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Steel and Composite Structures Volume 18, Number 1, January 2015 , pages 187-212 DOI: https://doi.org/10.12989/scs.2015.18.1.187 |
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Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories |
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Amina Attia, Abdelouahed Tounsi, E.A. Adda Bedia and S.R. Mahmoud
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| Abstract | ||
| In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates. | ||
| Key Words | ||
| functionally graded plate; higher-order plate theory; vibration; temperature-dependent properties | ||
| Address | ||
| (1) Amina Attia, Abdelouahed Tounsi, E.A. Adda Bedia: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (2) Abdelouahed Tounsi: Advanced Materials and Structures Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; (3) S.R. Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia; (4) S.R. Mahmoud: Mathematics Department, Faculty of Science, University of Sohag, Egypt. | ||