An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler–Pasternak elastic foundations

Salima Abdelbari , Abdelkader Fekrar , Houari Heireche , Hayat Saidi , Abdelouahed Tounsi , E.A. Adda Bedia

Abstract

This work presents a simple hyperbolic shear deformation theory for analysis of functionally graded plates resting on elastic foundation. The proposed model contains fewer number of unknowns and equations of motion than the first-order shear deformation model, but the transverse shear stresses account for a hyperbolic variation and respect the tangential stress-free boundary conditions on the plate boundary surface without introducing shear correction factors. Equations of motion are obtained from Hamilton\'s principle. The Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to demonstrate the accuracy of the proposed theory.

Key Words

shear deformation theory; vibration; functionally graded plate; elastic foundation

Address

Salima Abdelbari, Abdelkader Fekrar and Hayat Saidi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria
E.A. Adda Bedia — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Algerian National Thematic Agency of Research in Science and Technology (ATRST), Algeria

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