DOI QR코드

DOI QR Code

A robust identification of single crack location and size only based on pulsations of the cracked system

  • Received : 2006.05.16
  • Accepted : 2006.09.25
  • Published : 2007.04.20

Abstract

The purpose of the present work is to establish a method for predicting the location and depth of a crack in a circular cross section beam by only considering the frequencies of the cracked beam. An accurate knowledge of the material properties is not required. The crack location and size is identified by finding the point of intersection of pulsation ratio contour lines of lower vertical and horizontal modes. This process is presented and numerically validated in the case of a simply supported beam with various crack locations and sizes. If the beam has structural symmetry, the identification of crack location is performed by adding an off-center placed mass to the simply supported beam. In order to avoid worse diagnostic, it was demonstrated that a robust identification of crack size and location is possible if two tests are undertaken by adding the mass at the left and then right end of the simply supported beam. Finally, the pulsation ratio contour lines method is generalized in order to be extended to the case of rectangular cross section beams or more complex structures.

Keywords

References

  1. Adams, R., Cawley, P., Pye, C. and Stone, B. (1978), 'A vibration technique for non-destructively assessing the integrity of structures', J. Mech. Eng. Sci., 20, 93-100 https://doi.org/10.1243/JMES_JOUR_1978_020_016_02
  2. Cerri, M.N. and Vestroni, F. (2000), 'Detection of damage in beams subjected to diffused cracking', J. Sound Vib., 234(2), 259-276 https://doi.org/10.1016/0022-460X(72)90565-2
  3. Davies, W.G.R. and Mayes, I.W (1984a), 'The vibrational behaviour of a multi-shaft, multi-bearing system in the presence of a propagating transverse crack', Transactions the ASME J. Vib., Acoustics, Stress, Reliability Design, 106, 146-153 https://doi.org/10.1115/1.3269143
  4. Dilena, M. and Morassi, A (2002), 'Identification of crack location in vibrating beams from changes in node positions', J. Sound Vib., 255(5), 915-930 https://doi.org/10.1006/jsvi.2001.4194
  5. Dilena, M. and Morassi, A. (2004), 'The use of antiresonances for crack detection in beams', J. Sound Vib., 276, 195-214 https://doi.org/10.1016/j.jsv.2003.07.021
  6. Dimarogonas, A. (1996), 'Vibration of cracked structures: A state of the art review', Appl. Mech. Rev., 55, 831-857
  7. Gladwell, G. and Morassi, A .(1999), 'Estimating damage in a rod from changes in node positions', Inverse Problems Eng., 7, 215-233 https://doi.org/10.1080/174159799088027695
  8. Hadjileontiadis, L., Doukab, E. and Trochidisc, A. (2005), 'Fractal dimension analysis for crack identification in beam structures', Mech. Syst. Signal Proc., 19, 659-674 https://doi.org/10.1016/j.ymssp.2004.03.005
  9. Hearn, G. and Testa, R. (1991), 'Modal analysis for damage detection in structures', J. Struct. Eng., ASCE, 117, 3042-3063 https://doi.org/10.1061/(ASCE)0733-9445(1991)117:10(3042)
  10. Khiem, N. and Lien, T. (2004), 'Multi-crack detection for beam bythe natural frequencies', J. Sound Vib., 273, 175-184 https://doi.org/10.1016/S0022-460X(03)00424-3
  11. Kim, J.-T. and Stubbs, N. (2003), 'Crack detection in beam-type structures using frequency data', J. Sound Vib., 259(1), 145-160 https://doi.org/10.1006/jsvi.2002.5132
  12. Lalanne, M. and Ferraris, G. (1990), Rotordynamics-Prediction in Engineering. John Wiley and Sons
  13. Lees, A.W. and Friswell, M.I. (2001), 'The vibration signature of chordal cracks in asymmetric rotors', Proc. of 19th Int. Modal Analysis Conf., 1, 1-6
  14. Lele, S. and Maiti, S. (2002), 'Modeling of transverse vibration of short beams for crack detection and measurement of crack extension', J. Sound Vib., 257(3), 559-583 https://doi.org/10.1006/jsvi.2002.5059
  15. Li, B., Chen, X., Ma, J. and He, Z. (2005), 'Detection of crack location and size in structures using wavelet finite element methods', J. Sound Vib., 285,767-782 https://doi.org/10.1016/j.jsv.2004.08.040
  16. Liang, R., Choy, F. and Hu, J. (1991), 'Detection of cracks in beam structures using measurements of natural frequencies', .J Franklin Ins., 328(4), 505-518 https://doi.org/10.1016/0016-0032(91)90023-V
  17. Liang, R., Hu, J. and Choy, F. (1992), 'Theoretical study of crack-induced eigenfrequency changes on beam structures', Am. Soc. Civil Eng., J. Eng. Mech., 118(2),384-396 https://doi.org/10.1061/(ASCE)0733-9399(1992)118:2(384)
  18. Mayes, l.W and Davies, W.G.R. (1976), 'The vibrational behaviour of a rotating shaft system containing a transverse crack', IMechE Conf. on Vibrations in Rotating Machinery, Cambridge, United Kingdom, 1, 53-64
  19. Mayes, I.W. and Davies, W,G,R. (1984b), 'Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor', Transactions the ASME J Vib., Acoustics, Stress, and Reliability Design, 106, 139-145 https://doi.org/10.1115/1.3269142
  20. Mayes, I.W. and Davies, W,G,R. (1984b), 'Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor', Transactions the ASME J Vib., Acoustics, Stress, and Reliability Design, 106, 139-145 https://doi.org/10.1115/1.3269142
  21. Morassi, A. (2001), 'Identification of a crack on a rod based on changes in a pair of natural frequencies', J. Sound Vib., 242(4), 577-596
  22. Nahvi, H. and Jabbari, M. (2005), 'Crack detection in beams using experimental modal data and finite element model',Int. J. Mech. Sci., 47,1477-1497 https://doi.org/10.1016/j.ijmecsci.2005.06.008
  23. Narkis, Y. (1994), 'Identification of crack location in vibrating simply supported beams', J. Sound Vib., 172(4), 549-558 https://doi.org/10.1006/jsvi.1994.1195
  24. Nelson, H. and Nataraj, C. (1986), 'The dynamics of a rotor system with a cracked shaft', J. Vib., Acoustics, Stress Reliability Design, 108, 189-196 https://doi.org/10.1115/1.3269321
  25. Owolabi, G, Swamidas, A. and Seshadri, R. (2003), 'Crack detection in beams using changes in frequencies and amplitudes of frequency response functions', J. Sound Vib., 265,1-22 https://doi.org/10.1016/S0022-460X(02)01264-6
  26. Sinou, I.-I. and Lees, A.W. (2005), 'Influence of cracks in rotating shafts', J. Sound Vib., 285(4-5),1015-1037 https://doi.org/10.1016/j.jsv.2004.09.008
  27. Swamidas, A., Yang, X. and Seshadri, R. (2004), 'Identification of cracking in beam structures using Timoshenko and Euler formulations', J. Eng. Mech., 130(11), 1297-1308 https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1297)
  28. Wauer, I. (1990), 'Dynamics of cracked rotors: Literature survey', Appl. Mech. Rev., 43, 13-17 https://doi.org/10.1115/1.3119157

Cited by

  1. On the use of non-linear vibrations and the anti-resonances of Higher-Order Frequency Response Functions for crack detection in pipeline beam vol.43, 2012, https://doi.org/10.1016/j.mechrescom.2012.03.006
  2. A spectral approach for damage quantification in stochastic dynamic systems vol.88, 2017, https://doi.org/10.1016/j.ymssp.2016.11.018
  3. A Study on Health Monitoring of Structural Damages for Two Stories Model by Using Vibration Test vol.04, pp.04, 2014, https://doi.org/10.4236/ojce.2014.44030
  4. Identification of an open crack in a beam using an a posteriori error estimator of the frequency response functions with noisy measurements vol.28, pp.1, 2009, https://doi.org/10.1016/j.euromechsol.2008.02.006
  5. A new damage detection indicator for beams based on mode shape data vol.53, pp.4, 2015, https://doi.org/10.12989/sem.2015.53.4.725
  6. Crack identification in short shafts using wavelet-based element and neural networks vol.33, pp.5, 2007, https://doi.org/10.12989/sem.2009.33.5.543
  7. Study on damage detection software of beam-like structures vol.39, pp.1, 2007, https://doi.org/10.12989/sem.2011.39.1.077
  8. A simple method to detect cracks in beam-like structures vol.9, pp.4, 2007, https://doi.org/10.12989/sss.2012.9.4.335