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An analytical method for free vibration analysis of functionally graded sandwich beams

  • Bouakkaz, K. (Departement de Genie Civil, Universite Ibn Khaldoun) ;
  • Hadji, L. (Departement de Genie Civil, Universite Ibn Khaldoun) ;
  • Zouatnia, N. (Laboratoire de Structures, Geotechnique et Risques, Departement de Genie Civil, Universite de Chlef) ;
  • Adda Bedia, E.A. (Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes)
  • Received : 2016.03.10
  • Accepted : 2016.05.26
  • Published : 2016.07.25
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Abstract

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

Keywords

References

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  1. Modeling and analysis of functionally graded sandwich beams: A review pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1447178
  2. Free Vibration Analysis of a Functionally Graded Material Coated Aluminum Beam vol.58, pp.2, 2016, https://doi.org/10.2514/1.j059002