The effect of visco-Pasternak foundation on the free vibration behavior of exponentially graded sandwich plates with various boundary conditions

Fatima Bounouara, Salem Mohammed Aldosari, Abdelbaki Chikh, Abdelhakim Kaci, Abdelmoumen Anis Bousahla, Fouad Bourada, Abdelouahed Tounsi, Kouider Halim Benrahou, Hind Albalawi and Abdeldjebbar Tounsi

Abstract

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.

Key Words

Galerkin technique; Hamilton's principle; improved integral theory; sandwich-plates; vibrational behavior; Visco-Pasternak foundations

Address

Fatima Bounouara: 1)Département de Génie Civil, Faculté d'Architecture et de Génie Civil, Université des Sciences et de la Technologie d'Oran, BP 1505 El M'naouer, USTO, Oran, Algeria 2)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Salem Mohammed Aldosari: 1)Enhanced Composite and Structures Centre, School of Aerospace, Transport, and Manufacturing, Cranfield University, Cranfield MK43 0AL, UK 2)National Center for Aviation Technology, King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia Abdelbaki Chikh: 1)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2)Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria Abdelhakim Kaci:1)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2)Université Dr. Tahar Moulay, Faculté de Technologie, Département de Génie Civil et Hydraulique, BP 138 Cité En-Nasr 20000 Saida, Algérie Abdelmoumen Anis Bousahla: Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria Fouad Bourada:1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Science and Technology Department, Faculty of Science and Technology, Tissemsilt University, Algeria Abdelouahed Tounsi:1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 3)Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia Kouider Halim Benrahou:1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University (PNU), P.O. Box 84428, Riyadh 11671, Saudi Arabia Hind Albalawi: Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University (PNU), P.O. Box 84428, Riyadh 11671, Saudi Arabia Abdeldjebbar Tounsi: Industrial Engineering and Sustainable Development Laboratory, University of Relizane, Faculty of Science & Technology, Mechanical Engineering Department, Algeria

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