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Effects of edge crack on the vibration characteristics of delaminated beams

  • Liu, Yang (School of Mechanical and Aerospace Engineering, Nanyang Technological University) ;
  • Shu, Dong W. (School of Mechanical and Aerospace Engineering, Nanyang Technological University)
  • Received : 2013.03.04
  • Accepted : 2014.12.30
  • Published : 2015.02.25

Abstract

Delaminations and cracks are common failures in structures. They may significantly reduce the stiffness of the structure and affect their vibration characteristics. In the present study, an analytical solution is developed to study the effect of an edge crack on the vibration characteristics of delaminated beams. The rotational spring model, the 'free mode' and 'constrained mode' assumptions in delamination vibration are adopted. This is the first study on how an edge crack affects the vibration characteristic of delaminated beams and new nondimensional parameters are developed accordingly. The crack may occur inside or outside the delaminated area and both cases are studied. Results show that the effect of delamination length and thickness-wise location on reducing the natural frequencies is aggravated by an increasing crack depth. The location of the crack also influences the effect of delamination, but such influence is different between crack occurring inside and outside the delaminated area. The difference of natural frequencies between 'free mode' and 'constrained mode' increases then decreases as the crack moves from one side of the delaminated region to the other side, peaking at the middle. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.

Keywords

References

  1. Birman, V. and Simitses, G.J. (2001), "Vibration of sandwich panels and beams with matrix cracks in the facings", Compos. Sci. Technol., 61(11), 1605-1613. https://doi.org/10.1016/S0266-3538(01)00053-7
  2. Chondros, T.G. and Dimarogonas, A.D. (1998), "Vibration of a cracked cantilever beam", J. Vib. Acoust., 120(3), 742-746. https://doi.org/10.1115/1.2893892
  3. Chondros, T.G., Dimarogonas, A.D. and Yao, J. (1998a), "A continuous cracked beam vibration theory", J. Sound. Vib., 215(1), 17-34. https://doi.org/10.1006/jsvi.1998.1640
  4. Chondros, T.G., Dimarogonas, A.D. and Yao, J. (1998b), "Longitudinal vibration of a bar with a breathing crack", Eng. Fract. Mech., 61(5-6), 503-518. https://doi.org/10.1016/S0013-7944(98)00077-0
  5. Chondros, T.G., Dimarogonas, A.D. and Yao, J. (2001), "Vibration of a beam with a breathing crack", J. Sound. Vib., 239(1), 57-67. https://doi.org/10.1006/jsvi.2000.3156
  6. Della, C.N. and Shu, D. (2004), "Vibrations of beams with two overlapping delaminations", Compos. Struct., 66(1-4), 101-108. https://doi.org/10.1016/j.compstruct.2004.04.027
  7. Della, C.N. and Shu, D. (2005a), "Vibration of beams with double delaminations", J. Sound. Vib., 282(3-5), 919-935. https://doi.org/10.1016/j.jsv.2004.03.052
  8. Della, C.N. and Shu, D. (2005b), "Free vibration analysis of composite beams with overlapping delaminations", Eur. J. Mech. A-Solid., 24(3), 491-503.
  9. Della, C.N. and Shu, D. (2006), "Vibration of delaminated multilayer beams", Compos. Part B: Eng., 37(2-3), 227-236. https://doi.org/10.1016/j.compositesb.2005.05.006
  10. Della, C.N. and Shu, D. (2007), "Vibration of delaminated composite laminates: A review", Appl. Mech. Rev., 60(1-6), 1-20. https://doi.org/10.1115/1.2375141
  11. Della, C.N. and Shu, D. (2009), "Free vibrations of delaminated beams in prebuckled states: lower and upper Bounds", Struct. Eng. Mech., 31(1), 113-116. https://doi.org/10.12989/sem.2009.31.1.113
  12. Dimarogonas, A.D. (1996), "Vibration of cracked structures-a state of the art review", Eng. Fract. Mech., 55(5), 831-857. https://doi.org/10.1016/0013-7944(94)00175-8
  13. Fallah, N. and Mousavi, M. (2012), "An inverse approach for the calculation of flexibility coefficient of open-side cracks in beam type structures", Struct. Eng. Mech., 41(2), 285-297. https://doi.org/10.12989/sem.2012.41.2.285
  14. Gounaris, G.D., Papadopoulos, C.A. and Dimarogonas, A.D. (1996), "Crack identification in beams by coupled response measurement", Comput. Struct., 58(2), 299-305. https://doi.org/10.1016/0045-7949(95)00142-4
  15. Ibrahim, A.M., Ozturk, H. and Sabuncu, M. (2013), "Vibration analysis of cracked frame structures", Struct. Eng. Mech., 45(1), 33-52. https://doi.org/10.12989/sem.2013.45.1.033
  16. Karaagac, C., Ozturk, H. and Sabuncu, M. (2011), "Crack effects on the in-plane static and dynamic stabilities of a curved beam with an edge crack", J. Sound. Vib., 330(8), 1718-1736. https://doi.org/10.1016/j.jsv.2010.10.033
  17. Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16(6), 488-502. https://doi.org/10.1080/15376490902781175
  18. Kisa, M. (2004), "Free vibration analysis of a cantilever composite beam with multiple cracks", Compos. Sci. Technol., 64(9), 1391-1402. https://doi.org/10.1016/j.compscitech.2003.11.002
  19. Kisa, M. (2012), "Vibration and stability of axially loaded cracked beams", Struct. Eng. Mech., 44(3), 306-323.
  20. Kisa, M. and Gurel, M.A. (2005), "Modal analysis of cracked cantilever composite beams", Struct. Eng. Mech., 20(2), 143-160. https://doi.org/10.12989/sem.2005.20.2.143
  21. Kisa, M. and Gurel, M.A. (2007), "Free vibration analysis of uniform and stepped cracked beams with circular cross sections", Int. J. Eng. Sci., 45(2-8), 364-380. https://doi.org/10.1016/j.ijengsci.2007.03.014
  22. Kitipornchai, S., Ke, L.L., Yang, J. and Xiang, Y. (2009), "Nonlinear vibration of edge cracked functionally graded Timoshenko beams", J. Sound. Vib., 324(3-5), 962-982. https://doi.org/10.1016/j.jsv.2009.02.023
  23. Lee, J. (2000), "Free vibration analysis of delaminated composite beams", Comput. Struct., 74(2), 121-129. https://doi.org/10.1016/S0045-7949(99)00029-2
  24. Lee, S., Park, T., Voyiadjis, G.Z. and George, Z. (2003), "Vibration analysis of multi-delaminated beams", Compos. Part B-Eng., 34(7), 647-659. https://doi.org/10.1016/S1359-8368(03)00053-2
  25. Liu, Y. and Shu, D. (2012), "Free vibration analysis of rotating Timoshenko beams with multiple delaminations", Compos. Part B: Eng., 44(1) 733-739.
  26. Luo, H. and Hanagud, S. (2000), "Dynamics of delaminated beams", Int. J. Solid. Struct., 37(10), 1501-1519. https://doi.org/10.1016/S0020-7683(98)00325-4
  27. Mujumdar, P.M. and Suryanarayan, S. (1988), "Flexural vibrations of beams with delaminations", J. Sound. Vib., 125(3), 441-461. https://doi.org/10.1016/0022-460X(88)90253-2
  28. Parlapalli, M.R. and Shu, D. (2006), "Effects of bridging on buckling analysis of tri-layer beams with multiple delaminations", AIAA J., 44(9), 2109-2177.
  29. Parlapalli, M.R., Shu, D. and Chai, G.B. (2006), "Analytical model and numerical analysis of delamination buckling in layer beams", Diffus. De. B., 111, 75-78.
  30. Parlapalli, M.R., Shu, D. and Chai, G.B. (2008), "Buckling of composite beams with two enveloped delaminations: lower and upper bounds", Comput. Struct., 86(23-24), 2155-2165. https://doi.org/10.1016/j.compstruc.2008.06.008
  31. Pugno, N., Surace, C. and Ruotolo, R. (2000), "Evaluation of the non-linear dynamic response to harmonic excitation of a beam with several breathing cracks", J. Sound. Vib., 235(5), 749-762. https://doi.org/10.1006/jsvi.2000.2980
  32. Ramtekkar, G.S. (2009), "Free vibration analysis of delaminated beams using mixed finite element model", J. Sound. Vib., 328(4-5), 428-440. https://doi.org/10.1016/j.jsv.2009.08.008
  33. Ruotolo, R. and Surace, C. (2004), "Natural frequencies of a bar with multiple cracks", J. Sound. Vib., 272(1-2), 301-316. https://doi.org/10.1016/S0022-460X(03)00761-2
  34. Ruotolo, R., Surace, C., Crespo, P. and Storer, D. (1996), "Harmonic analysis of the vibrations of a cantilever beam with a closing crack", Comput Struct., 61(6), 1057-74. https://doi.org/10.1016/0045-7949(96)00184-8
  35. Saravanos, D.A. and Hopkins, D.A. (1996), "Effects of delaminations on the damped dynamic characteristics of composite laminates: analysis and experiments", J. Sound. Vib., 192(5), 977-993. https://doi.org/10.1006/jsvi.1996.0229
  36. Sayyad, F.B. and Kumar, B. (2012), "Identification of crack location and crack size in a simply supported beam by measurement of natural frequencies", J. Sound. Vib., 18(2), 183-190.
  37. Shifrin, E.I. and Ruotolo, R. (1999), "Natural frequencies of a beam with an arbitrary number of cracks", J. Sound. Vib., 222(3), 409-423. https://doi.org/10.1006/jsvi.1998.2083
  38. Tay, T.E. (2003), "Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001", Appl. Mech. Rev., 56(1), 1-31. https://doi.org/10.1115/1.1504848
  39. Wang, J.T.S., Liu, Y.Y. and Gibby, J.A. (1982), "Vibration of split beams", J. Sound. Vib., 84(4), 491-502. https://doi.org/10.1016/S0022-460X(82)80030-8
  40. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83(1), 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006
  41. Yang, J., Chen, Y., Xiang, Y. and Jia, X.L. (2008), "Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load", J. Sound. Vib., 312(1-2), 166-181. https://doi.org/10.1016/j.jsv.2007.10.034
  42. Zou, Y., Tong, L. and Steven, G.P. (2000), "Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures-A Review", J. Sound. Vib., 230(2) 357-378.

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