Simulation of in Plane and Lateral Vibration of a Graphene Plate, Based on the Clasic Plate Theory and the most General form of Strain Gradient Theory and Deriving the Constitutive Law Parameters from Molecular Mechanic Parameters

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Hassanpour, Saba | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47927 (45)
University: Sharif University of Technology
Department: Aerospace Engineering
Advisor(s): Dehghani Firouzabadi, Rohollah
Abstract:
Here the differential equations of a Graphene sheet deformation is determined by making use of the most general form of first Strain Gradient Elasticity (SGE) theory. In order to derive the equations of in-plane and out-of-plane deformations, the matrix representation of Strain Gradient constitutive law is used. Vibration of the nano-plate is studied by modeling the plate based on Kirchhoff theory and application of variation of energy, therefor the in-plane and out-of-plane vibration of the nano-plate is found through Navier analytical solution. After all natural frequencies are obtained based on SGE parameters. SGE parameters are determined by calculating the potential of a representative volume element (RVE) of an armchair graphene sheet, based on CHARMM potential force field constants. At last the mechanical properties and natural frequencies of in-plane vibration of the graphene is compared to that of the classic plate, and the results show that graphene is stiffer when including the SGE parameters
Keywords:
Graphene ; Strain Gradient Theory ; Molecular Mechanics ; Nanoplate ; Out of Plane Vibration ; In-Plane Vibration

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