Free Vibration Analysis of Polymer/Graphene Nanoplatelet/Fiber Truncated Conical Shells Embedded in an Elastic Foundation

Yousefi, Amir Hossein; Amirabadi, Hossein; Kiani, Farhad

doi:10.47176/jcme.42.2.9861

Free Vibration Analysis of Polymer/Graphene Nanoplatelet/Fiber Truncated Conical Shells Embedded in an Elastic Foundation

Document Type : Original Article

Authors

10.47176/jcme.42.2.9861

Abstract

In this paper, a semi-analytical solution is presented for the free vibration analysis of a three-phase polymer-based truncated conical shell reinforced with Graphene NanoPlatelets (GNPs) and glass fibers, embedded in an elastic foundation. The conical shell is modeled based on the First-order Shear Deformation Theory (FSDT), and the elastic foundation is modeled using the Pasternak model. The effective mechanical properties of the three-phase polymer/GNP/fiber composite are estimated utilizing the rule of mixture, Halpin-Tsai model, and the micromechanical relations. The set of the governing equations and associated boundary conditions are derived using Hamilton’s principle, and are solved analytically in the circumferential direction using trigonometric functions and numerically in the meridional direction via the Differential Quadrature Method (DQM). The natural frequencies and corresponding mode shapes are derived for various boundary conditions, including different combinations of clamped, simply supported, and free edges at both ends of the shell. Convergence of the presented numerical solution is examined, the accuracy of the presented results is confirmed, and the effects of various parameters on the natural frequencies of the shell are investigated including the circumferential wave number, semi-vertex angle of the cone, weight fraction of the fibers, weight fraction of the GNPs, and the boundary conditions.

Keywords

References

1. Rafiee, M. A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z., and Koratkar, N., “Enhanced Mechanical Properties of Nanocomposites at Low Graphene Content”, ACS Nano, Vol. 3(12), pp. 3884-3890, 2009.
1. Tam, M., Yang, Z., Zhao, S., Zhang, H., Zhang, Y., and Yang, J., “Nonlinear Bending of Elastically Restrained Functionally Graded Graphene Nanoplatelet Reinforced Beams with an Open Edge crack”, Thin-Walled Structures, Vol. 156, pp. 106972, 2020.
2. Afshari, H., and Adab, N., “Size-Dependent Buckling and Vibration Analyses of GNP Reinforced Microplates Based on the Quasi-3D Sinusoidal Shear Deformation Theory”, Mechanics Based Design of Structures and Machines, Vol. 50(1), pp. 184-205, 2020.
3. Elmarakbi, A., Ciardiello, R., Tridello, A., Innocente, F., Martorana, B., Bertocchi, F., Cristiano, F., Elmarakbi, M., and Belingardi, G., “Effect of Graphene Nanoplatelets on the Impact Response of a Carbon Fibre Reinforced Composite”, Materials Today Communications, Vol. 25, pp. 101530, 2020.
4. Afshari, H., “Effect of Graphene Nanoplatelet Reinforcements on the Dynamics of Rotating Truncated Conical Shells”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42(10), pp. 1-22, 2020.
5. She, G.L., Liu, H.B., and Karami, B., “Resonance Analysis of Composite Curved Microbeams Reinforced with Graphene Nanoplatelets”, Thin-Walled Structures, Vol. 160, pp. 107407, 2021.
6. Hoang, V. N. V., Ninh, D.G., Van Bao, H., and Le Huy, V., “Behaviors of Dynamics and Stability Standard of Graphene Nanoplatelet Reinforced Polymer Corrugated Plates Resting on the Nonlinear Elastic Foundations”, Composite Structures, Vol. 260, pp. 113253, 2021.
7. Liu, D., Zhou, Y., and Zhu, J., “On the Free Vibration and Bending Analysis of Functionally Graded Nanocomposite Spherical Shells Reinforced with Graphene Nanoplatelets: Three-Dimensional Elasticity Solutions”, Engineering Structures, Vol. 226, pp. 111376, 2021.
8. Zhang, L., Chen, Z., Habibi, M., Ghabussi, A., and Alyousef, R., “Low-Velocity Impac, Resonance, and Frequency Responses of FG-GPLRC Viscoelastic Doubly Curved Panel”, Composite Structures, Vol. 269, pp. 114000, 2021.
9. Tornabene, F., Bacciocchi, M., Fantuzzi, N., and Reddy, J. N., “Multiscale Approach for Three‐Phase CNT/Polymer/Fiber Laminated Nanocomposite Structures”, Polymer Composites, Vol. 40(1) , pp. 102-126, 2019.
10. Yousefi, A.H., Memarzadeh, P., Afshari, H., and Hosseini, S. J., “Agglomeration Effects on Free Vibration Characteristics of Three-Phase CNT/Polymer/Fiber Laminated Truncated Conical Shells”, Thin-Walled Structures, Vol. 157, pp. 107077, 2020.
11. Yousefi, A.H., Memarzadeh, P., Afshari, H., and Hosseini, S. J., “Optimization of CNT/Polymer/Fiber Laminated Truncated Conical Panels for Maximum Fundamental Frequency and Minimum Cost”, Mechanics Based Design of Structures and Machines, Vol. 51, pp. 3922-3944, 2023.
12. Yousefi, A.H., Memarzadeh, P., Afshari, H., and Hosseini, S.J., “Dynamic Characteristics of Truncated Conical Panels Made of FRPs Reinforced with Agglomerated CNTs”, Structures, Vol. 33, pp. 4701-4717, 2021.
13. Rafiee, M., Nitzsche, F., and Labrosse, M., “Modeling and Mechanical Analysis of Multiscale Fiber-Reinforced Graphene Composites: Nonlinear Bending, Thermal Post-Buckling and Large Amplitude Vibration”, International Journal of Non-Linear Mechanics, Vol. 103, pp. 104-112, 2018.
14. Karimiasl, M., Ebrahimi, F., and Mahesh, V., “On Nonlinear Vibration of Sandwiched Polymer-CNT/GPL-Fiber Nanocomposite Nanoshells”, Thin-Walled Structures, Vol. 146, pp. 106431, 2020.
15. Jeawon, Y., Drosopoulos, G., Foutsitzi, G., Stavroulakis, G., and Adali, S., “Optimization and Analysis of Frequencies of Multi-scale Graphene/Fibre Reinforced Nanocomposite Laminates with Non-uniform Distributions of Reinforcements”, Engineering Structures, Vol. 228, pp. 111525, 2021.
16. Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press; 2003.
17. Kaneko, T., “On Timoshenko's Correction for Shear in Vibrating Beams”, Journal of Physics D: Applied Physics, Vol. 8(16) , pp. 1927-1936, 1975.
18. Affdl, J.H., and Kardos, J., “The Halpin‐Tsai Equations: a Review”, Polymer Engineering & Science, Vol. 16(5) , pp. 344-352, 1976.
19. Naghdi, P., and Cooper, R., “Propagation of Elastic Waves in Cylindrical Shells, Including the Effects of Transverse Shear and Rotatory Inertia”, The Journal of the Acoustical Society of America, Vol. 28(1) , pp. 56-63, 1956.
20. Afshari, H., “Free Vibration Analysis of GNP-Reinforced Truncated Conical Shells with Different Boundary Conditions”, Australian Journal of Mechanical Engineering, Vol. 20, pp. 1363-1378, 2022.
21. Afshari, H., Ariaseresht, Y., Rahimian Koloor, S.S., Amirabadi, H., and Omidi Bidgoli, M., “Supersonic Flutter Behavior of a Polymeric Truncated Conical Shell Reinforced with Agglomerated CNTs”, Waves in Random and Complex Media, 2022, https://doi.org/10.1080/17455030.2022.2082581.
22. Afshari, H., and Amirabadi, H., “Vibration Characteristics of Rotating Truncated Conical Shells Reinforced with Agglomerated Carbon Nanotubes”, Journal of Vibration and Control, Vol. 28(15-16), pp. 1894–1914, 2021.
23. Amirabadi, H., Afshari, H., Afjaei, M. A., and Sarafraz, M., “Effect of Variable Thickness on the Aeroelastic Stability Boundaries of Truncated Conical Shells”, Waves in Random and Complex Media, 2022, https://doi.org/10.1080/17455030.2022.2157517.
24. Reddy, J. N., “Energy Principles and Variational Methods in Applied Mechanics”, John Wiley & Sons, Hoboken, New Jersey, 2017.
25. Bert, C.W., and Malik, M., “Differential Quadrature Method in Computational Mechanics: a Review”, Applied Mechanics Reviews, Vol. 49(1) , pp. 1-28, 1996.
27. Sofiyev, A., and Schnack, E., “The Vibration Analysis of FGM Truncated Conical Shells Resting on Two-Parameter Elastic Foundations”, Mechanics of Advanced Materials and Structures, Vol. 19(4), pp. 241-249, 2012.