Identification of damage in beam and plate structures using parameter dependent modal changes and thermographic methods

  • Z. Mróz
  • K. Dems
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 469)


The present chapter is concerned with the damage identification based on modal analysis and thermographic method.

The shift in the free frequency spectrum is considered and the additional parameter is introduced to the structure in order to increase the sensitivity to damage effect, for instance elastic or rigid support, and mass rigidly or elastically attached to a structure. The proper damage indices are introduced and their variation indicates damage location. The identification problem is next treated for a beam structure. The sensitivity analysis of free frequencies and associated modes is treated in detail and some approximate methods are discussed.

The second part of chapter is devoted to identification problem by means of measured boundary temperature in a steady-state heat conduction problem. The inverse problem is constructed by minimizing the properly defined distance norm of measured and model temperatures. The proper sensitivities of introduced identification functional with respect to translation, rotation and scale change of defect are calculated using a new class of path-dependent sensitivity integrals. Several numerical examples for a disk with a single crack-like cutout illustrate the presented approach.


Cantilever Beam Damage Index Plate Structure Damage Identification Support Position 
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.


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  1. Bicanic, N. and Chen, H. P. (1997), “Damage identification in framed structures using natural frequencies”, Int. J. Num. Meth. Eng., 40, 4451–4468MATHCrossRefGoogle Scholar
  2. Burczyński, T. and Polch, E. Z. (1994), “Path independent and boundary integral approach to sensitivity analysis and identification of cracks”, Inverse Problems in Eng. Medh, Eds. Bui et al., A. A. Balkema Publ., 355–361Google Scholar
  3. Cawley, P. and Adams, R. D. (1979), “The location of defects in structure from measurements of natural frequencies”, J. Strain Anal, 14, 49–57Google Scholar
  4. Cha, P. D., Dym, C. L. and Wong, W. C. (1998), “Identifying nodes and antynodes of complex structures with virtual elements”, J. Sound Vibr., 211, 249–264CrossRefGoogle Scholar
  5. Dems K. and Mróz Z. (1995) Shape sensitivity in mixed Dirichlet-Neumann boundary-value problems and associated class of path-independent integrals, Europ. J. Mech., A/Solids, 14,2,169–2003MATHGoogle Scholar
  6. Dems K. and Mróz Z. (1998), Sensitivity analysis and optimal design of external boundaries and interfaces for heat conduction systems, J. Thermal Stresses, 21, 461–488MathSciNetGoogle Scholar
  7. Dems K. and Mróz Z., (2001) Identification of damage in beam and plate structures using parameter dependent frequency changes, Eng. Comp., 18, 96–120MATHCrossRefGoogle Scholar
  8. Dems K., Korycki R., Rousselet B. (1997), Application of first and second-order sensitivities in domain optimization for steady conduction problems, J. Thermal Stresses, 20, 697–728MathSciNetGoogle Scholar
  9. Dems, K. and Mróz, Z. (1986), “On a class of conservation rules associated with sensitivity analysis in linear elasticity”, Int. J. Solids Struct., 22, 137–158Google Scholar
  10. Dems,.K. and Mróz, Z. (1989), “Sensitivity of buckling load and vibration frequency with respect to shape of stiffened and unstiffened plates”, Mech. Struct. Machines, 17, 431–457Google Scholar
  11. Doebling S.W. Farrar, C. R., Prime, M. B. and Sheritz, D. W. (1996), “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review”, Los Alamos Natl. Lab. Rep. LA — 13070 — MSGoogle Scholar
  12. Ewing D.J. (1984) Modal testing: theory and practice, Res. Stud. Press and J.Wiley&SonsGoogle Scholar
  13. Fox P.L. and Kapoor M.D., (1968) Rates of change of eigenvalues and eigenvectors, AIAA J., 6, 2426–2429MATHGoogle Scholar
  14. Friswell, M. I. and Mottershead, J. E. (1995), “Finite Element Model Updating in Structural. Dynamics”, Kluwer Ac. Publ.Google Scholar
  15. Friswell, M. I., Penny, J. E. T. and Garvey, S. D. (1997), “Parameter subset selection in damage location”, Inverse Prob. Eng., 5, 189–215Google Scholar
  16. Fritzen, C. P., Jennewein, D. and Kiefer, T. (1998), “Damage detection based on model updating methods”, Mech. Syst. Sign. Process., 12, 163–186CrossRefGoogle Scholar
  17. Gangadharan S.N., Nikolaidis E., Haftka R.T., (1991) Probabilistic system identification of two flexible joint models, AIAA J. 29, 1319–1326Google Scholar
  18. Garstecki, A. and Thermann, K. (1992), “Sensitivity of frames to variations of hinges in dynamic and stability problems”, Struct. Optim., 4, 108–114CrossRefGoogle Scholar
  19. Gudmundson, P. (1982), “Eigenfrequency changes of structures due to cracks, notches or other geometrical changes”, J. Mech. Phys. Solids, 30, 339–353CrossRefGoogle Scholar
  20. Hassiotis, S. and Jeong, G. D. (1993), “Assessment of structural damage from natural frequency measurements”, Comp. Struct., 40, 679–691CrossRefGoogle Scholar
  21. Hassiotis, S. and Jeong, G. D. (1995), “Identification of stiffness reduction using natural frequencies”, ASCEJ. Eng. Mech., 121, 1106–1113CrossRefGoogle Scholar
  22. Hearn, G. and Testa, R. B. (1991), “Modal analysis for damage detection in structures”, ASCE J. Struct. Eng, 117, 3042–3063Google Scholar
  23. Hinton, E. and Owen D.R.J. (1979), Introduction to Finite Element Computation, Pineridge Press, Swansea.Google Scholar
  24. Khot, N. S. and Berke, L. (1994), “A method for system identification using the optimality criteria optimization approach”, Struct. Optim., 7, 170–175CrossRefGoogle Scholar
  25. Kirsch U., (2003) A unified reanalysis approach for structural analysis, design and optimization, J. Struct. Multidisc. Optimization, 25, 67–86CrossRefGoogle Scholar
  26. Lee J., Haftka R.T., Griffin Jr. O.H., Watson L.T. and Sensmeier M.D., (1994) Detecting delaminations in a composite beam using antioptimization, Struct. Opt. 8, 93–100CrossRefGoogle Scholar
  27. Lekszycki, T. and Mróz, Z. (1983), “On optimal support reaction in viscoelastic vibrating structures”, J. Struct. Mech., 11, 67–79Google Scholar
  28. Lombardi M, Cinquini C., Contro R. and Haftka R., (1995), Antioptimization technique for designing composite structures, Proc. WCSMO-1, Goslar, Ed. N. Olhoff, G. Rozvany, p. 207–208, ElsevierGoogle Scholar
  29. Mills-Curran W.C., (1988) Calculation of eigenvector derivatives for structures with repeated eigenvalues, 26, 867–871MATHGoogle Scholar
  30. Mróz, Z. and Dems, K. (1999) “Methods of sensitivity analysis”, Handbook of Computational Solid Mechanics, Ed. M. Kleiber, Springer Verl.Google Scholar
  31. Mróz, Z. and Lekszycki, T. (1998), “Identification of damage in structures using parameter dependent modal response”, Proc. ISMA23: “Noise and Vibration Eng.”, Eds. P. Sas. K. U. Leuven, vol. I, 121–126Google Scholar
  32. Nelson R.B, (1976) Simplified calculation of eigenvector derivatives, AIAA J. 14, 1201–1205MATHMathSciNetGoogle Scholar
  33. Nikolakopoulos, P. G., Casters, D. E. and Papadopoulos C. A. (1997), “Crack identification in frame structures”, Comp. Struct., 64, 389–406MATHCrossRefGoogle Scholar
  34. Pandey, A. K. and Biswas, M. (1994), “Damage detection in structures using changes in flexibility”, J. Sound Vibr., 169, 3–17MATHCrossRefGoogle Scholar
  35. Pandey, A. K., Biswas, M. and Samman, M. M. (1991), “Damage detection from changes in curvature mode shapes”, J. Sound Vibr., 145, 321–332CrossRefGoogle Scholar
  36. Rizos, P. F., Aspragathos, N. and Dimarogonas, A. D. (1990), “Identification of crack location and magnitude in a cantilever beam from the vibration modes”, J. Sound Vibr., 138, 381–388CrossRefGoogle Scholar
  37. Sergeyev O. and Mróz Z., (2000) Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints, Comp. And Struct. 75, 167–185CrossRefGoogle Scholar
  38. Seyranian A.P., Lund E. and Olhoff N., (1994) Multiple eigenvalues in structural optimization problems, Struct. Optim. 8, 207–227CrossRefGoogle Scholar
  39. Sutter T.R., Camarda C.J., Walsh J.L. and Adelman H.M, (1988) A comparison of several methods for the calculation of vibration mode shape derivatives, AIAA J. 26, 1506–1511CrossRefGoogle Scholar
  40. Yao, G. C., Chang, K. C. and Lee, G. C. (1990), “Damage diagnosis of steel frames using vibrational signature analysis”, ASCVE J. Eng. Mech., 118, 1149–1158Google Scholar

Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Z. Mróz
    • 1
  • K. Dems
    • 2
  1. 1.Institute of Fundamental Technological ResearchWarsawPoland
  2. 2.Łódź Technical UniversityŁódźPoland

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