Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory

Abdelkader Safa, Lazreg Hadji, Mohamed Bourada and Nafissa Zouatnia

Abstract

An efficient shear deformation beam theory is developed for thermo-elastic vibration of FGM beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the on the surfaces of the beam without using shear correction factors. The material properties of the FGM beam are assumed to be temperature dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity are considered through the beam thickness. Based on the present refined beam theory, the equations of motion are derived from Hamilton\'s principle. The closed-form solutions of functionally graded beams are obtained using Navier solution. Numerical results are presented to investigate the effects of temperature distributions, material parameters, thermal moments and slenderness ratios on the natural frequencies. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Key Words

thermo-elastic vibration; functionally graded materials; Hamilton

Address

Abdelkader Safa: 1Department of Civil Engineering, Ahmed Zabana University Centre, Relizane, 48000, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Sidi Bel Abbes, Algeria Lazreg Hadji: Department of Mechanical Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000, Tiaret, Algeria; Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria Mohamed Bourada: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Sidi Bel Abbes, Algeria Nafissa Zouatnia: Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, Tiaret, 14000, Algeria

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