Skip to main content
SpringerLink
Log in
Book cover

Dynamics of Civil Structures, Volume 4 pp 207–217Cite as

Nonlinear Harmonic Identification of Cracks in Structures

  • Conference paper
  • First Online:

Abstract

The dynamic behavior of structures with breathing cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. Since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique is developed based on such a dependency. The main advantage of the proposed method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. In this paper the identification is tested against structure of increasing complexity to evaluate the applicability of the method to engineering applications. In particular, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Rizos PF, Aspragathos N, Dimarogonas AD (1990) Identification of crack location and magnitude in a cantilever beam from the vibration modes. J Sound Vib 138(3):381–388

    Article  Google Scholar 

  2. Shen MHH, Chu YC (1992) Vibrations of beams with a fatigue crack. Comput Struct 45(1):79–93

    Article  Google Scholar 

  3. Chu YC, Shen MHH (1992) Analysis of forced bilinear oscillators and the application to cracked beam dynamics. J Am Inst Aeronaut Astronaut 30(10):2512–2519

    Article  MATH  Google Scholar 

  4. Morassi A (1993) Crack-induced changes in eigenparameters of beam structures. J Eng Mech 119(9):1798–1803

    Article  Google Scholar 

  5. Vestroni F, Capecchi D (1996) Damage evaluation in cracked vibrating beams using experimental frequencies and finite element models. J Vib Control 2:69–86

    Article  Google Scholar 

  6. Chati M, Rand R, Mukherjee SJ (1997) Modal analysis of a cracked beam. J Sound Vib 207:249–270

    Article  MATH  Google Scholar 

  7. Matveev VV, Bovsunvsky AP (2002) Vibration-based diagnostics of fatigue damage of beam-like structures. J Sound Vib 249(1):23–40

    Article  Google Scholar 

  8. Sinha JK, Friswell MI, Edwards S (2002) Simplified models for the location of cracks in beam structures using measured vibration data. J Sound Vib 251:13–38

    Article  Google Scholar 

  9. Morassi A, Vestroni F (2008) Dynamic methods for damage detection in structures. Springer, New York, ISBN: 3211787763

    Book  MATH  Google Scholar 

  10. Kisa M, Brandon JA (2000) The effects of closure of cracks on the dynamics of a cracker cantilever beam. J Sound Vib 238(1):1–18

    Article  Google Scholar 

  11. Nandi A, Neogy S (2002) Modelling of a beam with a breathing edge crack and some observations for crack detection. J Vib Control 8(5): 673–693

    Article  MATH  Google Scholar 

  12. Yan AM, Kerschen G, De Boe P, Golinval JC (2005) Structural damage diagnosis under changing environmental conditions, Part II: local PCA for nonlinear cases. Mech Syst Signal Process 19:847–864

    Article  Google Scholar 

  13. Bovsunovsky AP, Surace C (2005) Considerations regarding superharmonic vibrations of a cracked beam and the variation in damping caused by the presence of the crack. J Sound Vib 288:865–886

    Article  Google Scholar 

  14. Andreaus U, Casini P, Vestroni F (2005) Nonlinear features in the dynamic response of a cracked beam under harmonic forcing. In: Proceedings of IDETC/CIE 2005, ASME 2005 international design engineering technical conferences & computers and information in engineering conference, vol 1, Long Beach, 24–28 September 2005, pp 1–7. ISBN: 9780791847404

    Google Scholar 

  15. Bovsunovsky AP, Bovsunovsky O (2007) Crack detection in beams by means of the driving force parameters variation at nonlinear resonance vibrations. Key Eng Mater 347:413–420

    Article  Google Scholar 

  16. Andreaus U, Casini P, Vestroni F (2007) Nonlinear dynamics of a cracked cantilever beam under harmonic excitation. Int J Non-Linear Mech 42(3):566–575

    Article  Google Scholar 

  17. Chatterjee A (2009) Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions. J Sound Vib 329(16):3325–3334. doi:10.1016/j.jsv.2010.02.026

    Article  Google Scholar 

  18. Semperlotti F, Wang KW, Smith EC (2009) Localization of a breathing crack using super-harmonic signals due to system nonlinearity. AIAA J 47(9):2076–2086

    Article  Google Scholar 

  19. Andreaus U, Baragatti P (2011) Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. J Sound Vib 330:721–742

    Article  Google Scholar 

  20. Casini P, Giannini O, Vestroni F (2012) Persistent and ghost nonlinear normal modes on the forced response of non-smooth systems. Physica D 241:2058–2067

    Article  MathSciNet  Google Scholar 

  21. Sinou J-J (2012) On the use of non-linear vibrations and the anti-resonances of higher-order frequency response functions for crack detection in pipeline beam. Mech Res Commun 43:87–95

    Article  Google Scholar 

  22. Nayfeh AH, Mook T (1995) Nonlinear oscillations. Wiley, New York, ISBN: 0471121428

    Book  Google Scholar 

  23. Tsyfansky SL, Beresnevich VI (2000) Non-linear vibration method for detection of fatigue cracks in aircraft wings. J Sound Vib 236:49–60

    Article  MATH  Google Scholar 

  24. Benfratello S, Cacciola P, Impollonia N, Masnata A, Muscolino G (2007) Numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under Gaussian excitation. Eng Fract Mech 74:2992–3001

    Article  Google Scholar 

  25. Andreaus U, Baragatti P (2012) Experimental damage detection of cracked beams by using nonlinear characteristics of forced response. Mech Syst Signal Process 31:382–404

    Article  Google Scholar 

  26. O. Giannini, P. Casini, F. Vestroni (2013) Nonlinear harmonic identification of breathing cracks in beams. Comput Struct 129:166–177, ISSN 0045-7949, http://dx.doi.org/10.1016/j.compstruc.2013.05.002

    Google Scholar 

  27. Zuo L, Currier A (1994) Non-linear real and complex modes of conewise linear systems. J Sound Vib 174:289–313

    Article  MATH  Google Scholar 

  28. Giannini O, Casini P, Vestroni F (2013) Nonlinear harmonic identification of breathing cracks in beams, Computers Structures, 129:166-177 http://dx.doi.org/10.1016/j.compstruc.2013.05.002.

    Article  Google Scholar 

  29. Casini P, Vestroni F (2011) Characterization of bifurcating nonlinear normal modes in piecewise linear mechanical systems. Int J Non-Linear Mech 46:142–150

    Article  Google Scholar 

  30. Kam TY, Lee TY (1992) Detection of cracks in structures using modal test data. Eng Fract Mech 42(2):381–387

    Article  Google Scholar 

Download references

Acknowledgment

This research was partially supported by the FY-2009/10 Grant PRIN 2009.

Author information

Authors and Affiliations

  1. Università degli Studi Niccolò Cusano, Via Don Carlo Gnocchi 3, 00166, Roma, Italy

    Oliviero Giannini

  2. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “la Sapienza”, Via Eudossiana 18, 00184, Roma, Italy

    Oliviero Giannini, Paolo Casini & Fabrizio Vestroni

Authors
  1. Oliviero Giannini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paolo Casini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fabrizio Vestroni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oliviero Giannini .

Editor information

Editors and Affiliations

  1. Engineering Department, University of Central Florida, Orlando, Florida, USA

    Fikret Necati Catbas

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Giannini, O., Casini, P., Vestroni, F. (2014). Nonlinear Harmonic Identification of Cracks in Structures. In: Catbas, F. (eds) Dynamics of Civil Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04546-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04546-7_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04545-0

  • Online ISBN: 978-3-319-04546-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation