Smart Structures and Systems

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On bending, buckling and vibration of graphene nanosheets based on the nonlocal theory

  • Liu, Jinjian (School of Urban Rail Transportation, Soochow University) ;
  • Chen, Ling (School of Urban Rail Transportation, Soochow University) ;
  • Xie, Feng (School of Urban Rail Transportation, Soochow University) ;
  • Fan, Xueliang (School of Urban Rail Transportation, Soochow University) ;
  • Li, Cheng (School of Urban Rail Transportation, Soochow University)
  • Received : 2015.07.06
  • Accepted : 2015.12.08
  • Published : 2016.02.25
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Abstract

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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