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Structural Engineering and Mechanics
  Volume 75, Number 6, September25 2020 , pages 737-746

Free vibration analysis of functionally graded beams with variable cross-section by the differential quadrature method based on the nonlocal theory
Noureddine Elmeiche, Hichem Abbad, Ismail Mechab and Fabrice Bernard

    This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler–Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.
Key Words
    free vibration; nonuniform width; Euler-Bernoulli beam; Nonlocal theory; Differential Quadrature Method; Functionally Graded Material
Noureddine Elmeiche, Hichem Abbad: Civil Engineering and Environmental Laboratory, Sidi Bel Abbes University, BP 89, Sidi Bel Abbes 22000, Algeria
Ismail Mechab: LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria.
Fabrice Bernard: Université de Rennes, INSA de Rennes - LGCGM, 20 avenue des Buttes de Coësmes, 35708 Rennes cedex 7, France

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