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Steel and Composite Structures
  Volume 16, Number 5, May 2014 , pages 507-519

A higher order shear deformation theory for static and free vibration of FGM beam
L. Hadji, T.H. Daouadji, A. Tounsi and E.A. Bedia

    In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded 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 beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.
Key Words
    mechanical properties; vibration; strength; deformation; modeling
(1) L. Hadji, T.H. Daouadji:
Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie;
(2) A. Tounsi, E.A. Bedia:
Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algérie.

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