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Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

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Abstract

In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti’s theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.

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References

  1. G. M. Owolabi, A. S. J. Swanidas and R. Seshadri, Crack detection in beams using changes in frequencies and amplitudes of frequency response function, J. Sound Vib., 265 (2003) 1–22.

    Article  Google Scholar 

  2. J. T. Kim, Y. S. Ryu, H. M. Cho and N. Stubbs, Damage identification in beam-type structures: frequency-based method vs mode-shape-based method, Eng. Struct., 25 (2003) 57–67.

    Article  Google Scholar 

  3. G. M. Dong and J. Chen, Crack identification in a rotor with an open crack, J. Mech. Sci. Technol., 23 (2009) 2964–2972.

    Article  MathSciNet  Google Scholar 

  4. K. N. Solanki and S. R. Daniewicz, Finite element analysis of plasticity-induced crack closure: an overview, Eng. Fract. Mech., 71 (2004) 149–171.

    Article  Google Scholar 

  5. V. Tvergaard, Crack growth predictions by cohesive zone model for ductile fracture, J. Mech. Phys. Solids, 52 (2004) 925–940.

    Article  MATH  Google Scholar 

  6. T. G. Chondros and A. D. Dimarogonas, Influence of a crack on the dynamic characteristics of structures, Journal of Vibration, Acoustics, Stress and Reliability in Design, 111 (1989) 251–256.

    Article  Google Scholar 

  7. R. Y. Liang, J. Hu and F. Choy, Theoretical study of crackinduced eigen frequency changes on beam structures, J. Eng. Mech., 118 (1992) 384–396.

    Article  Google Scholar 

  8. T. G. Chondros, A. D. Dimarogonas and J. Yao, A continuous cracked beam vibration theory, J. Sound Vib., 215 (1998) 17–34.

    Article  MATH  Google Scholar 

  9. O. S. Salawu, Detection of structural damage through changes in frequencies: a review, Eng. Struct., 19 (1997) 718–723.

    Article  Google Scholar 

  10. S. Chinchalkar, Detection of the crack location in beams using natural frequencies, J. Sound Vib., 247 (2001) 417–429.

    Article  Google Scholar 

  11. N. Khaji, M. Shafiei and M. Jalalpour, Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions, Int. J. Mech. Sci., 51 (2009) 667–681.

    Article  Google Scholar 

  12. A. K. Pandey and M. Biswas, Damage detection in structures using change in flexibility, J. Sound Vib., 169 (1994) 3–17.

    Article  MATH  Google Scholar 

  13. A. K. Pandey, M. Biswas and M. M. Samman, Damage detection from change in curvature mode shapes, J. Sound Vib., 145 (1991) 321–332.

    Article  Google Scholar 

  14. E. P. Carden and P. Fanning, Vibration based condition monitoring: a review, Structural Health Monitoring, 3 (2004) 355–377.

    Article  Google Scholar 

  15. C. R. Farrar and N. Lieven, Damage prognosis: the future of structural health monitoring, Philosophical Transactions of the Royal Society, 365 (2007) 623–632.

    Article  Google Scholar 

  16. M. Kisa and M. A. Gurel, Modal analysis of multi-cracked beams with circular cross section, Eng. Fract. Mech., 73 (2006) 963–977.

    Article  Google Scholar 

  17. H.-I. Yoon, I.-S. Son and S.-J. Ahn, Free vibration analysis of Euler-Bernoulli beam with double cracks, J. Mech. Sci. Technol., 21 (2007) 476–485.

    Article  Google Scholar 

  18. A. S. Sekhar, Multiple cracks effects and identification, Mech. Syst. Sig. Process, 22 (2008) 845–878.

    Article  Google Scholar 

  19. A. C. Chasalevris and C. A. Papadopoulos, Coupled horizontal and vertical bending vibrations of a stationary shaft with two cracks, J. Sound Vib., 309 (2008) 507–528.

    Article  Google Scholar 

  20. S. Caddemi and I. Calio, Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks, J. Sound Vib., 327 (2009) 473–489.

    Article  Google Scholar 

  21. M. Shafiee and N. Khaji, Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject to a concentrated moving load, Acta Mechanica, 221 (2011) 79–97.

    Article  Google Scholar 

  22. S. Caddemi and I. Caliò, The influence of the axial force on the vibration of the Euler-Bernoulli beam with an arbitrary number of cracks, Arch. Appl. Mech., 82 (2012) 827–839.

    Article  Google Scholar 

  23. A. C. Chasalevris and C. A. Papadopoulos, Identification of multiple cracks in beams under bending, Mech. Syst. Sig. Process, 20 (2006) 1631–1673.

    Article  Google Scholar 

  24. H. F. Lam, C. T. Ng and M. Veidt, Experimental characterization of multiple cracks in a cantilever beam utilizing transient vibration data following a probabilistic approach, J. Sound Vib., 305 (2007) 34–49.

    Article  Google Scholar 

  25. B. Faverjon and J. J. Sinou, Robust damage assessment of multiple cracks based on the frequency response function and the Constitutive Relation Error updating method, J. Sound Vib., 312 (2008) 821–837.

    Article  Google Scholar 

  26. R. J. Lin and F. P. Cheng, Multiple crack identification of a free-free beam with uniform material property variation and varied noised frequency, Eng. Struct., 30 (2008) 909–929.

    Article  Google Scholar 

  27. J. Lee, Identification of multiple cracks in a beam using natural frequencies, J. Sound Vib., 320 (2009) 482–490.

    Article  Google Scholar 

  28. S. Moradi and M. H. Kargozarfard, On multiple crack detection in beam structures, J. Mech. Sci. Technol., 27 (2013) 47–55.

    Article  Google Scholar 

  29. E. Khanmirza, N. Khaji and V. Johari Majd, Model updating of multistory shear buildings for simultaneous identification of mass, stiffness and damping matrices using two different soft-computing methods, Expert Syst. Appl., 38 (2011) 5320–5329.

    Article  Google Scholar 

  30. R. Perera, A. Ruiz and C. Manzano, An evolutionary multiobjective framework for structural damage localization and quantification, Eng. Struct., 29 (2007) 2540–2550.

    Article  Google Scholar 

  31. J. Xiang, Y. Zhong, X. Chen and Z. He, Crack detection in a shaft by combination of wavelet-based elements and genetic algorithm, Int. J. Solids Struct., 45 (2008) 4782–4795.

    Article  MATH  Google Scholar 

  32. M. T. Vakil-Baghmisheh, M. Peimani, M. H. Sadeghi and M. M. Ettefagh, Crack detection in beam-like structures using genetic algorithms, Appl. Soft Comput., 8 (2008) 1150–1160.

    Article  Google Scholar 

  33. M. Mehrjoo, N. Khaji, H. Moharrami and A. Bahreininejad, Damage detection of truss bridge joints using artificial neural networks, Expert Syst. Appl., 35 (2008) 1122–1131.

    Article  Google Scholar 

  34. S. Suresh, S. N. Omkar, R. Ganguli and V. Mani, Identification of crack location and depth in a cantilever beam using a modular neural network approach, Smart Mater. Struct., 13 (2004) 907–915.

    Article  Google Scholar 

  35. I. Karimi, N. Khaji, M. T. Ahmadi and M. Mirzayee, System identification of concrete gravity dams using artificial neural networks based on a hybrid FE-BE approach, Eng. Struct., 32 (2011) 3583–3591.

    Article  Google Scholar 

  36. M. Skrinar and T. Pliberšek, On the derivation of symbolic form of stiffness matrix and load vector of a beam with an arbitrary number of transverse cracks, Comput. Mater. Sci., 52 (2012) 253–260.

    Article  Google Scholar 

  37. B. Biondi and S. Caddemi, Euler-Bernoulli beams with multiple singularities in the flexural stiffness, Eur. J. Mech. A. Solids, 26 (2007) 789–809.

    Article  MATH  MathSciNet  Google Scholar 

  38. S. Caddemi and I. Calio, The exact explicit dynamic stiffness matrix of multi-cracked Euler-Bernoulli beam and applications to damaged frame structures, J. Sound Vib., 332 (2013) 3049–3063.

    Article  Google Scholar 

  39. W. M. Ostachowicz and M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beam, J. Sound Vib., 150 (1991) 191–201.

    Article  Google Scholar 

  40. C. K. Wang, Intermediate structural analysis, McGraw-Hill, Singapore (1983).

    Google Scholar 

  41. O. C. Zienkiewicz and R. L. Taylor, The finite element method, Butterworth and Heinmann (2000).

    MATH  Google Scholar 

  42. S. Timoshenko, D. H. Young and W. Weaver, Vibration problems in engineering, Wiley, New York (1974).

    Google Scholar 

  43. M. Krawczuk, A. Zak and W. Ostachowicz, Elastic beam finite element with a transverse elasto-plastic crack, Finite Elem. Anal. Des., 34 (2000) 61–73.

    Article  MATH  Google Scholar 

  44. R. Ruotolo and C. Surace, Damage assessment of multiple cracked beams: Numerical results and experimental validation, J. Sound Vib., 206 (1997) 567–588.

    Article  Google Scholar 

  45. D. E. Goldberg, Genetic algorithms in search, Optimization, and Machine Learning, Addison-Wesley (1989).

    MATH  Google Scholar 

  46. R. L. Haupt and S. E. Haupt, Practical genetic algorithms, 2nd ed., John Wiley and Sons (2004).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran

    N. Khaji

  2. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    M. Mehrjoo

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  1. N. Khaji
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  2. M. Mehrjoo
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Correspondence to N. Khaji.

Additional information

Recommended by Editor Yeon June Kang

Naser Khaji is Associate Professor of Earthquake Engineering at TarbiatModares University, Tehran, Iran, since 2002 where he has been teaching Advanced Engineering Mathematics, Seismic Hazard Analysis, FEM, and BEM. He earned his B.Sc. degree in Civil Engineering from Tehran University, Iran, in 1995, his M.Sc. degree in Hydraulic Structures from Tarbiat Modares University, Iran, in 1998, andhis Ph.D. degree in Earthquake Engineering from the University ofTokyo, Japan, in 2001. Dr. Khaji has published more than 35 papers in peer-reviewed national and international journals, and numerous conference articles. Dr. Khaji’s research interests include: Computational Mechanics, Fluid-Soil-Structure Interaction, Engineering Seismology, Earthquake Engineering, and Health Monitoring of Structures.

Mohsen Mehrjoo obtained his M.Sc. degree in Earthquake Engineering from Tarbiat Modares University, Tehran, Iran, in 2006. He is now a Ph.D. student at Islamic Azad University, Tehran, Iran, where he is studying Structural Engineering. Mr. Mehrjoohas published twopapers in peer-reviewed international journals, and a few conference articles.

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Khaji, N., Mehrjoo, M. Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms. J Mech Sci Technol 28, 823–836 (2014). https://doi.org/10.1007/s12206-013-1147-y

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  • DOI: https://doi.org/10.1007/s12206-013-1147-y

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