A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates

Imene Ait Sidhoum , Djilali Boutchicha , Samir Benyoucef , Abdelouahed Tounsi

Abstract

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

Key Words

vibration; functionally graded plate; plate theory; thickness-stretching effect

Address

Imene Ait Sidhoum and Djilali Boutchicha — Laboratoire de mecanique applique, Universite des Sciences et Technologie d\'ORAN Mouhamed Boudiaf,BP 1505 Elmnouar 31000, ORAN, Algeria
Samir Benyoucef — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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