A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation

Ali Meftah , Ahmed Bakora , Fatima Zohra Zaoui , Abdelouahed Tounsi , El Abbes Adda Bedia

Abstract

This paper presents a free vibration analysis of plates made of functionally graded materials and resting on twolayer elastic foundations by proposing a non-polynomial four variable refined plate theory. Undetermined integral terms are introduced in the proposed displacement field and unlike the conventional higher shear deformation theory (HSDT), the present one contains only four unknowns. Equations of motion are derived via the Hamilton\'s principles and solved using Navier\'s procedure. Accuracy of the present theory is demonstrated by comparing the results of numerical examples with the ones available in literature.

Key Words

vibration; functionally graded plate; elastic foundation; plate theory

Address

(1) Ali Meftah, Ahmed Bakora, Abdelouahed Tounsi, El Abbes Adda Bedia — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
(2) Fatima Zohra Zaoui — Laboratoire de Modelisation Numerique et Experimentale des Phenomenes Mecaniques, Faculty of Sciences and Technology, Departement de Génie Mécanique, University Abdelhamid Ibn Badis of Mostaganem, 27000, Algeria
(3) Abdelouahed Tounsi — Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, Faculté de Technologie, Département de génie civil, Algeria
(4) Abdelouahed Tounsi — Laboratoire de Modélisation et Simulation Multi-échelle, Départment de Physique, Faculté des Sciences Exactes, Départment de Physique, Université de Sidi Bel Abbés, Algeria.

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