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Research Papers

Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories

[+] Author and Article Information
S. Arghavan

 Department of Mechanical and Materials Engineering,The University of Western Ontario,London, ON, N6A 5B9, Canada

A. V. Singh1

 Department of Mechanical and Materials Engineering,The University of Western Ontario,London, ON, N6A 5B9, Canadaavsingh@uwo.ca

1

Corresponding author.

J. Nanotechnol. Eng. Med 2(3), 031005 (Jan 10, 2012) (6 pages) doi:10.1115/1.4004323 History: Received April 20, 2011; Revised April 28, 2011; Published January 10, 2012; Online January 10, 2012

Prospect of applications of graphene sheets in composites and other advanced materials have drawn attention from a broad spectrum of research fields. This paper deals with the methods to find mechanical properties of such nanoscale structures. First, the lattice structure method with the Poisson’s ratio of 0.16 and the thickness of 3.4 Å is used to obtain the Young’s moduli for the in-plane and out-of-plane deformation states. This method has the accuracy of molecular dynamics simulations and efficiency of the finite element method. The graphene sheet is modeled as a plane grid of carbon atoms taken as the nodal points, each of which carries the mass of the carbon atom and is assigned as a six degrees of freedom. The covalent bond between two adjacent carbon atoms is treated as an extremely stiff frame element with all three axial, bending, and torsional stiffness components. Subsequently, the computed Young’s moduli, approximately 0.11 TPa for bending and 1.04 TPa for the in-plane condition, are used for studying the vibrational behaviors of graphene sheets by the continuum plate theory. The natural frequencies and corresponding mode shapes of various shaped single layer graphene sheet ), such as rectangular, skewed, and circular, are computed by the two methods which are found to yield very close results. Results of the well-established continuum plate theory are very consistent with the lattice structure method, which is based on accurate interatomic forces.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometry of a graphene sheet

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Figure 2

In-plane Young’s modulus of elasticity for different sizes of rectangular SLGSs

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Figure 3

Young’s modulus of elasticity of bending modes for different sizes of rectangular SLGSs

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Figure 4

Density of different sizes of rectangular SLGSs based on number of carbon atoms

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Figure 5

In-plane natural frequencies of 30 deg skewed SLGSs, all edges are clamped

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Figure 6

In-plane natural frequencies of 60 deg skewed SLGSs, all edges are clamped

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Figure 7

In-plane natural frequencies of 90 deg skewed (rectangular) SLGSs, all edges are clamped

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Figure 8

Out-of-plane natural frequencies of 30 deg skewed SLGSs, all edges are clamped

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Figure 9

Out-of-plane natural frequencies of 60 deg skewed SLGSs, all edges are clamped

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Figure 10

Out-of-plane natural frequencies of 90 deg skewed (rectangular) SLGSs, all edges are clamped

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Figure 11

In-plane natural frequencies of clamped edge circular SLGSs

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Figure 12

Out-of-plane natural frequencies of clamped edge circular SLGSs

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Figure 13

First six in-plane mode shapes of a clamped edge circular SLGS

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Figure 14

First six out-of-plane mode shapes of a clamped edge circular SLGS

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