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August 2, 2023
Published
August 2, 2023
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Abstract

Elastic theory of graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. Levy’s approach has been employed to solve the governing differential equations for various boundary conditions. Nonlocal theories are employed to bring out the small scale effect of the nonlocal parameter on the natural frequencies of the graphene sheets. Present vibration results associated with various boundary conditions are in good agreement with those available in literature. Further, effects of (i) nonlocal parameter, (ii) size of the graphene sheets and (iii) boundary conditions on nondimensional vibration frequencies are investigated. The theoretical development as well as numerical solutions presented here in should serve as reference for nonlocal theories of nanoplates and nanoshells.

Keywords

Vibration, Graphene Sheets, Nonlocal Elasticity, Levy’s Solution, Boundary Conditions.

Article Details

How to Cite
Kumar, A., & Pradhan , S. (2023). Small Scale Effects and Vibration of Graphene Sheets with Various Boundry Conditions. Journal of Aerospace Sciences and Technologies, 64(2), 108–118. https://doi.org/10.61653/joast.v64i2.2012.419
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