Detection and Quantification of Structural Damage of a Beam-Like Structure Using Natural Frequencies
DOI: 10.4236/eng.2009.13020   PDF    HTML     5,730 Downloads   11,136 Views   Citations


Need for developing efficient non-destructive damage detection procedures for civil engineering structures is growing rapidly. This paper presents a methodology for detection and quantification of structural damage using modal information obtained from transfer matrix technique. Vibration characteristics of beam-like structure have been determined using the computer program developed based on the formulations presented in the paper. It has been noted from reported literature that detection and quantification of damage using mode shape information is difficult and further, extraction of mode shape information has practical difficulties and limitations. Hence, a methodology for detection and quantification of damage in structure using tranfer matrix technique based on the changes in the natural frequencies has been developed. With an assumption of damage at a particular segment of the beam-like structure, an iterative procedure has been formulated to converge the calculated and measured frequencies by adjusting flexural rigidity of elements and then, the intersections are used for detection and quantification of damage. Eventhough the developed methodology is iterative, computational effort is reduced considerably by using transfer matrix technique. It is observed that the methodology is capable of predicting the location and magnitude of damage quite accurately.

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S. SASMAL and K. RAMANJANEYULU, "Detection and Quantification of Structural Damage of a Beam-Like Structure Using Natural Frequencies," Engineering, Vol. 1 No. 3, 2009, pp. 167-176. doi: 10.4236/eng.2009.13020.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. M. Lifshitz and A. Rotem, “Determination of reinforcement unbonding of composites by a vibration technique,” Journal of Composite Materials, Vol. 3, pp. 412–423, 1969.
[2] P. Cawley and R.D. Adams, “The locations of defects in structures from measurements of natural frequencies,” Journal of Strain Analysis, Vol. 14, No. 2, pp. 49–57, 1979.
[3] W. M. West, “Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen,” Proceedings in Air Force Conference on Aircraft Structural Integrity, 1984.
[4] M. M. F. Yuen, “A numerical study of the eigenparameters of a damaged cantilever,” Journal of Sound and Vibration, Vol. 103, No. 3, pp. 301–310, 1985.
[5] F. Ismail, A. Ibrahim, and H.R. Martin, “Identification of fatigue cracks from vibration testing,” Journal of Sound and Vibration, Vol. 140, No. 2, pp. 305–317, 1990.
[6] P. F. Rizos, N. Aspragathos, and A.D. Dimarogonas, “Identification of crack location and magnitude in a cantilever beam from the vibration modes,” Journal of Sound and Vibration, Vol. 138, No. 3, pp. 381–388, 1990.
[7] G. Hearn, and R. G. Testa, “Modal analysis for damage detection in structures,” Journal of Structural Engineering, ASCE, Vol. 117, No. 10, pp. 3042–3063, 1991.
[8] D. Sanders, Y. I. Kim, and R.N. Stubbs, “Nondestructive evaluation of damage in composite structures using modal parameters,” Experimental Mechanics, Vol. 32, pp. 240–251, 1992.
[9] M. G. Srinivasan and C. A. Kot, “Effects of damage on the modal parameters of a cylindrical shell,” Proceedings of the 10th International Modal Analysis Conference, pp. 529–535, 1992.
[10] H. Baruh and S. Ratan, “Damage detection in flexible structures,” Journal of Sound and Vibration, Vol. 166, No. 1, pp. 21–30, 1993.
[11] G. L. Slater and S. Shelley, “Health monitoring of flexible structures using modal filter concepts,” Proceedings of the North American Conference on Smart Structures and Materials, Albuquerque, New Mexico, pp. 997–1007, 1993.
[12] Y. Narkis, “Identification of crack location in vibrating simply supported beams,” Journal of Sound and Vibration, Vol. 172, No. 4, pp. 549–558, 1994.
[13] F. K. Choy, R. Liang, and P. Xu, “Fault identification of beams on elastic foundation,” Computers and Geotechnics, Vol. 17, No. 2, pp. 157–176, 1995.
[14] C. P. Ratcliffe, “Damage detection using a modified laplacian operator on mode shape data,” Journal of Sound and Vibration, Vol. 204, No. 3, pp. 505–517, 1997.
[15] S. S. Law, Z. Y. Shi, and L. M. Zhang, “Structural damage detection from incomplete and noisy modal test data,” Journal of Engineering Mechanics, ASCE, Vol. 124, No. 11, pp. 1280–1288, 1998.
[16] Z. Y. Shi, S. S. Law, and L. M. Zhang, “Damage localization by directly using incomplete mode shapes,” Journal of Engineering Mechanics, ASCE, Vol. 126, No. 6, pp. 656–660, 2000.
[17] M. A.-B. Abdo and M. Hori, “A numerical study of structural damage detection using changes in the rotation of mode shapes,” Journal of Sound and Vibration, Vol. 251, No. 2, pp. 227–239, 2002.
[18] D. Wu and S. S. Law, “Damage localization in plate structures from uniform load surface curvature,” Journal of Sound and Vibration, Vol. 276, No. 1–2, pp. 227–244, 2004.
[19] M. K. Yoon, D. Heider, J. W. Gillespie, C. P. Ratcliffe, and R. M. Crane, “Local damage detection using the two-dimensional gapped smoothing method,” Journal of Sound and Vibration, Vol. 279, No. 1–2, pp. 119–139, 2004.
[20] A. Alvandi and C. Cremona, “Assessment of vibration-based damage identification techniques,” Journal of Sound and Vibration, Vol. 292, No. 1–2, pp. 179–202, 2006.
[21] S. Sasmal, K. Ramanjaneyulu, and N. Lakshmanan, “Transfer matrix method for identification of damage in structures using vibration characteristics,” SERC Research Report, No. RCS-RCS-MLP10741-RR-2005-2, 2005.
[22] V. Srinivas, S. Sasmal, and K. Ramanjaneyulu, “Studies on methodological developments in structural damage identification,” Structural Durability and Health Monitoring, Vol. 5, No. 2, pp. 133–160, 2009.
[23] E. G. Pestel and F. A. Leckie, Matrix Methods in Elasto-Mechanics, McGraw Hill Book Company Inc., New York, 1963.

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