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Research Paper

Vibration of Single- and Double-Layered Graphene Sheets

[+] Author and Article Information
Behrouz Arash

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

Quan Wang1

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canadaq_wang@umanitoba.ca

1

Corresponding author.

J. Nanotechnol. Eng. Med 2(1), 011012 (Feb 07, 2011) (7 pages) doi:10.1115/1.4003353 History: Received December 16, 2010; Revised December 20, 2010; Published February 07, 2011; Online February 07, 2011

Free vibration of single- and double-layered graphene sheets is investigated by employing nonlocal continuum theory and molecular dynamics simulations. Results show that the classical elastic model overestimated the resonant frequencies of the sheets by a percentage as high as 62%. The dependence of small-scale effects, sizes of sheets, boundary conditions, and number of layers on vibrational characteristic of single- and double-layered graphene sheets is studied. The resonant frequencies predicted by the nonlocal elastic plate theory are verified by the molecular dynamics simulations, and the nonlocal parameter is calibrated through the verification process. The simulation results reveal that the calibrated nonlocal parameter depends on boundary conditions and vibrational modes. The nonlocal plate model is found to be indispensable in vibration analysis of grapheme sheets with a length less than 8 nm on their sides.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 2

Dependence of the nonlocal parameter on the fundamental resonant frequency of square single-layered graphene sheets with CCCC boundary conditions

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Figure 3

Resonant frequencies of single-layered graphene sheets with CCCC boundary conditions

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Figure 4

Vibrational modes of single-layered graphene sheets: (a) atomistic first vibrational mode, (b) atomistic second vibrational mode, (c) continuum first vibrational mode, and (d) continuum second vibrational mode

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Figure 5

Fundamental resonant frequencies of square single- and double-layered graphene sheets with various boundary conditions

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Figure 6

Fundamental resonant frequencies of rectangular single-layered graphene sheets with CCCC boundary condition (b=2.46 nm)

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Figure 1

A single-layered graphene sheet: (a) continuum model and (b) atomistic model

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