Smart Structures and Systems

  • 제15권5호
  • /
  • Pages.1233-1252
  • /
  • 2015
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Crack identification in post-buckled beam-type structures

  • 투고 : 2013.11.04
  • 심사 : 2014.04.27
  • 발행 : 2015.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study investigates the problem of crack detection in post-buckled beam-type structures. The beam under the axial compressive force has a crack, assumed to be open and through the width. The crack, which is modeled by a massless rotational spring, divides the beam into two segments. The crack detection is considered as an optimization problem, and the weighted sum of the squared errors between the measured and computed natural frequencies is minimized by the bees algorithm. To find the natural frequencies, the governing nonlinear equations of motion for the post-buckled state are first derived. The solution of the nonlinear differential equations of the two segments consists of static and dynamic parts. The differential quadrature method along with an arc length strategy is used to solve the static part, while the same method is utilized for the solution of the linearized dynamic part and the extraction of the natural frequencies of the cracked beam. The investigation includes several numerical as well as experimental case studies on the post-buckled simply supported and clamped-clamped beams having open cracks. The results show that several parameters such as the amount of applied compressive force and boundary conditions influences the outcome of the crack detection scheme. The identification results also show that the crack position and depth can be predicted well by the presented method.

키워드

참고문헌

  1. Addessi, D., Lacarbonara, W. and Paolone, A. (2005a), "Free in-plane vibrations of highly buckled beams carrying a lumped mass", Acta Mech., 180(1-4), 133-156. https://doi.org/10.1007/s00707-005-0259-6
  2. Addessi, D., Lacarbonara, W. and Paolone, A. (2005b), "On the linear normal modes of planar pre-stressed curved beams", J. Sound Vib., 284(3-5), 1075-1097. https://doi.org/10.1016/j.jsv.2004.07.021
  3. Al-rasby, S.N. (1991), "Solution techniques in nonlinear structural analysis", Comput. Struct., 40(4), 985-993. https://doi.org/10.1016/0045-7949(91)90329-K
  4. Ashlock, D. (2006), Evolutionary computation for modeling and optimization, Springer, NY, USA.
  5. Buezas, F.S., Rosales, M.B. and Filipich, C.P. (2011), "Damage detection with genetic algorithms taking into account a crack contact model", Eng. Fract. Mech., 78(4), 695-712. https://doi.org/10.1016/j.engfracmech.2010.11.008
  6. Emam, S.A. (2009), "A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams", Compos. Struct., 90(2), 247-253. https://doi.org/10.1016/j.compstruct.2009.03.020
  7. Forde, B.W.R. and Stiemer, S.F. (1987), "Improved arc length orthogonality methods for nonlinear finite element analysis", Comput. Struct., 27(5), 625-630. https://doi.org/10.1016/0045-7949(87)90078-2
  8. Hua, Y.J, Zhu, Y.Y. and Cheng, C.J. (2008), "DQEM for large deformation analysis of structures with discontinuity conditions and initial displacements", Eng. Struct., 30(5), 1473-1487. https://doi.org/10.1016/j.engstruct.2007.10.007
  9. Huh, Y.C, Chung, T.Y, Moon, S.J, Kil, H.G. and Kim, J.K. (2011), "Damage detection in beams using vibratory power estimated from the measured accelerations", J. Sound Vib., 330(15), 3645-3665. https://doi.org/10.1016/j.jsv.2011.03.007
  10. Karaagac, C., Ozturk, H. and Sabuncu, M. (2009), "Free vibration and lateral buckling of a cantilever slender beam with an edge crack: Experimental and numerical studies", J. Sound Vib., 326(1-2), 235-250. https://doi.org/10.1016/j.jsv.2009.04.022
  11. Ke, L.L, Yang, J. and Kitipornchai, K. (2009), "Postbuckling analysis of edge cracked functionally graded timoshenko beams under end shortening", Compos. Struct., 90(2), 152-160. https://doi.org/10.1016/j.compstruct.2009.03.003
  12. Khorram, A., Bakhtiari-Nejad, F. and Rezaeian, M. (2012), "Comparison studies between two wavelet based crack detection methods of a beam subjected to a moving load", Int. J. Eng. Sci., 51, 204-215. https://doi.org/10.1016/j.ijengsci.2011.10.001
  13. Moradi, S., Razi, P. and Fatahi, L. (2011), "On the application of bees algorithm to the problem of crack detection of beam-type structures", Comput. Struct., 89(23-24), 2169-2175. https://doi.org/10.1016/j.compstruc.2011.08.020
  14. Nayfeh, A.H., Kreider, W. and Anderson, T.J. (1995), "Investigation of natural frequencies and mode shapes of buckled beams", AIAA J., 33(6), 1121-1126. https://doi.org/10.2514/3.12669
  15. Neukirch, S, Frelat, J., Goriely, A. and Maurini, C. (2012), "Vibrations of post-buckled rods: the singular inextensible limit", J. Sound Vib., 331(3), 704-720. https://doi.org/10.1016/j.jsv.2011.09.021
  16. Razi, P, Esmaeel, R.A. and Taheri, F. (2011), "Application of a robust vibration-based non-destructive method for detection of fatigue cracks in structures", Smart Mater. Struct., 20(11), 1-12.
  17. Reissner, E. (1972), "On one-dimensional finite-strain beam theory: The plane problem", J. Appl. Math. Phys., 23(5), 795-804. https://doi.org/10.1007/BF01602645
  18. Rosales, M.B, Filipich, C.P. and Buezas, F.S. (2009), "Crack detection in beam-like structures", Eng. Struct., 31(10), 2257-2264. https://doi.org/10.1016/j.engstruct.2009.04.007
  19. Roveri, N. and Carcaterra, A. (2012), "Damage detection in structures under traveling loads by Hilbert-Huang transform", Mech. Syst. Signal Pr., 28, 128-144. https://doi.org/10.1016/j.ymssp.2011.06.018
  20. Saavedra, P.N. and Cuitino, L.A. (2001), "Crack detection and vibration behavior of cracked beams", Comput. Struct., 79(16), 1451-1459. https://doi.org/10.1016/S0045-7949(01)00049-9
  21. Santillan, S.T, Virgin, L.N. and Plaut, R.H. (2006), "Post-buckling and vibration of heavy beam on horizontal or inclined rigid foundation", J. Appl. Mech., 73(4), 664-671. https://doi.org/10.1115/1.2165237
  22. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations", Int. J. Numer. Meth. Fl., 15(7), 791-798. https://doi.org/10.1002/fld.1650150704
  23. Sinha, J., Friswell, M. and Edwards, S. (2002) "Simplified models for the location of cracks in beam structures using measured vibration data", J. Sound Vib., 251(1), 13-38. https://doi.org/10.1006/jsvi.2001.3978
  24. Umesha, P.K, Ravichandran, R. and Sivasubramanian, K. (2009), "Crack detection and quantification in beams using wavelets", Comput. -Aided Civil Infrastruct. Eng., 24(8), 593-607. https://doi.org/10.1111/j.1467-8667.2009.00618.x
  25. VakilBaghmisheh, M.T., Peimani, M., Sadeghi, M.H., Ettefagh, M.M. and FakheriTabrizi, A. (2012), "A hybrid particle swarm-nelder-mead optimization method for crack detection in cantilever beams", Appl. Soft Comput., 12(8), 2217-2226. https://doi.org/10.1016/j.asoc.2012.03.030
  26. Wu, N. and Wang, Q. (2011), "Experimental studies on damage detection of beam structures with wavelet transform", J. Eng. Sci., 49(3), 253-261. https://doi.org/10.1016/j.ijengsci.2010.12.004
  27. Yazdchi, K. and GowhariAnaraki, A.R. (2008), "Carrying capacity of edge-cracked columns under concentric vertical loads", Acta Mech., 198(1-2), 1-19. https://doi.org/10.1007/s00707-007-0523-z
  28. Zhong, S. and Oyadiji, O. (2007), "Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform", Mech. Syst. Signal Pr., 21(4), 1853-1884. https://doi.org/10.1016/j.ymssp.2006.07.007

피인용 문헌

  1. Comparative analysis of image binarization methods for crack identification in concrete structures vol.99, 2017, https://doi.org/10.1016/j.cemconres.2017.04.018
  2. Updating Finite Element Model Using Stochastic Subspace Identification Method and Bees Optimization Algorithm vol.15, pp.2, 2018, https://doi.org/10.1590/1679-78254189