Structural Engineering and Mechanics

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A new crack size prediction method using damaged beam mode shape

  • Kindova-Petrova, Dimitrina D. (Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy)
  • Received : 2021.06.29
  • Accepted : 2021.08.06
  • Published : 2021.11.25
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Abstract

There are many mode shape damage localization methods but a few of them assess damage severity. In this paper a crack size prediction method using damaged beam mode shape is presented. The beam damaged sections are modelled by massless rotational springs, whose constants are calculated by the first and the second derivate of the mode shape using numerical differentiation. The method utilizes the relationship between the rotational spring constant and the size of an open single-sided crack with uniform depth in a rectangular cross section beam. The predicted crack depths are compared with the actual data from finite element models. The results obtained demonstrate that the proposed method correctly predicts the crack size in beam structures with single or multiple damages.

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References

  1. Adams, R.D., Cawley, P., Pye, C.J. and Stone, B.J. (1978), "A vibration technique for non-destructively assessing the integrity of structures", J. Mech. Eng. Sci., 20(2), 93-100. https://doi.org/10.1243/JMES_JOUR_1978_020_016_02.
  2. Allemang, R.J. and Brown, D.L. (1982), "A correlation coefficient for modal vector analysis", Proceedings of the 1st International Modal Analysis Conference, Orlando, USA, November.
  3. Barad, K.H., Sharma, D.S. and Vyas, V. (2013), "Crack detection in cantilever beam by frequency based method", Procedia Eng., 51, 770-775. https://doi.org/10.1016/j.proeng.2013.01.110.
  4. Bozyigit, B., Yesilce, Y. and Wahab, M.A. (2020), "Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures", Struct. Eng. Mech., 73(2), 109-121. http://doi.org/10.12989/sem.2020.73.2.109.
  5. Chondros, T.G. and Dimarogonas, A.D. (1980), "Identication of cracks in welded joints of complex structures", J. Sound Vib., 69(4), 531-538. https://doi.org/10.1016/0022-460X(80)90623-9.
  6. Dimarogonas, A.D. and Paipetis, S.A. (1983), Analytical Methods in Rotor Dynamics, Elsevier Applied Science, London, UK.
  7. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1996), "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review", Technical Report No. LA-13070-MS, Los Alamos National Laboratory, Los Alamos, USA.
  8. Fan, W. and Qiao, P. (2011), "Vibration-based damage identification methods: A review and comparative study", Struct. Hlth. Monit., 10(1), 83-111. https://doi.org/10.1177/1475921710365419.
  9. Hasrizam, C.M. and Fawazi, N. (2017), "Damage identification based on curvature mode shape using cubic polynomial regression and Chebyshev filters", IOP Conf. Ser.: Mater. Sci. Eng., 271(1), 012091. https://doi.org/10.1088/1757-899X/271/1/012091
  10. Ho, Y.K. and Ewins, D.J. (2000), "On the structural damage identification with mode shapes", Proceedings of Cost F3 Conference on System Identification and Structural Health Monitoring, Madrid, Spain, June.
  11. Lee, Y.S. and Chung, M.J. (2000), "A study on crack detection using eigenfrequency test data", Comput. Struct., 77(3), 327-342. https://doi.org/10.1016/S0045-7949(99)00194-7.
  12. Lieven, N.A.J. and Ewins, D.J. (1988), "Spatial correlation of modespaces: the coordinate modal assurance criterion (COMAC)", Proceedings of the 6th International Modal Analysis Conference, Hyatt Orlando, USA, February.
  13. MATLAB (2015), The MathWorks, Natick, Massachusetts, USA. https://www.mathworks.com/products/matlab.html.
  14. Mayes, R.L. (1992), "Error localization using mode shapes: an application to a two link robot arm", Proceedings of the 10th International modal Analysis Conference, San Diego, USA, February.
  15. Moughty, J.J. and Casas, J.R. (2017), "A state of the art review of modal-based damage detection in bridges: development, challenges, and solutions", Appl. Sci., 7(5), 510. https://doi.org/10.3390/app7050510.
  16. Ostachowicz, W.M. and Krawczuk, M. (1991), "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", J. Sound Vib., 150(2), 191-201. https://doi.org/10.1016/0022-460X(91)90615-Q.
  17. Pandey, A.K., Biswas, M. and Samman, M.M. (1991), "Damage detection from changes in curvature mode shapes", J. Sound Vib., 145(2), 321-332. https://doi.org/10.1016/0022-460X(91)90595-B.
  18. Petroski, H.J. (1981), "Simple static and dynamic models for the cracked elastic beam", Int. J. Fract., 17, 71-76. https://doi.org/10.1007/BF00036201.
  19. Rizos, P.F., Aspragathos, N. and Dimarogonas, A.D. (1990), "Identification of crack location and magnitude in a cantilever beam from the vibration modes", J. Sound Vib., 138(3), 381-388. https://doi.org/10.1016/0022-460X(90)90593-O.
  20. Roy, K. (2017), "Structural damage identification using mode shape slope and curvature", J. Eng. Mech., 143(9), 04017110. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001305.
  21. Rytter, A. (1993), "Vibration based inspection of civil engineering structures", Ph.D. Dissertation, Aalborg University, Aalborg.
  22. SAP2000 (2017), Computers and Structures, Walnut Creek, California, USA. https://www.csiamerica.com/products/sap2000.
  23. Sohn, H., Farrar, C.R., Hemez, F.M., Shunk, D.D., Stinemates, D.W., Nadler, B.R. and Czarnecki, J.J. (2004), "A review of structural health monitoring literature: 1996-2001", Technical Report No. LA-13976-MS, Los Alamos National Laboratory, Los Alamos, USA.
  24. Stubbs, N., Kim, J.T. and Topple, K. (1992), "An efficient and robust algorithm for damage localization in offshore platforms", Proceedings of ASCE 10th Structural Congress, San Antonio, USA, April.
  25. Tay, K.G., Kek, S.L. and Kahar, R.A. (2013), "Numerical differentiations spreadsheet calculator", Proceedings of the Seminar Kebangsaan Aplikasi Sains dan Matematik (SKASM2013), Batu Pahat, Johor, Malaysia, October.
  26. Yazdanpanah, O., Seyedpoor, S.M. and Bengar, H.A. (2015), "A new damage detection indicator for beams based on mode shape data", Struct. Eng. Mech., 53(4), 725-744. http://doi.org/10.12989/sem.2015.53.4.725.