eesti teaduste
akadeemia kirjastus
Proceedings of the Estonian Academy of Sciences. Physics. Mathematics
The influence of delamination on free vibrations of composite beams on Pasternak soil; pp. 220–234

Helle Hein

Free vibrations of delaminated beams resting on Pasternak soil are analysed. Differential stretching and bending–extension coupling are considered in the formulation. The influence of soil parameters, size and location of the delamination on the frequencies and mode shapes is investigated. Some numerical examples and comparisons are presented.


1. Zou, Y., Tong, L. and Steven, G. P. Vibration-based model-dependent damage(delamination) identification and health monitoring for composite structures – a review. J. Sound Vib., 2000, 230, 357–378.

2. Luo, H. and Hanagud, S. Dynamics of delaminated beams. Int. J. Solids Struct., 2000, 37, 1501–1519.

3. Ramkumar, R. L., Kulkarni, S. V. and Pipes, R. B. Free vibration frequencies of a delaminated beam. In 34th Annual Technical Conference Reinforced Plastics/Composite Institute. The Society of the Plastics Industry, 1979, 1–5. 

4. Wang, J. T. S., Liu, Y. Y. and Gibby, J. A. Vibrations of split beams. J. Sound Vib., 1982, 84, 491–502.

5. Mujumdar, P. M. and Suryanarayan, S. Flexural vibrations of beams with delaminations. J. Sound Vib., 1988, 125, 441–461.

6. Tracy, J. J. and Pardoen, G. C. Effect of delamination on the natural frequencies of composite laminates. J. Compos. Mater., 1989, 23, 1200–1215.

7. Shen, M. H. H. and Grady, J. E. Free vibrations of delaminated beams. AIAA J., 1992, 30, 1361–1370.

8. Wang, J. and Tong, L. A study of the vibration of delaminated beams using a nonlinear anti- interpenetration constraint model. Compos. Struct., 2002, 57, 483–488.

9. Brandinelli, L. and Massabo, R. Free vibrations of delaminated beam-type structures with crack bridging. Compos. Struct., 2003, 61, 129–142.

10. Shu, D. Vibration of sandwich beams with double delaminations. Compos. Sci. Technol., 1995, 54, 101–109.

11. Shu, D. and Della, C. N. Vibrations of multiple delaminated beams. Compos. Struct., 2004, 64, 467–477.

12. Lee, S., Park, T. and Voyiadjis, G. Z. Free vibration analysis of axially compressed laminated composite beam-columns with multiple delaminations. Composites Part B, 2002, 33, 605– 617.

13. Luo, S. N., Ming, F. Y. and Yuan, C. Z. Non-linear vibration of composite beams with an arbitrary delamination. J. Sound Vib., 2004, 271, 535–545.

14. Lee, J. Free vibration analysis of delaminated composite beams. Comput. Struct., 2000, 74, 121–129.

15. Vlasov, V. Z. and Leontiev, N. N. Beams, Plates and Shells on Elastic Foundation. Fizmatgiz, Moscow, 1960. 

16. Pasternak, P. L. On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants. Gosudarstvennoe Izdatel′stvo Literatury po Stroitel′stvu i Arkhitek- ture, Moscow, 1954. 

17. Coskun, I. and Engin, H. Non-linear vibrations of a beam on an elastic foundation. J. Sound Vib., 1999, 223, 335–354.

18. Chen, C. N. Vibration of prismatic beam on an elastic foundation by the differential quadrature element method. Comput. Struct., 2000, 77, 1–9.

19. Karami, G., Malekzadeh, P. and Shahpari, S. A. A DQEM for vibration of shear deformable nonuniform beams with general boundary conditions. Eng. Struct., 2003, 25, 1169–1178.

20. Eisenberger, M. Vibration frequencies for beams on variable one- and two-parameter elastic foundations. J. Sound Vib., 1994, 176, 577–584.

21. Elishakoff, I. Some unexpected results in vibration of non-homogeneous beams on elastic foundation. Chaos0 Solitons Fractals, 2001, 12, 2177–2218.

22. Alemdar, B. N. and Gülkan, P. Beams on generalized foundations: supplementary element matrices. Eng. Struct., 1997, 19, 910–920.

23. Reddy, J. N. and Miravete, A. Practical Analysis of Composite Laminates. CRC, Boca Raton, 1995. 

24. Chen, W. Q., Lü, C. F. and Bian, Z. G. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Appl. Math. Model., 2004, 28, 877–890.

25. De Rosa, M. A. and Maurizi, M. J. The influence of concentrated masses and Pasternak soil on the free vibrations of Euler beams – exact solution. J. Sound Vib., 1998, 212, 573–581.

26. Jones, R. M. A. Mechanics of Composite Materials. Taylor and Francis Inc., Philadelphia, 1999. 

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