Abstract
Fiber-reinforced polymer composite materials have gained extensive application in aerospace, automotive, marine, and civil infrastructure owing to their exceptional specific strength, stiffness, and design flexibility. However, delamination - a critical interlaminar failure mode compromises structural integrity and dynamic performance. This comprehensive study investigates the vibration behavior of carbon fiber-reinforced polymer (CFRP) composite plates subjected to varying delamination extents, laminate stacking sequences, and boundary constraints through integrated analytical and finite element methodologies. The governing differential equations are derived using the Rayleigh-Ritz energy method based on classical laminated plate theory, and numerical simulations are performed using ANSYS finite element software. The investigation examines delamination sizes ranging from 0% to 56.25% of plate area, three distinct stacking configurations ([0/90/45/90], [0/45], [0/90]), and all sides clamped (CCCC), simply supported (SSSS), cantilever (CFFF), and free edges (FFFF) boundary conditions. Results demonstrate that natural frequencies decrease systematically with increasing delamination size, with maximum reduction of 5-8% occurring for the largest delamination extent (56.25%) across all boundary condition.. Furthermore, CNT integration enhances both natural frequencies (up to 29.8% increase at 2.5 wt% CNT loading) and damping characteristics (42.1% improvement). These findings support improved design and vibration control of advanced composite structures.
References
Agarwal, B. D., Broutman, L. J., & Chandrashekhara, K. (2017). Analysis and performance of fiber composites (4th ed.). John Wiley & Sons.
Agarwal, K., Kuchipudi, S. K., Girard, B., & Houser, M. (2018). Mechanical properties of fiber reinforced polymer composites: A comparative study of conventional and additive manufacturing methods. Journal of Composite Materials, 52(23), 3173–3181. https://doi.org/10.1177/0021998318762297
Ajayan, P. M., & Tour, J. M. (2007). Nanotube composites. Nature, 447(7148), 1066–1068. https://doi.org/10.1038/4471066a
Balakrishnan, P., John, M. J., Pothen, L., Sreekala, M., & Thomas, S. (2016). Natural fibre and polymer matrix composites and their applications in aerospace engineering. In S. Rana & R. Fangueiro (Eds.), Advanced composite materials for aerospace engineering: Processing, properties and applications (pp. 365–383). Woodhead Publishing. https://doi.org/10.1016/B978-0-08-100037-3.00012-2
Burlayenko, V. N., & Sadowski, T. (2010). Influence of skin/core debonding on free vibration behavior of foam and honeycomb cored sandwich plates. International Journal of Non-Linear Mechanics, 45(10), 959–968. https://doi.org/10.1016/j.ijnonlinmec.2009.07.002
Cavallo, T., Zappino, E., & Carrera, E. (2017). Free-vibration analysis of space vehicle structures made by composite materials. Composite Structures, 183, 53–62. https://doi.org/10.1016/j.compstruct.2017.01.010
Chattopadhyay, A., Gu, H., & Dragomir-Daescu, D. (1999). Dynamics of delaminated composite plates with piezoelectric actuators. AIAA Journal, 37(2), 248–254. https://doi.org/10.2514/2.697
Coleman, J. N., Khan, U., Blau, W. J., & Gun'ko, Y. K. (2006). Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites. Carbon, 44(9), 1624–1652. https://doi.org/10.1016/j.carbon.2006.02.038
Das, S., & Sarangi, S.K. (2016). Static analysis of functionally graded composite beams. IOP Conference Series: Materials Science and Engineering, 149, Article 012138. https://doi.org/10.1088/1757-899X/149/1/012138
Della, C. N., & Shu, D. (2005). Vibration of beams with double delaminations. Journal of Sound and Vibration, 282(3-5), 919–935. https://doi.org/10.1016/j.jsv.2004.03.052
Dey, S., Mukhopadhyay, T., Spickenheuer, A., Adhikari, S., & Heinrich, G. (2016). Bottom up surrogate based approach for stochastic frequency response analysis of laminated composite plates. Composite Structures, 140, 712–727. https://doi.org/10.1016/j.compstruct.2016.01.039
Friedrich, K., & Almajid, A. A. (2013). Manufacturing aspects of advanced polymer composites for automotive applications. Applied Composite Materials, 20(2), 107–128. https://doi.org/10.1007/s10443-012-9258-7
Garcia, C., Trendafilova, I., Zucchelli, A., & Contreras, J. (2018). The effect of nylon nanofibers on the dynamic behaviour and the delamination resistance of GFRP composites. MATEC Web of Conferences, 148, Article 14001. https://doi.org/10.1051/matecconf/201814814001
García-Macías, E., Castro-Triguero, R., Saavedra Flores, E. I., Friswell, M. I., & Gallego, R. (2016). Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates. Composite Structures, 140, 473–490. https://doi.org/10.1016/j.compstruct.2015.12.044
Ghiasi, H., Fayazbakhsh, K., Pasini, D., & Lessard, L. (2010). Optimum stacking sequence design of composite materials Part II: Variable stiffness design. Composite Structures, 93(1), 1–13. https://doi.org/10.1016/j.compstruct.2010.06.001
Ghoneam, S. M. (1995). Dynamic analysis of open cracked laminated composite beams. Composite Structures, 32(1-4), 3–11. https://doi.org/10.1016/0263-8223(95)00023-2
Hammami, M., El Mahi, A., Karra, C., & Haddar, M. (2016). Nonlinear behaviour of glass fibre reinforced composites with delamination. Composites Part B: Engineering, 92, 350–359. https://doi.org/10.1016/j.compositesb.2016.02.031
Hirwani, C. K., Patil, R. K., Panda, S. K., Mahapatra, S. S., Mandal, S. K., Srivastava, L., & Buragohain, M. K. (2016a). Experimental and numerical analysis of free vibration of delaminated curved panel. Aerospace Science and Technology, 54, 353–370. https://doi.org/10.1016/j.ast.2016.05.009
Hirwani, C. K., Sahoo, S. S., & Panda, S. K. (2016b). Effect of delamination on vibration behaviour of woven Glass/Epoxy composite plate–An experimental study. IOP Conference Series: Materials Science and Engineering, 115(1), Article 012010. https://doi.org/10.1088/1757-899X/115/1/012010
Hwu, C., Hsu, H. W., & Lin, Y. H. (2017). Free vibration of composite sandwich plates and cylindrical shells. Composite Structures, 171, 528–537. https://doi.org/10.1016/j.compstruct.2017.03.042
Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354, 56-58. https://doi.org/10.1038/354056a0
Imran, M. (2026). Effect of Delamination, Stacking Sequence, and Boundary Conditions on the Vibration Response of CNT-Reinforced CFRP Plates. Reports in Mechanical Engineering, 7(1), 54–70. https://doi.org/10.31181/rme534
Imran, M., Khan, R., & Badshah, S. (2018a). Finite element analysis to investigate the influence of delamination size, stacking sequence and boundary conditions on the vibration behavior of composite plate. Iranian Journal of Materials Science & Engineering, 15(4), 1–12.
Imran, M., Khan, R., & Badshah, S. (2018b). Vibration analysis of cracked composite laminated plate and beam structures. Romanian Journal of Acoustics and Vibration, 15(1), 3–13.
Imran, M., Khan, R., & Badshah, S. (2019). Investigating the effect of delamination size, stacking sequences and boundary conditions on the vibration properties of carbon fiber reinforced polymer composite. Materials Research, 22(2), Article e20180478. https://doi.org/10.1590/1980-5373-MR-2018-0478
Jadhav, V., & Bhoomkar, M. M. (2016). Experimental and numerical FEM analysis of cracked composite cantilever beam by vibration techniques. International Journal of Engineering Science, 6(4), 3347-3351.
Juhász, Z., Turcsán, T., Tóth, T. B., & Szekrényes, A. (2018). Sensitivity analysis for frequency based prediction of crack size in composite plates with through-the-width delamination. International Journal of Damage Mechanics, 27(6), 859–876. https://doi.org/10.1177/1056789517709893
Kim, H. Y., & Hwang, W. (2002). Effect of debonding on natural frequencies and frequency response functions of honeycomb sandwich beams. Composite Structures, 55(1), 51–62. https://doi.org/10.1016/S0263-8223(01)00136-2
Kumar, G. A. Y., & Kumar, K. M. S. (2017). Free vibration analysis of smart composite beam. Materials Today: Proceedings, 4(2), 2487–2491. https://doi.org/10.1016/j.matpr.2017.02.101
Lee, J., Gurdal, Z., & Griffin, O. H. (1993). Layer-wise approach for the bifurcation problem in laminated composites with delaminations. AIAA Journal, 31(2), 331–338. https://doi.org/10.2514/3.11672
Lee, S. K., Kim, M. W., Park, C. J., Choi, M. J., Kim, G., Cho, J.-M., & Choi, C.-H. (2016). Effect of fiber orientation on acoustic and vibration response of a carbon fiber/epoxy composite plate: Natural vibration mode and sound radiation. International Journal of Mechanical Sciences, 117, 162–173. https://doi.org/10.1016/j.ijmecsci.2016.08.023
Liu, Y., & Shu, D. (2014). Free vibration of delaminated beams with an edge crack. Procedia Engineering, 75, 78–82. https://doi.org/10.1016/j.proeng.2013.11.016
Luo, H., & Hanagud, S. (1996). Delamination modes in composite plates. Journal of Aerospace Engineering, 9(4), 106–113. https://doi.org/10.1061/(ASCE)0893-1321(1996)9:4(106)
Mallik, P. K. S., & Rao, D. S. (2017). Vibration control on composite beams with multiple piezoelectric patches using finite element analysis. International Research Journal of Engineering and Technology, 7(4), 906–911.
Mehar, K., Panda, S. K., Dehengia, A., & Kar, V. R. (2016). Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment. Journal of Sandwich Structures & Materials, 18(2), 151–173. https://doi.org/10.1177/1099636215613324
Mohammed, D. (2017). Effect of fiber angles on dynamic response of cantilever composite beams. ZANCO Journal of Pure and Applied Sciences, 29(1), 157–163.
Mujumdar, P. M., & Suryanarayan, S. (1988). Flexural vibrations of beams with delaminations. Journal of Sound and Vibration, 125(3), 441–461. https://doi.org/10.1016/0022-460X(88)90253-2
Odegard, G. M., Gates, T. S., Wise, K. E., Park, C., & Siochi, E. J. (2003). Constitutive modeling of nanotube-reinforced polymer composites. Composites Science and Technology, 63(11), 1671–1687. https://doi.org/10.1016/S0266-3538(03)00063-0
Penn, L. S., Chiao, T. T., & Chou, T. W. (1989). The effect of matrix shrinkage on damage accumulation in composites. Journal of Composite Materials, 23(6), 570–586. https://doi.org/10.1177/002199838902300603
Pingulkar, P., & Suresha, B. (2016). Free vibration analysis of laminated composite plates using finite element method. Polymers & Polymer Composites, 24(7), 529–538. https://doi.org/10.1177/096739111602400712
Reif, J., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z., & Koratkar, N. (2009). Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884–3890. https://doi.org/10.1021/nn9010472
Sadeghpour, E., Sadighi, M., & Ohadi, A. (2016). Free vibration analysis of a debonded curved sandwich beam. European Journal of Mechanics - A/Solids, 57, 71–84. https://doi.org/10.1016/j.euromechsol.2015.11.006
Sharma, A., Sharma, A. K., Raghav, A. K., & Kumar, V. (2016). Vibrational study of square plate with thermal effect and circular variation in density. Romanian Journal of Acoustics and Vibration, 13(2), 146–152.
Shen, M.-H., & Grady, J. E. (1992). Free vibrations of delaminated beams. AIAA Journal, 30(5), 1361–1370. https://doi.org/10.2514/3.11072
Shu, D. (1995). Vibration of sandwich beams with double delaminations. Composites Science and Technology, 54(1), 101–109. https://doi.org/10.1016/0266-3538(95)00050-X
Shu, D., & Della, C. N. (2004). Vibrations of multiple delaminated beams. Composite Structures, 64(3-4), 467–477. https://doi.org/10.1016/j.compstruct.2003.09.047
Shukla, A., & Harsha, S. P. (2016). Vibration response analysis of last stage LP turbine blades for variable size of crack in root. Procedia Technology, 23, 232–239. https://doi.org/10.1016/j.protcy.2016.03.022
Thostenson, E. T., Ren, Z., & Chou, T.-W. (2001). Advances in the science and technology of carbon nanotubes and their composites: A review. Composites Science and Technology, 61(13), 1899–1912. https://doi.org/10.1016/S0266-3538(01)00094-X
Tsai, K. H., Hwan, C. L., Lin, M. J., Lo, C. C., & Hwang, J. L. (2017). Free vibration of braided composite plates with a center hole. China Mechanical Engineering Journal, 38(2), 135–144.
Tseng, H. C., Chang, R. Y., & Hsu, C. H. (2017). Numerical prediction of fiber orientation and mechanical performance for short/long glass and carbon fiber-reinforced composites. Composites Science and Technology, 144, 51–56. https://doi.org/10.1016/j.compscitech.2017.02.020
Vo, T. P., Thai, H. T., & Aydogdu, M. (2017). Free vibration of axially loaded composite beams using a four-unknown shear and normal deformation theory. Composite Structures, 178, 406–414. https://doi.org/10.1016/j.compstruct.2017.07.022
Yurddaskal, M., Ozmen, U., Kir, M., & Okutan Baba, B. (2018). The effect of foam properties on vibration response of curved sandwich composite panels. Composite Structures, 183, 278–285. https://doi.org/10.1016/j.compstruct.2017.03.059
Zhang, Z., He, M., Liu, A., Singh, H. K., Ramakrishnan, K. R., Hui, D., Shankar, K., & Morozov, E. V. (2018). Vibration-based assessment of delaminations in FRP composite plates. Composites Part B: Engineering, 144, 254–266. https://doi.org/10.1016/j.compositesb.2018.03.003
Zhang, Z., Shankar, K., Morozov, E. V., & Tahtali, M. (2016). Vibration-based delamination detection in composite beams through frequency changes. Journal of Vibration and Control, 22(2), 496–512. https://doi.org/10.1177/1077546314533584

