Experimental, analytical, and finite element vibration analyses of delaminated composite plates

Document Type : Article


Department of Mechanical Engineering, International Islamic University, Islamabad, Pakistan


The vibration of the delaminated composites concerns the structure safety and dynamic behavior of the composite structures as it can be vital in the presence of delamination. In this research paper, the finite element simulations, numerical simulations and the experimental work are combined to analyze the vibration behavior at different delamination size, different stacking sequences and different boundary conditions. The finite element analysis software packages like Ansy and Abqus are used to fetch the vibration response of carbon fiber reinforced polymer composite plate for different boundary conditions, stacking sequences and delamination sizes. Experiments are carried out to study the vibration behavior. Numerical results were obtained using the first order shear deformation theory. Rayleigh-Ritz method was used to derive the governing equations to find the natural frequencies and the results were computed using Matlab tool. The results from finite element, numerical and experimental analysis were then compared and verified that the maximum percentage of error is ignorable. It is seen that the natural frequencies of carbon fiber reinforced polymer decreased with an increase in delamination size subjected to all boundary conditions. The higher values of natural frequencies found for all sides clamped boundary conditions.


1. Shooshtari, A. and Dalir, M.A. "Nonlinear free vibration analysis of clamped circular fiber metal laminated plates", Scientia Iranica, Transactions B, Mechanical Engineering, 22(3), pp. 813-824 (2015).
2. Kamar, N.T., Drzal, L.T., Lee, A., and Askeland, P. "Nanoscale toughening of carbon fiber reinforced/ epoxy polymer composites (CFRPs) using a triblock copolymer", Polymer, 111, pp. 36-47 (2017).
3. Jiang, Z., Wen, H., and Ren, S. "Modeling delamination of FRP laminates under low velocity impact", In IOP Conference Series: Materials Science and Engineering, 242, pp. 1-7 (2017).
4. Aksencer, T. and Aydogdu, M. "Vibration of a rotating composite beam with an attached point mass", Composite Structures, 190, pp. 1-9 (2018).
5. Imran, M., Khan, R., and Badshah, S. "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, 16(1), pp. 11-21 (2019).
6. Agarwal, B.D., Broutman, L.J., and Chandrashekhara, K., Analysis and Performance of Fiber Composites, John Wiley & Sons (2017).
7. Imran, M. "Pre-stress and free vibration optimization of composite ocean current turbine blade", International Journal of Science, Engineering and Innovative Research, 3, pp. 1-5 (2015).
8. Imran, M., Khan, R., and Badshah, S. "Vibration analysis of cracked composite laminated plate", Pakistan Journal of Scientific and Industrial Research Series A: Physical Sciences, 61(2), pp. 84-90 (2018).
9. Imran, M., Khan, R., and Badshah, S. "Vibration analysis of cracked composite laminated plate and beam structures", Romanian Journal of Acoustics and Vibration, 15(1), pp. 3-13 (2018).
10. Imran, M., Khan, R., and Badshah, S. "A review on the effect of delamination on the performance of composite plate", Pakistan Journal of Scientific and Industrial Research Series A: Physical Sciences, 61(3), pp. 173-182 (2018).
11. Yelve, N.P., Mitra, M., and Mujumdar, P. "Detection of delamination in composite laminates using Lamb wave based nonlinear method", Composite Structures, 159, pp. 257-266 (2017).
12. Saghafi, H., Ghaffarian, S., Salimi-Majd, D., and Saghafi, H. "Investigation of interleaf sequence effects on impact delamination of nano-modified woven composite laminates using cohesive zone model", Composite Structures, 166, pp. 49-56 (2017).
13. Kharghani, N. and Guedes Soares, C. "Behavior of composite laminates with embedded delaminations", Composite Structures, 150, pp. 226-239 (2016).
14. Shao, D., Hu, S., Wang, Q., and Pang, F. "Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions", Composites Part B: Engineering, 108, pp. 75-90 (2017).
15. Imran, M., Khan, R., and Badshah, S. "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), pp. 1-7 (2019).
16. Venkate Gowda, C., Rajanna, N., and Udupa, N.G.S. "Investigating the effects of delamination location and size on the vibration behaviour of laminated composite beams", Materials Today: Proceedings, 4(10), pp. 10944-10951 (2017).
17. Imran, M., Badshah, S., and Khan, R. "Vibration analysis of cracked composite laminated plate: A review", Mehran University Research Journal of Engineering and Technology, 38(3), pp. 705-716 (2019).
18. Imran, M., Khan, R., and Badshah, S. "Experimental investigation of the influence of stacking sequence and delamination size on the natural frequencies of delaminated composite plate", Pakistan Journal of Scientific & Industrial Research Series A: Physical Sciences, 62(3), pp. 223-230 (2019).
19. Jadhav, V. and Bhoomkar, D.M. "Experimental and numerical FEM analysis of cracked composite cantilever beam by vibration techniques", International Journal of Engineering Science, 6(4), pp. 3347-3351 (2016).
20. Lee, S., Park, T., and Voyiadjis, G.Z. "Free vibration analysis of axially compressed laminated composite beam-columns with multiple delaminations", Composites Part B: Engineering, 33(8), pp. 605-617 (2002).
21. Luo, S.-N., Yi-Ming, F., and Zhi-Yuan, C. "Nonlinear vibration of composite beams with an arbitrary delamination", Journal of Sound and Vibration, 271, pp. 535-545 (2004).
22. Wang, J., Liu, Y., and Gibby, J. "Vibrations of split beams", Journal of Sound and Vibration, 84(4), pp. 491-502 (1982).
23. Nanda, N. and Sahu, S.K. "Free vibration analysis of delaminated composite shells using different shell theories", International Journal of Pressure Vessels and Piping, 98, pp. 111-118 (2012).
24. Yam, L.H., Wei, Z., Cheng, L., and Wong, W.O. "Numerical analysis of multi-layer composite plates with internal delamination", Computers & Structures, 82, pp. 627-637 (2004).
25. Wei, Z., Yam, L.H., and Cheng, L. "Detection of internal delamination in multi-layer composites using wavelet packets combined with modal parameter analysis", Composite Structures, 64, pp. 377-387 (2004).
26. Kim, H.S., Chattopadhyay, A., and Ghoshal, A. "Dynamic analysis of composite laminates with multiple delamination using improved layerwise theory", AIAA Journal, 41(9), pp. 1771-1779 (2003).
27. Luo, H., Hanagud, S., Luo, H., and Hanagud, S."Delaminated beam nonlinear dynamic response calculation and visualization", In 38th Structures, Structural Dynamics, and Materials Conference, pp. 490- 499 (1997).
28. Yashavantha Kumar, G.A. and Sathish Kumar, K.M. "Free vibration analysis of smart composite beam", Materials Today: Proceedings, 4(2), pp. 2487-2491 (2017).
29. Mohammed, D. "Effect of fiber angles on dynamic response of cantilever composite beam", Zanco Journal of Pure and Applied Sciences, 29(1), pp. 157-163 (2017).
30. Mallik, P.K.S. and Rao, D.S. "Vibration control on composite beams with multiple piezoelectric patches using finite element analysis", International Research Journal of Engineering and Technology (IRJET), 4(7), pp. 906-911 (2017).
31. Shukla, A. and Harsha, S.P. "Vibration response analysis of last stage LP turbine blades for variable size of crack in root", Procedia Technology, 23, pp. 232-239 (2016).
32. Yurddaskal, M., Ozmen, U., Kir, M., and Okutan Baba, B. "The effect of foam properties on vibration response of curved sandwich composite panels", Composite Structures, 183, pp. 278-285 (2018).
33. Juhasz, Z., Turcsan, T., Toth, T. B., and Szekrenyes, A. "Sensitivity analysis for frequency based prediction of crack size in composite plates with through-thewidth delamination", International Journal of Damage Mechanics, 27(6), pp. 859-876 (2017).
34. Hirwani, C.K., Patil, R.K., Panda, S.K., Mahapatra, S.S., Mandal, S.K., Srivastava, L., et al. "Experimental and numerical analysis of free vibration of delaminated curved panel", Aerospace Science and Technology, 54, pp. 353-370 (2016).
35. Sadeghpour, E., Sadighi, M., and Ohadi, A. "Free vibration analysis of a debonded curved sandwich beam", European Journal of Mechanics-A/Solids, 57, pp. 71-84 (2016).
36. Zhang, Z., He, M., Liu, A., Singh, H.K., Ramakrishnan, K.R., Hui, D., et al. "Vibration-based assessment of delaminations in FRP composite plates", Composites Part B: Engineering, 144, pp. 254-266 (2018).
37. Hirwani, C., Sahoo, S., and Panda, S. "Effect of  elamination on vibration behaviour of woven Glass/Epoxy composite plate-An experimental study", In IOP Conference Series: Materials Science and Engineering, 115, pp. 1-14 (2016).
38. Vo, T.P., Thai, H.-T., and Aydogdu, M. "Free vibration of axially loaded composite beams using a four-unknown shear and normal deformation theory", Composite Structures, 178, pp. 406-414 (2017).
39. Zhu, P., Lei, Z.X., and Liew, K.M. "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Composite Structures, 94(4), pp. 1450-1460 (2012).
40. Kumar, Y. "The Rayleigh-Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review", Journal of Vibration and Control, 24(7), pp. 1250-1227 (2017).
41. Vescovini, R., Dozio, L., D'Ottavio, M., and Polit, O. "On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates", Composite Structures, 192, pp. 460-474 (2018).
42. Oliveri, V. and Milazzo, A. "A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels", Computers and Structures, 196, pp. 263-276 (2018).
43. Sayyad, A.S. and Ghugal, Y.M. "Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature", Composite Structures, 171, pp. 486-504 (2017).
44. Ardestani, M.M., Zhang, L., and Liew, K. "Isogeometric analysis of the effect of CNT orientation on the static and vibration behaviors of CNT-reinforced skew composite plates", Computer Methods in Applied Mechanics and Engineering, 317, pp. 341-379 (2017).