An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells

Zakaria Belabed , Mahmoud M. Selim , Omar Slimani , Noureddine Taibi , Abdelouahed Tounsi , Muzamal Hussain

Abstract

In this study, a simple and efficient higher order shear deformation theory is formulated for free vibration analysis of functionally graded (FG) shells. By introducing the undetermined integral terms in displacement field, the number of generated unknowns and their related governing equations is reduced in contrast to previously published theories, and therefore the differentiability of governing motion equations is decreased, this motivation turns the present theory simpler and easily exploited for functionally graded shell mechanical simulation. Both strains and stress rise through the thickness coordinate as function of hyperbolical distribution. The Hamilton's principle is deployed to derive the governing and motion equations. Closed form solutions are obtained for free vibration problems using Navier's method. Furthermore, detailed comparisons with other shear deformation theories are presented to illustrate the efficiency and accuracy of the developed theory. From this perspective, various perceptions on the impact of some important parameters such as material distribution, geometrical configuration, thickness and curvature ratios are studied and discussed. The non-trivial aspects in predicting the free vibration responses of FG shells are also pointed out.

Key Words

analytical solutions; free vibration; functionally graded (FG) shells; shear deformation shell theory

Address

Zakaria Belabed — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Department of Technology, Institute of Science and Technology, Naama University Center, BP 66, 45000 Naama, Algeria
Mahmoud M. Selim — Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj 710-11912, Saudi Arabia
Omar Slimani — FIMAS Laboratory, Department of Civil Engineering, Faculty of Technology, Tahri Mohamed University, 08000 Bechar, Algeria
Noureddine Taibi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelouahed Tounsi — Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, 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
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan

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