Analytical solution for imperfect functionally graded beams resting on viscoelastic foundation

Mamia Benchohra, Imene Laoufi, Amina Attia, Abdelmoumen Anis Bousahla, Abdeldjebbar Tounsi, Abdelouahed Tounsi, Murat Yaylaci, Ayed Eid Alluqmani and S.R. Mahmoud

Abstract

In this research the bending behavior and free vibration characteristics of imperfect functionally graded (IFG) beams are examined. The investigation incorporates cases where these beams are resting on both elastic and viscoelastic foundations. It is assumed that the IFG beam's material properties change continuously with thickness in accordance with the volume percentage of its constituent parts. The study employs a refined three-variable first-order shear deformation theory to consider kinematic relations. Hamilton's principle is employed to derive equations of motion. The development of the present theory is similar to the first-order simple shear deformation theory. With the assumption that the IFG beam is simply supported, this research presents the analytical solution. In order to showcase the precision of the developed theory, comparisons are conducted between the results derived from existing theories and present results of the proposed theory. Finally, a comprehensive discussion on the effects of span-to-depth ratio, porosity volume percentage, and viscoelastic foundations is provided.

Key Words

bending; functionally graded material; porosity; vibration; viscoelastic foundation

Address

Mamia Benchohra: Département de Technologies, Institut des Sciences, Centre Universitaire Nour Bachir Bachir El-Bayadh, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria Imene Laoufi: Department of Civil Engineering and Publics Works, Innovative Materials Laboratory and Renewable Energies, University of Relizane, Algeria Amina Attia: Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, Civil Engineering Department, University of Ain Temouchent, Algeria Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria Abdeldjebbar Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Mechanical Engineering Department, Faculty of Science and Technology, University of Rélizane, Algeria Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Murat Yaylaci: Department of Civil Engineering, Recep Tayyip Erdogan University, 53100, Rize, Turkey; Turgut Kiran Maritime Faculty, Recep Tayyip Erdogan University, 53900, Rize, Turkey; Murat Yaylaci-Luzeri R&D Engineering Company, 53100, Rize, Turkey Ayed Eid Alluqmani: Department of Civil Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah, Saudi Arabia S.R. Mahmoud: GRC Department, Applied College, King Abdulaziz University. Jeddah 21589, Saudi Arabia

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