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Vibration of Single Layer Graphene Sheet Based on Nonlocal Elasticity and Higher Order Shear Deformation Theory

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Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for the vibration of nanoplates such as graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the size effect on the natural frequencies of graphene sheets. Effects of (i) nonlocal parameter, (ii) length (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the vibration frequencies are investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories of graphene sheets.
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Keywords: GRAPHENE SHEETS; HIGHER ORDER SHEAR DEFORMATION THEORY; NONLOCAL ELASTICITY; VIBRATION

Document Type: Research Article

Publication date: 2010-06-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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