Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exp
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O R I G I NA L
Fatima Zohra Zaoui · Djamel Ouinas · Abdelouahed Tounsi · Jaime Aurelio Viña Olay · Belkacem Achour · Mabrouk Touahmia
Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exponential-trigonometric two-dimensional higher shear deformation theory Received: 1 April 2020 / Accepted: 17 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The objective of this paper is to provide a computational method to analyze free vibrations of advanced composite plates in thermal environments according to a recently developed higher-order shear deformation theory. This method is based upon the assumptions that displacements field include just four unknowns and considers a combination of trigonometric and exponential shear shape functions which satisfy shear stress free boundary conditions on the plate surfaces. The FG plates are simply supported and subjected to uniform, linear, nonlinear and sinusoidal temperature rise. The temperature field considered is assumed to vary in the thickness direction and constant in the axial directions of plates. It is supposed that the constituent materials possess temperature-dependent properties changing across the thickness with a simple power law function. The equations of motion are obtained by employing Hamilton’s principle and solved based on Navier’s method to determine natural frequencies of the FG plate. A parametric study for FGM plates with different values of power law index and under different sets of thermal environmental conditions has been carried out. The obtained results are compared for temperature-dependent and temperature-independent FG Plates and validated with available results in the literature. Keywords Vibration · Functionally graded plate · Shear deformation theory · Temperature-dependent properties · Hamilton’s principle F. Z. Zaoui (B) · D. Ouinas Laboratory of numerical and experimental modelling of the mechanical phenomena, Mechanical Engineering Department, Faculty of Sciences and Technology, Ibn Badis University, 27000 Mostaganem, Algeria E-mail: [email protected]; [email protected] A. Tounsi Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, Sidi Bel Abbes University, 22000 Sidi Bel Abbés, Algeria A. Tounsi Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran, Eastern Province 31261, Kingdom of Saudi Arabia J. A. Viña Olay Department of Materials Science and Metallurgical Engineering, University of Oviedo, Gijón, Spain B. Achour · M. Touahmia Civil Engineering Department, University of Ha’il, Ha’il, Kingdom of Saudi Arabia
F. Z. Zaoui et al.
1 Introduction Functionally graded materials (FGMs) are a new family of advanced composites. They are fabricated from the combination of ceramics that provides a high temperature resistance due to its low thermal conductivity and metals which possess good fracture toughness [1]. FGMs are characterized by a sm
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