### Numerical and experimental studies for crack detection of a beam-like structure using element stiffness index distribution method

#### Abstract

In this paper, numerical and experimental studies for crack detection of structures using "element stiffness index distribution" are presented. The element stiffness index distribution is defined as a vector of norms of sub-matrices corresponding to element stiffness matrices calculated from the reconstructed global stiffness matrix of the beam. When there is a crack at an element, the element stiffness index of that element will be changed. By inspecting the change in the element stiffness index distribution, the crack can be detected. A significant peak in the element stiffness index distribution is the indicator of the crack existence. The crack location is determined by the location of the peak and the crack depth can be determined from the height of the peak. The global stiffness matrix is calculated from the measured frequency response functions instead of mode shapes to avoid limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of beam-like structures are provided. The experiment is carried out to justify the efficiency of the proposed method.

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A. D. Dimarogonas. Vibration of cracked structures: a state of the art review. Engineering Fracture Mechanics, 55, (5), (1996), pp. 831–857. doi:10.1016/0013-7944(94)00175-8.

T. G. Chondros and A. D. Dimarogonas. Identification of cracks in welded joints of complex structures. Journal of Sound and Vibration, 69, (4), (1980), pp. 531–538. doi:10.1016/0022-460x(80)90623-9.

R. Y. Liang, J. Hu, and F. Choy. Theoretical study of crack-induced eigenfrequency changes on beam structures. Journal of Engineering Mechanics, 118, (2), (1992), pp. 384–396. doi:10.1061/(asce)0733-9399(1992)118:2(384).

J. Hu and R. Y. Liang. An integrated approach to detection of cracks using vibration characteristics. Journal of the Franklin Institute, 330, (5), (1993), pp. 841–853. doi:10.1016/0016-0032(93)90080-e.

R. Ruotolo and C. Surace. Damage assessment of multiple cracked beams: numerical results and experimental validation. Journal of Sound and Vibration, 206, (4), (1997), pp. 567–588. doi:10.1006/jsvi.1997.1109.

M.-H. H. Shen and J. E. Taylor. An identification problem for vibrating cracked beams. Journal of Sound and Vibration, 150, (3), (1991), pp. 457–484. doi:10.1016/0022-460x(91)90898-t.

J. Lee. Identification of multiple cracks in a beam using natural frequencies. Journal of Sound and Vibration, 320, (3), (2009), pp. 482–490. doi:10.1016/j.jsv.2008.10.033.

J. A. Loya, L. Rubio, and J. Fernandez-Saez. Natural frequencies for bending vibrations of Timoshenko cracked. Journal of Sound and Vibration, 290, (3), (2006), pp. 640–653. doi:10.1016/j.jsv.2005.04.005.

M. Kisa, J. Brandon, and M. Topcu. Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods. Computers & Structures, 67, (4), (1998), pp. 215–223. doi:10.1016/s0045-7949(98)00056-x.

A. K. Pandey, M. Biswas, and M. M. Samman. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 145, (2), (1991), pp. 321–332. doi:10.1016/0022-460x(91)90595-b.

M. M. A. Wahab and G. De Roeck. Damage detection in bridges using modal curvatures: application to a real damage scenario. Journal of Sound and Vibration, 226, (2), (1999), pp. 217–235. doi:10.1006/jsvi.1999.2295.

S. Zhong and S. O. Oyadiji. Detection of cracks in simply-supported beams by continuous wavelet transform of reconstructed modal data. Computers & Structures, 89, (1), (2011), pp. 127–148. doi:10.1016/j.compstruc.2010.08.008.

A. K. Pandey and M. Biswas. Damage detection in structures using changes in flexibility. Journal of Sound and Vibration, 169, (1), (1994), pp. 3–17. doi:10.1006/jsvi.1994.1002.

B. Jaishi and W.-X. Ren. Damage detection by finite element model updating using modal flexibility residual. Journal of Sound and Vibration, 290, (1), (2006), pp. 369–387. doi:10.1016/j.jsv.2005.04.006.

S. Caddemi and I. Calio. Exact reconstruction of multiple concentrated damages on beams. Acta Mechanica, 225, (11), (2014), pp. 3137–3156. doi:10.1007/s00707-014-1105-5.

S. Caddemi and I. Calio. The exact explicit dynamic stiffness matrix of multi-cracked Euler-Bernoulli beam and applications to damaged frame structures. Journal of Sound and Vibration, 332, (12), (2013), pp. 3049–3063. doi:10.1016/j.jsv.2013.01.003.

K. V. Nguyen and Q. V. Nguyen. Element stiffness index distribution method for multi-crack detection of a beam-like structure. Advances in Structural Engineering, 19, (7), (2016), pp. 1077–1091. doi:10.1177/1369433216634461.

P. C. Hansen. Regularization tools version 4.0 for Matlab 7.3. SIAM Numerical Algorithms, 46, (2), (2007), pp. 189–194. doi:10.1007/s11075-007-9136-9.

P. C. Hansen. The truncated SVD as a method for regularization. BIT Numerical Mathematics, 27, (4), (1987), pp. 534–553. doi:10.1007/bf01937276.

K. V. Nguyen. Mode shapes analysis of a cracked beam and its application for crack detection. Journal of Sound and Vibration, 333, (3), (2014), pp. 848–872. doi:10.1016/j.jsv.2013.10.006.

DOI: https://doi.org/10.15625/0866-7136/8422

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