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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August 2011
Research Papers
Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories
S. Arghavan,
S. Arghavan
Department of Mechanical and Materials Engineering,The University of Western Ontario
,London, ON, N6A 5B9, Canada
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A. V. Singh
e-mail: avsingh@uwo.ca
A. V. Singh
Department of Mechanical and Materials Engineering,The University of Western Ontario
,London, ON, N6A 5B9, Canada
Search for other works by this author on:
S. Arghavan
Department of Mechanical and Materials Engineering,The University of Western Ontario
,London, ON, N6A 5B9, Canada
A. V. Singh
Department of Mechanical and Materials Engineering,The University of Western Ontario
,London, ON, N6A 5B9, Canada
e-mail: avsingh@uwo.ca
J. Nanotechnol. Eng. Med. Aug 2011, 2(3): 031005 (6 pages)
Published Online: January 10, 2012
Article history
Received:
April 20, 2011
Revised:
April 28, 2011
Online:
January 10, 2012
Published:
January 10, 2012
Citation
Arghavan, S., and Singh, A. V. (January 10, 2012). "Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories." ASME. J. Nanotechnol. Eng. Med. August 2011; 2(3): 031005. https://doi.org/10.1115/1.4004323
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