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Assessment of new 2D and quasi-3D nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates

  • Bendaho, Boudjema (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Belabed, Zakaria (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Benatta, Mohamed Atif (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2019.03.12
  • Accepted : 2019.04.30
  • Published : 2019.07.25
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Abstract

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

Keywords

References

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