Effects of changing materials properties for vibration of FGM beam using integral shear deformation model

Mokhtar Ellali , Mashhour A. Alazwari , Mokhtar Bouazza , Mohamed A. Eltaher , Noureddine Benseddiq

Abstract

The objective of this work is to study the effects of the modification of material properties on the vibration of the FGM beam using an integral shear strain model. In the present theory, the rotational displacement is replaced by an integral term in the displacement fields. The use of a shear correction factor is not necessary because our model gives a parabolic description of shear stress through the thickness while satisfying the conditions of zero shear stresses on the bottom and top surfaces of the beam. The FGM beam is assumed that the beam is a mixture of metal and ceramic, and that its properties change depending on the power functions of the thickness of the beam such as: linear, quadratic, cubic and inverse quadratic. By applying Hamilton's principle, general formulas were obtained to obtain the frequencies of the FGM beam. The effects of changing compositional characteristics of materials presented by volume fraction of FGM beams with simply supported edges on free vibration and some mode shapes are investigated.

Key Words

effects of changing materials properties; FGM beam; integral shear deformation model; vibration

Address

Mokhtar Ellali — Smart Structures Laboratory, University of Ain Témouchent-Belhadj Bouchaib,46000, Algeria
Mashhour A. Alazwari — Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
Mokhtar Bouazza — Department of Civil Engineering, University Tahri Mohammed of Bechar, Bechar 08000, Algeria; Laboratory of Materials and Hydrology (LMH), University of Sidi Bel Abbes, Sidi Bel Abbes 2200, Algeria
Mohamed A. Eltaher — Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt; Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
Noureddine Benseddiq — Mechanics Laboratory of Lille, CNRS UMR 8107, University of Lille 1, 59655 Villeneuve d

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