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Numerical analysis for free vibration of functionally graded beams using an original HSDBT

  • Sahouane, Abdelkader (Department of Civil Engineering, Ibn Khaldoun University) ;
  • Hadji, Lazreg (Department of Mechanical Engineering, Ibn Khaldoun University) ;
  • Bourada, Mohamed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2019.03.23
  • Accepted : 2019.04.10
  • Published : 2019.07.25
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Abstract

This work presents a free vibration analysis of functionally graded beams by employing an original high order shear deformation theory (HSDBT). This theory use only three unknowns, but it satisfies the stress free boundary conditions on the top and bottom surfaces of the beam without requiring any shear correction factors. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. In order to investigate the free vibration response, the equations of motion for the dynamic analysis are determined via the Hamilton's principle. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

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References

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