Free vibration analysis of power-law and sigmoidal sandwich FG plates using refined zigzag theory

Aman Garg , Simmi Gupta , Hanuman D. Chalak , Mohamed-Ouejdi Belarbi , Abdelouahed Tounsi , Li Li , A.M. Zenkour

Abstract

Free vibration analysis of power law and sigmoidal sandwich plates made up of functionally graded materials (FGMs) has been carried out using finite element based higher-order zigzag theory. The present model satisfies all-important conditions such as transverse shear stress-free conditions at the plate's top and bottom surface along with continuity condition for transverse stresses at the interface. A Nine-noded C0 finite element having eleven degrees of freedom per node is used during the study. The present model is free from the requirement of any penalty function or post-processing technique and hence is computationally efficient. The present model's effectiveness is demonstrated by comparing the present results with available results in the literature. Several new results have been proposed in the present work, which will serve as a benchmark for future works. It has been observed that the material variation law, power-law exponent, skew angle, and boundary condition of the plate widely determines the free vibration behavior of sandwich functionally graded (FG) plate.

Key Words

free vibration; higher-order zigzag theory; power-law; sandwich FG plate; sigmoidal law

Address

Aman Garg — Department of Civil and Environmental Engineering, The NorthCap University, Gurugram, Haryana, 122017, India
Simmi Gupta — Department of Civil Engineering, National Institute of Technology Kurukshetra, Haryana, 136119, India
Hanuman D. Chalak — Department of Civil Engineering, National Institute of Technology Kurukshetra, Haryana, 136119, India
Mohamed-Ouejdi Belarbi — Laboratoire de Recherche en Génie Civil, LRGC. Université de Biskra, B.P. 145, R.P. 07000, Biskra, Algeria
Abdelouahed Tounsi — 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 6Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, 22000 Sidi Bel Abbes, Algeria
Li Li — State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
A.M. Zenkour — Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, Egypt

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