Research Papers

Energy Loss in Carbon Nanotube Beam Oscillators due to Anelastic Relaxation

[+] Author and Article Information
Zhong Zhou, Vijay K. Vasudevan

Mechanical Engineering Program, School of Dynamic Systems,  University of Cincinnati, Cincinnati, OH 45221-0072

Dong Qian1

Mechanical Engineering Program, School of Dynamic Systems,  University of Cincinnati, Cincinnati, OH 45221-0072dong.qian@uc.edu


Corresponding author.

J. Eng. Mater. Technol 134(3), 031005 (May 07, 2012) (8 pages) doi:10.1115/1.4006506 History: Received September 26, 2011; Revised December 23, 2011; Published May 04, 2012; Online May 07, 2012

We present a semi-analytical approach to study the energy dissipation in carbon nanotube (CNT) beam oscillators under gigahertz excitation. The energy dissipation properties are quantified by the quality factor (Q factor) and associated anelastic properties. Our study reveals that the Q factor is related to the tube radius through an inverse relation for both single walled CNTs (SWCNTs) and multiwalled CNTs (MWCNTs) beam oscillators. At frequency close to the resonance range, significant energy dissipation is observed due to the activation of phonon modes that serve as a major mechanism for energy dissipation in SWCNTs. For MWCNTs, a registration dependent potential (RDP) is introduced to study the effect of intertube registration. Interlayer friction arising from the π bond overlap is shown to contribute significantly to the additional energy dissipation. Based on the extensive simulation studies, an analytical formula for estimating the Q factors of MWCNTs is proposed. Validation of the analytical prediction with the available experimental data yields a good agreement and quantifies the roles of different factors contributing to the energy dissipation through anelastic relaxation.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Schematic showing a cantilevered CNT beam under dynamic bending

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Figure 2

Comparison between RDP and LJ. (a) The interlayer energy difference between AA and AB stacking of graphite as a function of interlayer distance. (b) The interlayer energy corrugation against parallel sliding for two graphene sheets 3.34 Å apart.

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Figure 3

Definition of the transverse distances between two carbon atoms and parameters used in the RDP model

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Figure 4

Force and displacement of a (10, 10) SWCNT, from dynamic bending at F0=0.16nN and f=ω/2π=7.96GHz

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Figure 5

Complex bending moduli of cantilevered CNTs with different outer radius: (a) storage modulus and (b) loss modulus

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Figure 6

The quality factor Q versus outer radius dependence for SW-, DW-, and TWCNTs

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Figure 7

Comparison of Q factor of CNTs with different number of tube walls

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Figure 8

Q factor of DWCNT (5, 5)/(10, 10) with different length to diameter ratio

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Figure 9

Complex bending moduli of cantilevered CNTs under different loading frequencies: (a) storage modulus and (b) loss modulus

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Figure 10

The quality factor Q versus frequency dependence for SW- and DWCNTs




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