Finite element formulation for free vibration analysis of porous FGM beams under thermal excitation

Hadj Youzera, Sid Ahmed Meftah, Abdelouahed Tounsi, Mofareh Hassan Ghazwani and Ali Alnujaie

Abstract

In the present paper, the finite element approach for thermo-mechanical vibration analysis of porous FGM beam under various thermal load variations is studied. Three types of thermal loading variations are typically considered when accounting on porosities in a beam, usually, uniform, linear and nonlinear temperature rises. The proposed finite element is formulated according to the HSDT kinematical models, coupled with the Hamilton's principle to define the governing equations of motion. This leads to formulate, one-dimensional finite element that includes shear and thermal stress for free vibration analysis. Based on the obtained natural frequencies, a conceptual analysis is conducted to show the effects of the power-law exponents, porosity distributions, porosity volume fractions, thermal load, and the beam slenderness on the fundamental frequencies of FGM beams, under different boundary conditions.

Key Words

axial-bending coupling; FGM beam; finite element method; free vibration; porosity; shear locking; temperature effect

Address

Hadj Youzera: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli B.P. 305, R.P. 29000 Mascara, Algérie Sid Ahmed Meftah: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université Djillali Liabes, Sidi Bel Abbes, Algérie Abdelouahed Tounsi: 1) Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia, 2) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Mofareh Hassan Ghazwani and Ali Alnujaie: 1) Department of Mechanical Engineering, College of Engineering and Copmuter Sciences, Jazan University, P.O Box 45124, Jazan, Saudi Arabia, 2) Engineering and Technology Research Center, P.O. Box 114, Jazan 82817, Saudi Arabia

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