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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Fatigue Cracks Detection in Rectangular Plates with Circular Hole with the Use of Elastic Waves

Discontinuity, Nonlinearity, and Complexity 6(4) (2017) 477--488 | DOI:10.5890/DNC.2017.12.006

Marek Barski; Adam Stawiarski; Piotr Pająk

Department of Mechanical Engineering, Cracow University of Technology, 37 Jana Pawła II Street, 31-864, Cracov, Poland

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The current work is devoted to the problem of fatigue cracks detection and evaluation in the case of isotropic rectangular plates with circular holes. The cutout is located in the geometrical center of the plate. The structure is subjected to the cyclic tension. It causes the formation of the fatigue cracks in the vicinity of the hole. This type of damages can be effectively detected by the analyzing of elastic waves propagation. In the presented work the propagation of the elastic waves in the vicinity of a hole is simulated with the use of the finite element method. It is assumed that the elastic waves are excited and picked up by piezoelectric sensors. The most effective position of the piezoelectric actuator is looked for while the position of the array of sensors is fixed. Four different possibilities of the location of the actuator are studied. Moreover, the advanced algorithm of crack detection and evaluation is also discussed.


  1. [1]  Rytter, A. (1993), Vibration based inspection of civil engineering structures, Ph.D. Dissertation, Department of Building Technology and Structural Engineering/ Aalborg University, Denmark.
  2. [2]  Park, G., Muntges, D.E., and Inman, D.J. (2001), Self-Monitoring and Self-Healing Jointed Structures, Damage Assessment of Structures, Key Engineering Materials, 204-205, 75-84.
  3. [3]  Achenbach, J.D. (1984),Wave propagation in elastic solids, North-Holland Publ. Co., New York.
  4. [4]  Rose, J.L., (1999), Ultrasonic waves in solid media, Cambridge University Press.
  5. [5]  Viktorov, A. (1967), Rayleigh and Lamb waves - physical theory and applications, Plenum Press, New York.
  6. [6]  Lamb, H. (1917), On waves in an elastic plate, Proceedings of the Royal Society, A Mathematical, Physical and Engineering Sciences, 93, 114-128.
  7. [7]  Lord, R. (1885), On Waves Propagated along the Plane Surface of an Elastic Solid, Proceedings of the London Mathematical Society, s1-17(1), 4-11.
  8. [8]  Su, Z. and Ye, L. (2009), Identification of damage using Lamb waves, Springer.
  9. [9]  Rose, J.L. and Avioli, M.J. (2000), Elastic waves analysis for broken rail detection, 15th World Conference on Non- Destructive Testing, Rome.
  10. [10]  Haig, A.G., Mudge, P., and Balachandran, W. (2008), Advanced transducer development for long range ultrasonic inspection systems, Proceedings of the 4th International Conference on Emerging Technologies in Non-Destructive Testing, 79-82.
  11. [11]  Li, J. and Rose, J.L. (2001), Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder, Journal of Acoustical Society of America, 109, 457-464.
  12. [12]  Diamanti, K. and Soutis, C. (2010), Structural health monitoring techniques for aircraft composite structures, Progress in Aerospace Sciences, 46(8), 342-352.
  13. [13]  Hedl, R., Finda, J., and Parthasarathy, G. (2011), Advanced approach for multi-site damage monitoring on aircraft fuselage panel using sparse PZT actuator/sensor arrays, Structural Health Monitoring, Condition Based Maintenance and Intelligent Structure - Proceedings of the 8th InternationalWorkshop on Structural Health Monitoring, 1, 643-650.
  14. [14]  Saravanos, D.A. and Heyliger, P.R. (1995), Coupled layerwise analysis of composite beams with embedded piezoelectric sensors and actuartors, Journal of Intelligent Material Systems and Structures, 6, 350 - 362.
  15. [15]  Saravanos, D.A., Birman,V. and Hopkins, D.A. (1994), Detection of delamination in composite beams using piezoelectric sensors, Proceedings of the 35th Structures, Structural Dynamics and Materials Conference of the AIAA.
  16. [16]  Wu, T.T. and Liu, Y.H. (1999), On the measurement of anisotropic elastic constants of fiber-reinforced composite plate using ultrasonic bulk wave and laser generated Lamb wave, Ultrasonics, 37(6), 405-412.
  17. [17]  Moreno, E. and Acevedo, P. (1998), Thickness measurement in composite materials using Lamb waves, Ultrasonics, 35, 581-586.
  18. [18]  Grondel, S., Assad, J., Delebarre, C., Blanquet, P., and Moulin E. (1999), The propagation of lamb waves in multilayered plates: phase velocity measurement, Measurement Science and Technology, 10(5), 348-353.
  19. [19]  Chang, Z. and Mal, A. (1999), Scattering of Lamb waves from a rivet hole with edge cracks, Mechanics of Materials, 31, 197-204.
  20. [20]  Fromme, P. and Sayir, M.B. (2002), Detection of cracks at rivet holes using guided waves, Ultrasonics 40, 199-203.
  21. [21]  Grahn, T. (2003), Lamb wave scattering from a circular partly through-thickness hole in a plate, Wave Motion, 37, 63-80.
  22. [22]  Hong, M., Su, Z., Lu, Y., Sohn H., and Qing X. (2015), Locating fatigue damage using temporal signal features of nonlinear Lamb waves, Mechanical Systems and Signal Processing, 60-61, 182-197.
  23. [23]  McKeon, J.C.P. and Hinders,M.K. (1999), Lamb wave scattering from a through hole, Journal of Sound and Vibration, 224(5), 843-862.
  24. [24]  Barski, M., Stawiarski, A., and Pają, P. (2015), Numerical study of the optimal position of a Lamb wave actuator for detection of fatigue damage in an isotropic plate with a circular hole, Dynamical Systems, Mathematical and Numerical Approaches, Eds.: Awrejcewicz J., Ka′zierczak M., Mrozowski J., Olejnik, 69-80.
  25. [25]  Stawiarski, A., Barski, M., and Pają, P. (2015), Fatigue crack identyfication by dynamic analysis of elastic waves propagation, Dynamical Systems, Mathematical and Numerical Approaches, Eds.: Awrajcewicz J., Ka′zierczak M., Mrozowski J., Olejnik, 489-500.