In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton\'s principle. By using Navier\'s method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.
(1) Boudjema Bendaho, Zakaria Belabed, Mohamed Bourada, Fouad Bourada, Abdelouahed Tounsi — Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
(2) Zakaria Belabed — Department of Technology, Institute of Science and Technology, Ctr Univ Naama, BP 66, 45000, Algeria
(3) Mohamed Atif Benatta — 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 — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
(5) Fouad Bourada — Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algérie.
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