Finite element based free vibration analysis of sandwich FGM plates under hygro-thermal conditions using zigzag theory

Aman Garg, Neeraj Kumar Shukla, M. Ramkumar Raja, Hanuman D. Chalak, Mohamed-Ouejdi Belarbi, Abdelouahed Tounsi, Li Li and A.M. Zenkour

Abstract

In the present work, a comparative study has been carried out between power, exponential, and sigmoidal sandwich FGM plates for free vibration conditions under hygro-thermal conditions. Rules of mixture is used to determine effective material properties across the thickness for power-law and sigmoid sandwich FGM plates. Exponential law is used to plot effective material properties for exponentially graded sandwich FGM plates. Temperature and moisture dependent material properties were used during the analysis. Free vibration analysis is carried out using recently proposed finite element based HOZT. Present formulation satisfies interlayer transverse stress continuity conditions at interfaces and transverse shear stressfree conditions at the plate's top and bottom surfaces. The present model is free from any penalty or post-processing requirements. Several new results are reported in the present work, especially for unsymmetric sandwich FGM plates and exponential and sigmoidal sandwich FGM plates.

Key Words

exponential; finite element; free vibration; power-law; sandwich FGM; sigmoidal

Address

Aman Garg: State Key Laboratory of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China Neeraj Kumar Shukla: Department of Electrical Engineering, College of Engineering, King Khalid University, Abha-62314, Kingdom of Saudi Arabia M. Ramkumar Raja: Department of Electrical Engineering, College of Engineering, King Khalid University, Abha-62314, Kingdom of Saudi Arabia Hanuman D. Chalak: Department of Civil Engineering, National Institute of Technology Kurukshetra, Haryana, India – 136119 Mohamed-Ouejdi Belarbi: 1)Laboratoire de recherche en Génie Civil, LRGC, Université de Biskra. B.P.145, R.P.7000, Biskra, Algeria 2)School of Engineering, Lebanese American University, Byblos, Lebanon Abdelouahed Tounsi: 1)YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 2)Department of Civil and Environmental Engineering, King Fahd University of Petroleum &Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia 3)Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, 22000 Sidi Bel Abbes, Algeria Li Li: State Key Laboratory of Intelligent Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China A.M. Zenkour: 1)Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia 2)Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, Egypt

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