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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 471))

Abstract

A damage identification procedure for beams under static loads is presented. Damage is modelled through a damage distribution function which determines a variation of the beam stiffness with respect to a reference condition. Using the concept of the equivalent superimposed deformation, the equations governing the static problem are recast in a Fredholm’s integral equation of the second kind in terms of bending moments. The solution of this equation is obtained through an iterative procedure as well as in closed form. The latter is explicitly dependent from the damage parameters, thus, it can be conveniently used to set-up a damage identification procedure. Some numerical results are presented both to prove the validity of the proposed solution procedure, and to show its preformance in damage identification in presence of measurement noise.

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Bibliography

  • R. D. Adams, P. Cawley, C. J. Pye, and B. J. Stone. A vibration technique for nondestructively assessing the integrity of structures. Journal of Mechanical Engineering Science, 20: 93–100, 1991.

    Article  Google Scholar 

  • M. R. Banan, M. R. Banan, and K. D. Hjelmstad. Parameter estimation of structures from static response. I computational aspects. Journal of Structural Engineering, 120: 3243–3258, 1994a.

    Article  Google Scholar 

  • M. R. Banan, M. R. Banan, and K. D. Hjelmstad. Parameter estimation of structures from static response. II numerical simulation studies. Journal of Structural Engineering, 120: 3259–3283, 1994b.

    Article  Google Scholar 

  • C. Bilello. Theoretical and experimental Investigation on Damaged Beams under Moving Systems. PhD. Thesis, Dip. Ing. Strut. e Geotec., Università degli Studi di Palermo, 2001.

    Google Scholar 

  • M. N. Cerri and F. Vestroni. Detection of damage in beams subjected to diffused cracking. Journal of Sound and Vibration, 234: 259–276, 2000.

    Article  Google Scholar 

  • P. Cornwell, S. W. Doebling, and C. R. Farrar. Application of the strain energy damage detection method to plate-like structures. Journal of Sound and Vibration, 224: 359–374, 1999.

    Article  Google Scholar 

  • C. Davini, F. Gatti, and A. Morassi. A damage analysis of steelbeams. Meccanica, 22: 321–332, 1992.

    Google Scholar 

  • M. Di Paola. A new approach for the static analysis of linear elastic redundant trusses with uncertainties. Probabilistic Engineering Mechanics, under review, 2002.

    Google Scholar 

  • M. Di Paola and C. Bilello. An integral equation for damage identification of Euler-Bernoulli beams under static loads. Journal of Engineering Mechanics, under review, 2002.

    Google Scholar 

  • G. D. Gounaris, C. A. Papadopoulus, and A. D. Dimarogonas. Crack identification in beams by coupled response measurements. Computer 6 Structures, 58: 299–302, 1996.

    Article  MATH  Google Scholar 

  • P. Hajela and F. J. Soeiro. Recent developments in damage detection based on system identification methods. Structural Optimization, 2: 1–10, 1989.

    Article  Google Scholar 

  • P. Hajela and F. J. Soeiro. Structural damage detection based on static and modal analysis. AIAA Journal, 28: 1110–1115, 1990.

    Article  Google Scholar 

  • G. Hearn and R. B. Testa. Modal analysis for damage detection in structures. Journal of Structural Engineering, 117: 1798–1803, 1993.

    Google Scholar 

  • K. D. Hjelmstad and S. Shin. Damage detection and assessment of structures from static response. Journal of Engineering Mechanics, 123: 568–576, 1997.

    Article  Google Scholar 

  • K. D. Hjelmstad, S. L. Wood, and S. J. Clark. Mutual residual energy method for parameter estimation in structures. Journal of Structural Engineering, 118: 223–242, 1991.

    Article  Google Scholar 

  • U. Lee and J. Shin. A frequency response function-based structural damage identification method. Computer e.4 Structures, 80: 117–132, 2002.

    Article  Google Scholar 

  • H. Luo and S. Hanagud. An integral equation for changes in the structural dynamics characteristics of damaged structures. Int. Journal of Solids and Structures, 34: 4557–4579, 1997.

    Article  MATH  Google Scholar 

  • A. K. Pandey, M. Biswas, and M. M. Samman. Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration, 145: 321–332, 1991.

    Article  Google Scholar 

  • C. P Ratcliffe. A frequency and curvature based experimental method for locating damage in structure. Journal of Vibration and Acoustic, 226: 1029–1042, 1999.

    Google Scholar 

  • R. P. C. Sampaio, N. M. M. Maia, and J. M. M. Silva. Damage detection using frequencyresponse-function curvature method. Journal of Sound and Vibration, 226: 1029–1042, 1999.

    Article  Google Scholar 

  • M. Sanayei and O. Onipede. Assessment of structures using static test data. AIAA Journal, 29: 1156–1179, 1991.

    Article  Google Scholar 

  • M. Sanayei and S. F. Scampoli. Structural element stiffness identification from static test data. Journal of Engineering Mechanics, 117: 1021–1036, 1991.

    Article  Google Scholar 

  • H. Sato. Free vibration of beams with abrupt changes of cross-section. Journal of Sound and Vibration, 89: 59–64, 1983.

    Article  MATH  Google Scholar 

  • Z. Y. Shi, S. S. Law, and L. M. Zhang. Structural damage localization from modal strain energy changes. Journal of Sound and Vibration, 218: 825–844, 1998.

    Article  Google Scholar 

  • S. K. Thyagarajan, M. J. Schulz, and P. F. Pai. Detecting structural damage using frequency response functions. Journal of Sound and Vibration, 210:162–170, 1998. F. G. Tricorni. Lezioni sulle Equazioni Integrali. Editore Gheroni, 1958.

    Google Scholar 

  • F. Vestroni and D. Capecchi. Damage evaluation in cracked vibrating beams using experimental frequencies and finite elements models. Journal of Vibration and Control, 2: 69–86, 1996.

    Article  Google Scholar 

  • F. Vestroni and D. Capecchi. Damage detection in beam structures based on frequency measurements. Journal of Engineering Mechanics, 126: 761–768, 2000.

    Article  Google Scholar 

  • X. Wang, N. Hu, H. Fukunga, and Z. H. Yao. Damage detection in beam structures based on frequency measurements. Engineering Structures, 23: 610–621, 2001.

    Article  Google Scholar 

  • Z. Wang, R. M. Lin, and M. K. Lim. Structural damage detection using measured FRF data. Computer Methods Applied Mechanics, 147: 187–197, 1997.

    Article  MATH  Google Scholar 

  • M. M. F. Yuen. A numerical study of the eigenparameters of damaged cantilever beam. Journal of Sound and Vibration, 103: 301–310, 1985.

    Article  Google Scholar 

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© 2003 Springer-Verlag Wien

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Di Paola, M., Bilello, C. (2003). Damage Identification of Beams Using Static Test Data. In: Davini, C., Viola, E. (eds) Problems in Structural Identification and Diagnostics: General Aspects and Applications. International Centre for Mechanical Sciences, vol 471. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2536-6_8

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  • DOI: https://doi.org/10.1007/978-3-7091-2536-6_8

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-20492-4

  • Online ISBN: 978-3-7091-2536-6

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