory frequency with amplitude for different length ratios

Figure 9

Variation of maximum frequency with amplitude for various length ratios (L2=500 Å, RC=1.957 Å, RO=5.423 Å)

Figure 10

Representation of maximum extension configuration

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