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Title: Thermal vibration of a rectangular single-layered graphene sheet with quantum effects

The thermal vibration of a rectangular single-layered graphene sheet is investigated by using a rectangular nonlocal elastic plate model with quantum effects taken into account when the law of energy equipartition is unreliable. The relation between the temperature and the Root of Mean Squared (RMS) amplitude of vibration at any point of the rectangular single-layered graphene sheet in simply supported case is derived first from the rectangular nonlocal elastic plate model with the strain gradient of the second order taken into consideration so as to characterize the effect of microstructure of the graphene sheet. Then, the RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet simply supported on an elastic foundation is derived. The study shows that the RMS amplitude of the rectangular single-layered graphene sheet predicted from the quantum theory is lower than that predicted from the law of energy equipartition. The maximal relative difference of RMS amplitude of thermal vibration appears at the sheet corners. The microstructure of the graphene sheet has a little effect on the thermal vibrations of lower modes, but exhibits an obvious effect on the thermal vibrations of higher modes. The quantum effect is more important for the thermal vibration of highermore » modes in the case of smaller sides and lower temperature. The relative difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet decreases monotonically with an increase of temperature. The absolute difference of maximal RMS amplitude of thermal vibration of a rectangular single-layered graphene sheet increases slowly with the rising of Winkler foundation modulus.« less
Authors:
;  [1]
  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
Publication Date:
OSTI Identifier:
22303995
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 115; Journal Issue: 23; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
77 NANOSCIENCE AND NANOTECHNOLOGY; AMPLITUDES; GRAPHENE; MICROSTRUCTURE; NANOSTRUCTURES; OSCILLATIONS; STRAINS