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Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle

  • Gafour, Youcef (University Djillali Liabes- Faculty of Technology) ;
  • Hamidi, Ahmed (Civil Engineering and Hydraulic Department, Faculty Technology, University of Bechar) ;
  • Benahmed, Abdelillah (Laboratory of Modeling and Multi-Scale Simulation, Department of Physics, Faculty of Exact Science, University of Sidi Bel Abbes) ;
  • Zidour, Mohamed (University of Tiaret) ;
  • Bensattalah, Tayeb (University of Tiaret)
  • Received : 2019.03.07
  • Accepted : 2019.10.01
  • Published : 2020.01.25
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Abstract

This work focuses on the behavior of non-local shear deformation beam theory for the vibration of functionally graded (FG) nanobeams with porosities that may occur inside the functionally graded materials (FG) during their fabrication, using the non-local differential constitutive relations of Eringen. For this purpose, the developed theory accounts for the higher-order variation of transverse shear strain through the depth of the nanobeam. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is verified by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameters, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM beam are represented by numerical examples.

Keywords

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