Free vibration analysis of FG plates under thermal environment via a simple 4-unknown HSDT

Amina Attia , Amina Tahar Berrabah , Abdelmoumen Anis Bousahla , Fouad Bourada , Abdelouahed Tounsi , S.R. Mahmoud

Abstract

A 4-unknown shear deformation theory is applied to investigate the vibration of functionally graded plates under thermal environment. The plate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the plate thickness. Three types of thermal loadings, uniform, linear and nonlinear temperature rises along the plate thickness are taken into account. The present theory contains four unknown functions as against five or more in other higher order shear deformation theories. The through-the-thickness distributions of transverse shear stresses of the plate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem dependent shear correction factor. Analytical solutions for the free vibration analysis are derived based on Fourier series that satisfy the boundary conditions (Navier's method). Benchmark solutions are firstly considered to evaluate the accuracy of the proposed model. Comparisons with the solutions available in literature revealed the good capabilities of the present model for the simulations of vibration responses of FG plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.

Key Words

free vibrations; functionally graded plates; shear deformation

Address

Amina Attia — Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, University of Ain Temouchent, Department of civil engineering. Algeria
Amina Tahar Berrabah — 2Faculty of Science and Technology, University of Ain Temouchent, Department of civil engineering. Algeria
Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Université de Sidi Bel Abbés, Algeria
Fouad Bourada — Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria/ Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algérie
Abdelouahed Tounsi — Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria/ Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algérie/ 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, Dhahran, Saudi Arabia
S.R. Mahmoud — GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia

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