Buy article PDF
The purchased file will be sent to you
via email after the payment is completed.
US$ 35
|
Structural Engineering and Mechanics Volume 75, Number 6, September25 2020 , pages 737-746 DOI: https://doi.org/10.12989/sem.2020.75.6.737 |
|
|
|
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
|
||
| Abstract | ||
| 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 | ||
| Address | ||
| 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 | ||