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Earthquakes and Structures Volume 13, Number 3, September 2017 , pages 255-265 DOI: https://doi.org/10.12989/eas.2017.13.3.255 |
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An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities |
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Mourad Benadouda, Hassen Ait Atmane, Abdelouahed Tounsi, Fabrice Bernard and S.R Mahmoud
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| Abstract | ||
| In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton\'s principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam. | ||
| Key Words | ||
| wave propagation; functionally graded beam; porosity; higher-order shear deformation beam theories | ||
| Address | ||
| Mourad Benadouda and Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Hassen Ait Atmane: 1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Département de genie civil, Faculté de genie civil et d\' architecture, Univesite Hassiba Benbouali de Chlef, Algerie Fabrice Bernard: INSA Rennes, Rennes, France S.R Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia | ||