Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation

Lynda Amel Chaabane , Fouad Bourada , Mohamed Sekkal , Sara Zerouati , Fatima Zohra Zaoui , Abdeldjebbar Tounsi , Abdelhak Derras , Abdelmoumen Anis Bousahla , Abdelouahed Tounsi

Abstract

In this investigation, study of the static and dynamic behaviors of functionally graded beams (FGB) is presented using a hyperbolic shear deformation theory (HySDT). The simply supported FG-beam is resting on the elastic foundation (Winkler-Pasternak types). The properties of the FG-beam vary according to exponential (E-FGB) and power-law (P-FGB) distributions. The governing equations are determined via Hamilton\'s principle and solved by using Navier\'s method. To show the accuracy of this model (HySDT), the current results are compared with those available in the literature. Also, various numerical results are discussed to show the influence of the variation of the volume fraction of the materials, the power index, the slenderness ratio and the effect of Winkler spring constant on the fundamental frequency, center deflection, normal and shear stress of FG-beam.

Key Words

functionally graded beam; bending; stress; natural frequency; shear deformation theory; Winkler-Pasternak foundation parameters

Address

Lynda Amel Chaabane, Sara Zerouati: LGCE, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria. Fouad Bourada, Mohamed Sekkal, Abdelhak Derras, Abdeldjebbar Tounsi, Abdelouahed Tounsi :Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Fouad Bourada: Département des Sciences et de la Technologie, Centre Universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algérie Fatima Zohra Zaoui: Laboratoire de Modélisation Numérique et Expérimentale des Phénomènes Mécaniques, Faculté des Sciences et Technologie, Département de Génie Mécanique, Université Abdelhamid Ibn Badis of Mostaganem, 27000, Algeria Abdelmoumen Anis Bousahla: 5Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria, 6Centre Universitaire Ahmed Zabana de Relizane, Algérie Abdelouahed Tounsi: Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia

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