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Vibration of composite beams with two overlapping delaminations

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Abstract.

Delaminations in composite laminates may develop from small cracks due to fabrication and impact loading, or from places of high stress concentration. The locations of the delaminations are not determinate. In this research, an analytical solution for the free vibration of a composite beam with two overlapping delaminations is presented. The delaminated beam is analyzed as seven interconnected beams using the delaminations as their boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Classical beam theory is applied to each of the beams. Complex vibration behaviors emerge for different sizes and locations of the delaminations. Comparison with analytical results reported in the literature verifies the validity of the present solution.

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References

  1. Wang, J.T.S., Liu, Y.Y., Gibby, J.A.: Vibration of split beams. J. Sound Vib. 84(4), 491–502 (1982)

    Google Scholar 

  2. Mujumdar, P.M., Suryanarayan, S.: Flexural vibrations of beams with delaminations. J. Sound Vib. 125(3), 441–461 (1988)

    Google Scholar 

  3. Shu, D., Fan, H.: Free vibration of a bimaterial split beam. Compos Part B 27(1), 79–84 (1996)

    Google Scholar 

  4. Hu, J.S., Hwu, C.: Free vibration of delaminated composite sandwich beams. AIAA J. 33(10), 1911–1918 (1995)

    Google Scholar 

  5. Tracy, J.J., Pardoen, G.C.: Effect of delamination on the natural frequencies of composite laminates. J. Compos Mater 23(12), 1200–1215 (1989)

    Google Scholar 

  6. Valoor, M.T., Chandrashekhara, K.: A thick composite-beam model for delamination prediction by using neural networks. Compos Sci Tech 60(9), 1773–1779 (2000)

    Google Scholar 

  7. Shen, M.-H.H., Grady, J.E.: Free vibrations of delaminated beams. AIAA J. 30(5), 1361–1370 (1992)

    Google Scholar 

  8. Luo, H., Hanagud, S.: Dynamics of delaminated beams. Int. J. Sol. Strucs. 37(10), 1501–1519 (2000)

    Google Scholar 

  9. Saravanos, D.A., Hopkins, D.A.: Effects of delaminations on the damped characteristics of composite laminates: analytical and experiments. J. Sound Vib. 192(5), 977–993 (1996)

    Google Scholar 

  10. Chakraborty, A., Roy Mahapatra, D., Gopalakrishnan, S.: Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities. Compos. Struc. 55(1), 23–36 (2002)

  11. Zak, A., Krawczuk, M., Ostachowicz, W.: Numerical and experimental investigation of free vibration of multilayer delaminated composite beams and plates. Comput. Mech. 26(3), 309–315 (2000)

    Google Scholar 

  12. Zak, A., Krawczuk, M., Ostachowicz, W.: Vibration of a delaminated composite plate with closing delamination. J. Intell. Mater. Sys. Struc. 12(8), 545–551 (2001)

    Google Scholar 

  13. Chattopadhyay, A., Radu, A.G., Dragomir-Daescu, D.: A higher order theory for dynamic stability analysis of delaminated composite plates. Comput. Mech. 26(3), 302–308 (2000)

    Google Scholar 

  14. Radu, A.G., Chattopadhyay, A.: Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach. Int. J. Sol. Struc. 39(7), 1949–1965 (2002)

    Google Scholar 

  15. Hu, N., Fukunaga, H., Kameyama, M., Aramaki, Y., Chang, F.K.: Vibration analysis of delaminated composite beams and plates using higher-order finite element. Int. J. Mech. Sci. 44(7), 1479–1503 (2002)

    Google Scholar 

  16. Shu, D.: Vibration of sandwich beams with double delaminations. Compos. Sci. Tech. 54(1), 101–109 (1995)

    Google Scholar 

  17. Lestari, W., Hanagud, S.: Health monitoring of structures: multiple delamination dynamics in composite beams. In: Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference and Adaptive Structures Forum, St. Louis, MO, April 1999

  18. Lee, S., Park, T., Voyiadjis, G.Z.: Vibration analysis of multiple-delaminated beams. Compos. Part B 34(7), 647–659 (2003)

    Google Scholar 

  19. Shu, D., Della, C.N.: Vibrations of multiple delaminated beams. Compos. Struc. 64(3–4), 467–477 (2004)

    Google Scholar 

  20. Shu, D., Della, C.N.: Free vibration analysis of composite beams with two non-overlapping delaminations. Int. J. Mech. Sci. 46(4), 509–526 (2004)

    Google Scholar 

  21. Ju, F., Lee, H.P., Lee, K.H.: Free-vibration analysis of composite beams with multiple delaminations. Compos. Eng. 4(7), 715–730 (1994)

    Google Scholar 

  22. Lee, J.: Free vibration analysis of delaminated composite beams. Comput. Struct. 74(2), 121–129 (2000)

    Google Scholar 

  23. Ju, F., Lee, H.P., Lee, K.H.: Finite element analysis of free vibration of delaminated composite plates. Compos. Eng. 5(2), 195–209 (1995)

    Google Scholar 

  24. Cho, M., Kim, J.-S.: Higher-order zig-zag theory for laminated composites with multiple delaminations. J. Appl. Mech. 68(6), 869–877 (2001)

    Google Scholar 

  25. Kim, S.H., Chattopadhyay, A., Ghoshal, A.; Characterization of delamination effect on composite laminates using a new generalized layerwise approach. Comput. Struc. 81(15), 1555–1566 (2003)

    Google Scholar 

  26. Kim, S.H., Chattopadhyay, A., Ghoshal, A.: Dynamic analysis of composite laminates with multiple delaminations using improved layerwise theory. AIAA J. 41(9), 1771–1779 (2003)

    Google Scholar 

  27. Shu, D., Mai, Y.-W.: Delamination buckling with bridging. Compos. Sci. Tech. 47(1), 25–33 (1993)

    Google Scholar 

  28. Shu, D., Mai, Y.-W.: Buckling of delaminated composites re-examined. Compos. Sci. Tech. 47(1), 35–41 (1993)

    Google Scholar 

  29. Shu, D., Mai, Y.-W.: Effect of stitching on interlaminar delamination extension in composite laminates. Compos. Sci. Tech. 49(2), 165–71 (1993)

    Google Scholar 

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Correspondence to Dongwei Shu.

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Christian N Della wishes to thank Nangyang Technological University for the scholarship.

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Della, C., Shu, D. & Zhao, Y. Vibration of composite beams with two overlapping delaminations. ACTA MECH SINICA 21, 47–55 (2005). https://doi.org/10.1007/s10409-004-0006-6

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  • DOI: https://doi.org/10.1007/s10409-004-0006-6

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