Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates

Ali Doğan

doi:10.38088/jise.1581290

EN

Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates

Abstract

This study investigated the buckling and free vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under uniaxial loads. The current study researches the buckling and vibration behavior of CNTRC plates using single-walled CNTs (SWCNTs). SWCNTs were accepted to be regular and aligned, with a consistent pattern. CNT topologies were studied, including four different FG distributions of CNTs over thickness. Hamilton's principle was used to get the equations of motion for composite plates. The equations obtained for the solution were obtained by using the Navier solution method to solve the equation of motion. The results were compared using the FEM (Ansys) approach. The findings were proved to be compatible with FEM (Ansys). Then, it was understood from the parametric work that volume fractions, thickness ratios and FG distributions have a significant effect on the buckling and vibration response of FG-CNTRC plates. The findings were presented with graphs and tables.

Keywords

References

[1] Yas, M. H., and Samadi, N. (2012). Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation, International Journal of Pressure Vessels and Piping, 98: 119-128.
[2] Lei, Z. X., Zhangc, L.W., and Liew, K., M. (2015). Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach. International Journal of Pressure Vessels and Piping, 266: 773-791.
[3] Kumar, P., and Srinivas, J. (2017). Free vibration, bending and buckling of a FG-CNT reinforced composite beam, Comparative analysis with hybrid laminated composite beam. Multidiscipline Modeling in Materials and Structures, 13(4): 590-611.
[4] Civalek, Ö., Dastjerdi, S., and Akgöz, B. (2020). Buckling and free vibrations of CNT-reinforced cross-ply laminated composite plates”, Mechanics Based Design of Structures and Machines, 98:119-128.
[5] Dastjerdi, R. M., and Mohammadi, H. M. (2017). Free Vibration and Buckling Analyses of Functionally Graded Nanocomposite Plates Reinforced by Carbon Nanotube”, Mechanics of Advanced Composite Structures, 4: 59-73.
[6] Nguyen, P. D., Papazafeiropoulos, G., Vu Q. V., and Duc N. D. (2022). Buckling response of laminated FG-CNT reinforced composite plates: Analytical and finite element approach. Aerospace Science and Technology, 121: 107368.
[7] Foroutan, K., Carrera, H., and Ahmadi, H. (2021). Static and dynamic hygrothermal post buckling analysis of sandwich cylindrical panels with an FG-CNTRC core surrounded by nonlinear viscoelastic foundations. Composites Structures, 259: 113214.
[8] Efraim, E., and Eisenberger, M., (2007). Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. Journal of Sound and Vibration, 299: 720-738. doi:10.1016/j.jsv.2006.06.068

[9] Nguyen, T. K., Karam Sab, K., and Bonnet, G. (2008). First-order shear deformation plate models for functionally graded materials. Composite Structures, 83: 25-36. doi:10.1016/j.compstruct.2007.03.004
[10] Zhang, L. W., Lei, Z. X., and Liew, K. M. (2015). Buckling analysis of FG-CNT reinforced composite thick skew plates using an element-free approach. Composites Part B, 75: 36-46.
[11] Kiani, Y. (2016). Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers. Computers and Mathematics with Applications, 72: 2433-2449. doi.org/10.1016/j.camwa.2016.09.007
[12] Kiani, Y. (2016). Shear buckling of FG-CNT reinforced composite plates using Chebyshev-Ritz method. Composites Part B, 105: 176-187. doi.org/10.1016/j.compositesb.2016.09.001
[13] Kiani, Y. (2017). Buckling of FG-CNT-reinforced composite plates subjected to parabolic loading. Acta Mechanica, 228: 1303-1319. DOI 10.1007/s00707-016-1781-4
[14] Mota, A. F., Loja, M. A. R., Barbosa, J. I., and Rodrigues, J. A. (2020). Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior. Mathematical and Computational Applications, 25 (2): 1-25. doi:10.3390/mca25020025
[15] Sahan, M. F. (2015). Transient analysis of cross ply laminated shells using FSDT: Alternative formulation. Steel and Composite Structures, 18(4), 889-907., Doi: 10.12989/scs.2015.18.4.889
[16] Sahan, M. F. (2016). Dynamic analysis of linear viscoelastic cross-ply laminated shallow spherical shells. Composite Structures,149: 261-270. Doi: 10.1016/j.compstruct.2016.04.045
[17] Dogan, A. (2009) Free Vibration analysis of laminated composites plates and cylindrical shallow shells. Ph.D. Thesis, Çukurova University, Adana, Türkiye.
[18] Dogan, A. (2012). Investigation of the effect of shell plan-form dimensions on mode-shapes of the laminated composite cylindrical shallow shells using SDSST and FEM. Steel and Composite Structures, 12 (4): 303-324.
[19] Dogan, A. (2018). The effect of curvature on transient analysis of laminated composite cylindrical shells on elastic foundation”. Pamukkale University Journal of Engineering Sciences (PAJES), 24(6): 960-966.
[20] Dogan, A. (2019). Buckling Analysis of Symmetric Laminated Composite Plates.: ISTE-CE’xx2019- International Conference on Innovation, Sustainability, Technology and Education in Civil Engineering, 13-15 June, 2019, Iskenderun, Hatay / TURKIYE., 2019.
[21] Dogan, A. (2020). Buckling analysis of laminated composite plates under the effect of uniaxial and biaxial loads. Turkish Journal of Engineering (TUJE), 4(4): 218-225.
[22] Dogan, A. (2022). Quasi-static and dynamic response of functionally graded viscoelastic plates. Composite Structures, 280, 114883.
[23] Dogan, A and Sahan, M. F. (2023) Viscoelastic damped response of laminated composite shells subjected to various dynamic loads. Mechanics Based Design of Structures and Machines, 51(8):4685-4708. doi.org/10.1080/15397734.2021.1975296
[24] Dogan, A. (2024). Dynamic response of laminated functionally graded carbon nanotube-reinforced composite viscoelastic plates. Mechanics Based Design of Structures and Machines, 52(8):5562-5589.
[25] Dogan, A. (2025). Dynamic and quasi-static behavior of laminated FG-CNTRC viscoelastic double-curved shells. Mechanics Based Design of Structures and Machines. doi.org/10.1080/15397734.2025.2466645
[26] Temel, B., and Sahan, M. F. (2013). An alternative solution method for the damped response of laminated Mindlin plates. Composites: Part B, 47: 107-117.doi.org/10.1016/j.compositesb.2012.10.039
[27] Özbey, M. B., and Calim, F. F. (2025). Dynamic analysis of viscoelastic functionally graded nanoplate. Mechanics Based Design of Structures and Machines. doi.org/10.1080/15397734.2024.2449481
[28] Yildirim, S., and Tutuncu, N. (2024). Inertio-elastic instability of functionally graded nanotube-reinforced composite disks. The Journal of Strain Analysis for Engineering Design, 75: 36-46. doi.org/10.1177/03093247241302911
[29] Noori, A. R., and Temel, B. (2021). A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(22): 6370-6387. doi.org/10.1177/09544062211010837
[30] Temel, B., and Sahan, M. F. (2013). Transient analysis of orthotropic, viscoelastic thick plates in the Laplace domain. European Journal of Mechanics - A/Solids, 37: 96-105. doi.org/10.1016/j.euromechsol.2012.05.008.
[31] Rasoli, H., Noori, A.R., and Temel B. (2024). Static analysis of functionally graded porous beam-column frames by the complementary functions method. Structures, 62: 106136. doi.org/10.1016/j.istruc.2024.106136
[32] Xiao, J., Li, S., Li, M., Fu, Y., Yan, L., Song, X., and Ke, Y. (2020). Electric field-assisted alignment of carbon nanotubes in the interlayers of CFRP composites to enhance the properties, 190: 108706. doi.org/10.1016/j.compositesa.2024.108706
[33] Cao, S., Yan, X., Zhang, Y., Wu, X., Wang, L., Shi, B., Li, K., Feng, C, Wang, Q., and Wu, B. (2025). Mechanical Performance of Diamine Silane Modified Carbon Nanotubes Reinforced Epoxy Resin Composites. Coatings, 15(1):60. doi.org/10.3390/coatings15010060
[34] Wolfram Research, Inc. (2017). Mathematica (Version 11.1) [Computer software]. http://www.wolfram.com/
[35] Swanson Analysis System Inc. (2023). ANSYS (Release 23) [Computer software]. http://www.ansys.com/

Details

Primary Language

English

Subjects

Numerical Modelization in Civil Engineering , Structural Dynamics , Construction Materials , Production Technologies

Journal Section

Research Article

Authors

Ali Doğan ^*
0000-0002-2825-8068
Türkiye

Early Pub Date

July 28, 2025

Publication Date

December 15, 2025

Submission Date

November 7, 2024

Acceptance Date

April 25, 2025

Published in Issue

Year 2025 Volume: 9 Number: 2

DOI

https://doi.org/10.38088/jise.1581290

IZ

https://izlik.org/JA95DP75SB

Cite

RIS / Bibtex

APA

Doğan, A. (2025). Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates. Journal of Innovative Science and Engineering, 9(2), 171-186. https://doi.org/10.38088/jise.1581290

AMA

1.Doğan A. Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates. JISE. 2025;9(2):171-186. doi:10.38088/jise.1581290

Chicago

Doğan, Ali. 2025. “Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates”. Journal of Innovative Science and Engineering 9 (2): 171-86. https://doi.org/10.38088/jise.1581290.

EndNote

Doğan A (December 1, 2025) Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates. Journal of Innovative Science and Engineering 9 2 171–186.

IEEE

[1]A. Doğan, “Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates”, JISE, vol. 9, no. 2, pp. 171–186, Dec. 2025, doi: 10.38088/jise.1581290.

ISNAD

Doğan, Ali. “Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates”. Journal of Innovative Science and Engineering 9/2 (December 1, 2025): 171-186. https://doi.org/10.38088/jise.1581290.

JAMA

1.Doğan A. Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates. JISE. 2025;9:171–186.

MLA

Doğan, Ali. “Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates”. Journal of Innovative Science and Engineering, vol. 9, no. 2, Dec. 2025, pp. 171-86, doi:10.38088/jise.1581290.

Vancouver

1.Ali Doğan. Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates. JISE. 2025 Dec. 1;9(2):171-86. doi:10.38088/jise.1581290

Öz

Buckling and Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Rectangular Plates

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite