Structural Engineering and Mechanics

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

  • Mohammed Houssem Eddine Guerine (Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama) ;
  • Zakaria Belabed (Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, Lebanese American University) ;
  • Sherain M.Y. Mohamed (Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Saad Althobaiti (Department of Sciences and Technology, Ranyah University Collage, Taif University) ;
  • Mahmoud M. Selim (Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University)
  • Received : 2024.05.26
  • Accepted : 2024.06.24
  • Published : 2024.07.10
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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.

Keywords

Acknowledgement

The authors extend their appreciation to Taif University, Saudi Arabia, for supporting this work through project number (TU-DSPP-2024-66).

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