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Wind and Structures Volume 23, Number 1, July 2016 , pages 59-73 DOI: https://doi.org/10.12989/was.2016.23.1.059 |
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An analytical method for free vibration analysis of functionally graded sandwich beams |
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K. Bouakkaz, L. Hadji, N. Zouatnia and E.A. Adda Bedia
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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. | ||
| Key Words | ||
| functionally graded material; sandwich beam; hamilton\'s principle; vibration | ||
| Address | ||
| K. Bouakkaz and L. Hadji: Département de Génie Civil, Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie; Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie N. Zouatnia: Laboratoire de Structures, Géotechnique et Risques, Département de Génie Civil, Université de Chlef, Algérie E.A. Adda Bedia: Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie | ||