Perturbation Methods for Damaged Structures

  • Srinivasan Gopalakrishnan
  • Massimo Ruzzene
  • Sathyanarayana Hanagud
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)


In this chapter, analysis methods for notch type and line type defects are presented, which are based on perturbation techniques. The line defect could be a horizontal crack (through width delamination) or through width vertical crack (fiber breaks). Modeling of some of these defects were addressed in the last chapter and the methods presented here represent another approach to the simplified modeling of these defects.


Mode Shape Line Defect Curvature Mode Damage Extent ABAQUS Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Atluri SN (1986) Computational methods in the mechanics of fracture. North Holland, AmsterdamMATHGoogle Scholar
  2. 2.
    Christides S, Barr ADS (1984) One-dimensional theory of cracked Euler–Bernoulli beams. Int J Mech Sci 26(11-12):639–648CrossRefGoogle Scholar
  3. 3.
    Doebling SW, Farrar C, Prime MB, Daniel WS (1996) Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review, LA-13070-MS, May 1996Google Scholar
  4. 4.
    Doyle JF (1997) Wave propagation in structures. Springer, New YorkMATHCrossRefGoogle Scholar
  5. 5.
    Gudmundson P (1984) The dynamic behavior of slender structures with cross-sectional cracks. J Mech Phys Solids 31: 329–345CrossRefGoogle Scholar
  6. 6.
    Haisty BS, Springer WT (1988) A general beam element For use in damage assessment of complex structures. ASME J Vib Acoust Stress Reliab Des 110:356–359Google Scholar
  7. 7.
    Hellan K (1984) Introduction To fracture mechanics. McGraw-Hill, New YorkGoogle Scholar
  8. 8.
    Hu N et al (2001) Damage assessment of structures using modal test data. Int J Solids Struct 38:3111–3126Google Scholar
  9. 9.
    Jones DS (1982) The theory of generalized functions. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  10. 10.
    Kim JT, Stubbs N (2001) Crack detection in beam type structures using frequency data. J Sound Vib 259(1):146–160Google Scholar
  11. 11.
    Krawczuk M (2002) A rectangular plate finite element with an open crack. Comput. StructGoogle Scholar
  12. 12.
    Krawczuk M (2005) Application of spectral beam finite element with a crack and iterative search technique for damage detection. Finite Elem Anal Des 38(6):537–548CrossRefGoogle Scholar
  13. 13.
    Krawczuk M, Ostachowicz W (2002) Identification of delamination in composite beams by genetic algorithm. Sci Eng Compos Mater 10(2):147–155CrossRefGoogle Scholar
  14. 14.
    Krawczuk M, Ostachowicz W (1995) Modelling and vibration analysis of a cantilever composite beam with a transverse open crack. J Sound Vib 183(1):69–89MATHCrossRefGoogle Scholar
  15. 15.
    Krawczuk M, Palacz M, Ostachowicz W (2004) Wave propagation in plate structures for crack detection. Finite Elem Anal Des 40(9–10): 991–1004CrossRefGoogle Scholar
  16. 16.
    Leissa A (1993) Vibration of plates Acoustical Society of America, WashingtonGoogle Scholar
  17. 17.
    Lestari W (2001) Damage of composite structures: detection technique, Dynamic response and residual strength, Ph.D. Thesis, Georgia Institute of Technology, July 2001Google Scholar
  18. 18.
    Luo H, Hanagud S (1997) An integral equation for changes in the structural characteristics of damaged structures. International Journal of Solids and Structures 34(35-36): 4557–4579Google Scholar
  19. 19.
    Ostachowicz W, Krawczuk M (1990) Analysis of the effect of cracks on the natural frequencies of a cantilever beam. J Sound Vib 138:115–134CrossRefGoogle Scholar
  20. 20.
    Qian GL, Gu SN, Jiang JS (1991) The dynamic behavior AN crack detection of a beam with a crack. J Sound Vib 138:233–243CrossRefGoogle Scholar
  21. 21.
    Sharma VK, Ruzzene M, Hanagud S (2006) Perturbation methods for the analysis of the dynamic behavior of damaged plates. Inter J Solids Struct 43:4648–4672MATHCrossRefGoogle Scholar
  22. 22.
    Shen MH, Pierre C (1990) Natural modes of Euler–Bernoulli beams with symmetric cracks. J Sound Vib 138: 115–134CrossRefGoogle Scholar
  23. 23.
    Staszewski WJ, Boller C, Tomlinson G (2004) Health monitoring of aerospace structures smart sensors and signal processing. Wiley, ChichesterGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Srinivasan Gopalakrishnan
    • 1
  • Massimo Ruzzene
    • 2
  • Sathyanarayana Hanagud
    • 3
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.School of Aerospace Engineering, School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations