Analytical evaluation of frequencies of bidirectional FG thick beams in thermal environment and resting on different foundation

Ismail Benaberrahmane, Mohamed Mekerbi, Rabbab Bachir Bouiadjra, Samir Benyoucef, Mahmoud M. Selim, Abdelouahed Tounsi and Muzamal Hussain

Abstract

This paper presents a theoretical study of the free vibration of functionally graded beam which has variable material properties along its length and thickness. These properties are also assumed to be temperature-dependent. The beam is supposed to be simply supported and resting on several kinds of foundations. The governing equations are found analytically using a quasi-3D model that contains undetermined integral forms and involves few unknowns to derive. Navier's method is employed to determine and compute the vibration characteristics of bidirectional functionally graded (BDFG) beam on foundation. The accuracy of the present method for BDFG beam with temperature-dependency has been validated. Then the effects of the grading indexes, geometrical properties, temperature-dependent material properties, type of foundations and other parameters on the free vibration of BDFG beam are analyzed and discussed via a detailed parametric study.

Key Words

bidirectional functionally graded beams; different foundation; quasi-3D model; temperature-dependent materials

Address

Ismail Benaberrahmane: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria Mohamed Mekerbi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; Department of Civil Engineering, University of Ferhat Abbas Sétif 1, Algeria Rabbab Bachir Bouiadjra: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; Department of Civil Engineering, University Mustapha Stambouli of Mascara, Algeria Samir Benyoucef: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria Mahmoud M. Selim: Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj 710-11912, Saudi Arabia Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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