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Geomechanics and Engineering Volume 9, Number 3, September 2015 , pages 361-372 DOI: https://doi.org/10.12989/gae.2015.9.3.361 |
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A refined exponential shear deformation theory for free vibration of FGM beam with porosities |
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Lazreg Hadji, T. Hassaine Daouadji and E. Adda Bedia
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| Abstract | ||
| In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. 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 | ||
| (1) Lazreg Hadji, T. Hassaine Daouadji: Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie; (2) Lazreg Hadji, T. Hassaine Daouadji, E. Adda Bedia: Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algeéie. | ||