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Wind and Structures
  Volume 25, Number 4, October 2017 , pages 329-342

An analytical solution for bending and vibration responses of functionally graded beams with porosities
Nafissa Zouatnia, Lazreg Hadji and Amar Kassou

    This work presents a static and free vibration analysis of functionally graded metal–ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. A new displacement field containing integrals is proposed which involves only three variables. Based on the suggested theory, the equations of motion are derived from Hamilton\'s principle. This theory involves only three unknown functions and accounts for parabolic distribution of transverse shear stress. In addition, the transverse shear stresses are vanished at the top and bottom surfaces of the beam. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the deflections, stresses and natural frequencies on the bending and free vibration responses of functionally graded beams.
Key Words
    bending, Free vibration; Functionally graded materials; integral; Hamilton
Nafissa Zouatnia and Amar Kassou: Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef, Algeria, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria
Lazreg Hadji : Département of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, Tiaret (14000), Algeria;
Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria

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