Free vibration investigation of functionally graded plates with temperaturedependent properties resting on a viscoelastic foundation

Abdeldjebbar Tounsi , Adda Hadj Mostefa , Amina Attia , Abdelmoumen Anis Bousahla , Fouad Bourada , Abdelouahed Tounsi , Mohammed A. Al-Osta

Abstract

The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables' unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates' thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steadystate thermal loads and power-law material properties are supposed to be graded across the plate's thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton's principle and Navier's approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

Key Words

free vibration; functionally graded plates; simple FSDT; temperature-dependent properties; viscoelastic foundation

Address

Abdeldjebbar Tounsi — Industrial Engineering and Sustainable Development Laboratory, University of Rélizane, Faculty of Science & Technology, Mechanical Engineering Department, Algeria
Adda Hadj Mostefa — Industrial Engineering and Sustainable Development Laboratory, Department of Civil Engineering, University of Rélizane, Faculty of Science & Technology, Algeria
Amina Attia — Engineering and Sustainable Development Laboratory, Faculty of science and Technology, Civil Engineering Department, University of Ain Temouchent, Algeria
Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
Fouad Bourada — Département des Sciences et de la Technologie, Université de Tissemsilt, BP 38004 Ben Hamouda, Algérie; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia
Mohammed A. Al-Osta — Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia; Interdisciplinary Research Center for Construction and Building Materials, KFUPM, 31261 Dhahran, Saudi Arabia

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