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Wind and Structures Volume 21, Number 3, September 2015 , pages 273-287 DOI: https://doi.org/10.12989/was.2015.21.3.273 |
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Influence of the porosities on the free vibration of FGM beams |
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L. Hadji and E.A. Adda Bedia
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| Abstract | ||
| In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton\'s principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams. | ||
| Key Words | ||
| functionally graded beam; shear deformation theory; porosity; vibration | ||
| Address | ||
| L. Hadji:Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie; Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie E.A. Adda Bedia: Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie | ||