Forced vibration of a functionally graded porous beam resting on viscoelastic foundation

Ali Alnujaie, Şeref D. Akbas, Mohamed A. Eltaher and Amr Assie

Abstract

This paper concerns with forced dynamic response of thick functionally graded (FG) beam resting on viscoelastic foundation including porosity impacts. The dynamic point load is proposed to be triangle point loads in time domain. In current analysis the beam is assumed to be thick, therefore, the two-dimensional plane stress constitutive equation is proposed to govern the stress-strain relationship through the thickness. The porosity and void included in constituent is described by three different distribution models through the beam thickness. The governing equations are obtained by using Lagrange's equations and solved by finite element method. In frame of finite element analysis, twelve-node 2D plane element is exploited to discretize the space domain of beam. In the solution of the dynamic problem, Newmark average acceleration method is used. In the numerical results, effects of porosity coefficient, porosity distribution and foundation parameters on the dynamic responses of functionally graded viscoelastic beam are presented and discussed. The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.

Key Words

dynamic response; functionally graded beam; porosity; viscoelastic foundation; numerical finite element method

Address

Ali Alnujaie: Department of Mechanical Engineering, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia Şeref D. Akbas: Department of Civil Engineering, Bursa Technical University, 16330, Bursa, Turkey Mohamed A. Eltaher: 1.) Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia 2.) Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Amr Assie: 1.) Department of Mechanical Engineering, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia 2.) Department of Mechanical Design & Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

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