On the free vibration behavior of carbon nanotube reinforced nanocomposite shells: A novel integral higher order shear theory approach

Mohammed Houssem Eddine Guerine , Zakaria Belabed , Abdelouahed Tounsi , Sherain M.Y. Mohamed , Saad Althobaiti , Mahmoud M. Selim

Abstract

This paper formulates a new integral shear deformation shell theory to investigate the free vibration response of carbon nanotube (CNT) reinforced structures with only four independent variables, unlike existing shell theories, which invariably and implicitly induce a host of unknowns. This approach guarantees traction-free boundary conditions without shear correction factors, using a non-polynomial hyperbolic warping function for transverse shear deformation and stress. By introducing undetermined integral terms, it will be possible to derive the motion equations with a low order of differentiation, which can facilitate a closed-form solution in conjunction with Navier's procedure. The mechanical properties of the CNT reinforcements are modeled to vary smoothly and gradually through the thickness coordinate, exhibiting different distribution patterns. A comparison study is performed to prove the efficacy of the formulated shell theory via obtained results from existing literature. Further numerical investigations are current and comprehensive in detailing the effects of CNT distribution patterns, volume fractions, and geometrical configurations on the fundamental frequencies of CNT-reinforced nanocomposite shells present here. The current shell theory is assumed to serve as a potent conceptual framework for designing reinforced structures and assessing their mechanical behavior.

Key Words

advanced reinforced nanocomposites; carbon nanotubes; free vibration; higher order shear deformation shell theory; indeterminate integral terms

Address

Mohammed Houssem Eddine Guerine — Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama, BP 66, 45000 Naama, Algeria
Zakaria Belabed — Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama, BP 66, 45000 Naama, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi — Department of Civil and Environmental Engineering, Lebanese American University, 309 Bassil Building, Byblos, Lebanon; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia
Sherain M.Y. Mohamed — Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Saad Althobaiti — Department of Sciences and Technology, Ranyah University Collage, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mahmoud M. Selim — Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

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