Free Vibration of Functionally Graded Shells with Graphene Platelets Reinforcement using Improved First-Order Shear Deformation Theory
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Abstract
This paper presents a semi-analytical formulation for the free vibration of functionally graded shells with graphene platelets reinforcement using improved first-order shear deformation theory. The effective Young’s modulus of the functionally graded material (FGM) is determined using Voigt’s model, while the effective Young’s modulus of the graphene platelet (GPL) reinforcement is predicted by the Halpin–Tsai micromechanical model. Additionally, the effective Poisson’s ratio and density are calculated using the rule of mixtures. The governing equations for FGM shells reinforced with GPL are formulated using the improved first-order shear deformation theory (FSDT). The equations of motion are derived using Hamilton’s principle, and the numerical solutions are obtained through Navier’s method. The present results demonstrate excellent agreement with various shear deformation theories reported in the existing literature. The numerical results indicate that the FGM shells reinforced with GPL pattern B yield the highest natural frequency. This is because the maximum GPL content is distributed near the top and bottom surfaces, where the normal stresses are highest. Furthermore, this GPL distribution effectively satisfies the actual normal stress requirements of the shells.
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References
Ansari, R., Hassani, R., Gholami, R. and Rouhi, H. (2020). Nonlinear Bending Analysis of Arbitrary-Shaped Porous Nanocomposite Plates using a Novel Numerical Approach. International Journal of Non-Linear Mechanics, 126. https://doi.org/10.1016/j.ijnonlinmec.2020.103556
Benounas, S., Belarbi, M.O., Van Vinh, P., Daikh, A.A. and Fantuzzi, N. (2024). Finite Element Model for Free Vibration Analysis of Functionally Graded Doubly Curved Shallow Shells by using an Improved First-Order Shear Deformation Theory. Structures, 64. https://doi.org/10.1016/j.istruc.2024.106594
Garg, A., Belarbi, M.O., Chalak, H.D. and Chakrabarti, A. (2021). A Review of the Analysis of Sandwich FGM Structures. Composite Structures, 258. https://doi.org/10.1016/j.compstruct.2020.113427
Halpin, J.C. and Kardos, J.L. (1976). The Halpin-Tsai Equations: A Review. Polymer Engineering & Science, 16(5), 344-352. https://doi.org/10.1002/pen.760160512
Jiammeepreecha, W. (2017). Effects of Internal Pressure and Constraint Volume on Vibration of Spherical Membrane. RMUTI Journal Science and Technology, 10(2), 40-60. https://ph01.tci-thaijo.org/index.php/rmutijo/article/view/96525
Jones, R.M. (2018). Mechanics of Composite Materials. CRC Press.
Khalaf, A.S. and Hasan, H.M. (2024). Nonlinear Forced Vibration of Functionally Graded Hybrid Three-Phase Nanocomposite Toroidal Shell Segments Reinforced by Carbon Nanotubes (CNTs) and Graphene Nanoplatelets (GPLs). Thin-Walled Structures, 199. https://doi.org/10.1016/j.tws.2024.111876
Matsunaga, H. (2008). Free Vibration and Stability of Functionally Graded Shallow Shells According to a 2D Higher-Order Deformation Theory. Composite Structures, 84(2), 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006
Qatu, M.S. (2004). Vibration of Laminated Shells and Plates. Academic Press.
Reddy, J.N. (2003). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2nd ed). CRC Press. https://doi.org/10.1201/b12409
Roun, S., Nguyen, V.L. and Rungamornrat, J. (2025). Free Vibration and Buckling Analyses of Functionally Graded Plates with Graphene Platelets Reinforcement. Journal of Computing and Information Science in Engineering, 25(1). https://doi.org/10.1115/1.4064665
Shen, H.S. (2009). Functionally Graded Materials Nonlinear Analysis of Plates and Shells. CRC Press.
Thai, H.T. and Kim, S.E. (2015). A Review of Theories for the Modeling and Analysis of Functionally Graded Plates and Shells. Composite Structures, 128, 70-86. https://doi.org/10.1016/j.compstruct.2015.03.010
Tjong, S.C. (2013). Recent Progress in the Development and Properties of Novel Metal Matrix Nanocomposites Reinforced with Carbon Nanotubes and Graphene Nanosheets. Materials Science and Engineering: R: Reports, 74(10), 281-350. https://doi.org/10.1016/j.mser.2013.08.001
Van Vinh, P. and Tounsi, A. (2022). Free Vibration Analysis of Functionally Graded Doubly Curved Nanoshells using Nonlocal First-Order Shear Deformation Theory with Variable Nonlocal Parameters. Thin-Walled Structures, 174. https://doi.org/10.1016/j.tws.2022.109084
Van Vinh, P., Van Chinh, N. and Tounsi, A. (2022). Static Bending and Buckling Analysis of Bi-Directional Functionally Graded Porous Plates using an Improved First-Order Shear Deformation Theory and FEM. European Journal of Mechanics - A/Solids, 96. https://doi.org/10.1016/j.euromechsol.2022.104743
Wang, A., Chen, H., Hao, Y. and Zhang, W. (2018). Vibration and Bending Behavior of Functionally Graded Nanocomposite Doubly-Curved Shallow Shells Reinforced by Graphene Nanoplatelets. Results in Physics, 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062
Worku, A.K. and Ayele, D.W. (2023). Recent Advances of Graphene-Based Materials for Emerging Technologies. Results in Chemistry, 5. https://doi.org/10.1016/j.rechem.2023.100971
Yee, K. and Ghayesh, M.H. (2023). A Review on the Mechanics of Graphene Nanoplatelets Reinforced Structures. International Journal of Engineering Science, 186. https://doi.org/10.1016/j.ijengsci.2023.103831
Zhao, S., Zhao, Z., Yang, Z., Ke, L.L., Kitipornchai, S. and Yang, J. (2020). Functionally Graded Graphene Reinforced Composite Structures: A Review. Engineering Structures, 210. https://doi.org/10.1016/j.engstruct.2020.110339
Zhao, T., Bayat, M.J., Kalhori, A. and Asemi, K. (2024). Free Vibration Analysis of Functionally Graded Multilayer Hybrid Composite Cylindrical Shell Panel Reinforced by GPLs and CNTs Surrounded by Winkler Elastic Foundation. Engineering Structures, 308. https://doi.org/10.1016/j.engstruct.2024.117975
Zingoni, A. (2015). Liquid-Containment Shells of Revolution: A Review of Recent Studies on Strength, Stability and Dynamics. Thin-Walled Structures, 87, 102-114. https://doi.org/10.1016/j.tws.2014.10.016
