An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory

Latifa Ould Larbi , Lazreg Hadji , Mohamed Ait Amar Meziane , E.A. Adda Bedia

Abstract

In this paper, a simple first-order shear deformation theory is presented for dynamic behavior of functionally graded beams. Unlike the existing first-order shear deformation theory, the present one contains only three unknowns and has strong similarities with the classical beam theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. Equations of motion and boundary conditions are derived from Hamilton\' s s principle. Analytical solutions of simply supported FG beam are obtained and the results are compared with Euler-Bernoulli beam and the other shear deformation beam theory results. Comparison studies show that this new first-order shear deformation theory can achieve the same accuracy of the existing first-order shear deformation theory.

Key Words

free vibration; functionally graded materials; boundary conditions; shear deformation theories; Hamilton\'s principle

Address

Latifa Ould Larbi — Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali, Chlef, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria; Laboratoire des Matériaux & Hydrologie, Université de Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algeria
Lazreg Hadji — Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali, Chlef, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria
Mohamed Ait Amar Meziane — Department of Civil Engineering, Faculty of Applied Sciences, Ibn Khaldoun University, BP 78 Zaaroura, Tiaret (14000), Algeria
E.A. Adda Bedia — Department of Civil Engineering, Faculty of Applied Sciences, Ibn Khaldoun University, BP 78 Zaaroura, Tiaret (14000), Algeria; Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria

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