Structural Engineering and Mechanics

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Size-dependent dynamic stability of a FG polymer microbeam reinforced by graphene oxides

  • Wang, Yuewu (Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University) ;
  • Xie, Ke (Institute of Systems Engineering, China Academy of Engineering Physics) ;
  • Fu, Tairan (Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University)
  • Received : 2019.07.04
  • Accepted : 2019.11.12
  • Published : 2020.03.25
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Abstract

The dynamic stability of a functionally graded polymer microbeam reinforced by graphene oxides subjected to a periodic axial force is investigated. The microbeam is assumed to rest on an elastic substrate and is subjected to various immovable boundary restraints. The weight fraction of graphene oxides nanofillers is graded across the beam thickness. The effective Young's modulus of the functionally graded graphene oxides reinforced composite (FG-GORC) was determined using modified Halpin-Tsai model, with the mixture rule used to evaluate the effective Poisson's ratio and the mass density. An improved third order shear deformation theory (TSDT) is used in conjunction with the Chebyshev polynomial-based Ritz method to derive the Mathieu-Hill equations for dynamic stability of the FG-GORC microbeam, in which the scale effect is taken into account based on modified couple stress theory. Then, the Mathieu-Hill equation was solved using Bolotin's method to predict the principle unstable regions of the FG-GORC microbeams. The numerical results show the effects of the small scale, the graphene oxides nanofillers as well as the elastic substrate on the dynamic stability behaviors of the FG-GORC microbeams.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, NSFC, China Postdoctoral Science Foundation

This study was supported by the National Key Research and Development Program of China (No. 2016YFC0802500), the National Natural Science Foundation of China (No. 51976097), the Science Fund for Creative Research of Groups of NSFC (No. 51621062), and the China Postdoctoral Science Foundation (2018M641333). We thank Prof. D.M. Christopher for editing the English

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