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Identification of Contact Acoustic Nonlinearities of Subsurface Cracks Located at Free-Edges

Part of the Lecture Notes in Civil Engineering book series (LNCE,volume 253)


Structural health monitoring (SHM) is the continuous on-board monitoring of a structure’s condition during operation by integrated systems of sensors. Standard methods of SHM are vibration-based methods like the electromechanical impedance (EMI) method. This method uses a piezoelectric transducer that is attached to a mechanical structure of interest. The transducer is supplied by a harmonic voltage that results in a typically harmonic oscillation of both transducer and structure and allows to monitor the combined dynamic response by measuring the supplied current, and thus, the impedance. Changes of the impedance reflect changes of the structure and can be used to conclude on a potential damage. Today, linear response is typically evaluated by the EMI. Critical damages like delamination in fiber reinforced polymer components could also provoke nonlinear response that might allow more conclusions on the damage. This contribution demonstrates the existence of contact acoustic nonlinearity in an aluminum beam with a free-edge-delamination-like subsurface crack at the end. The investigation is based on transfer frequency response functions between an exciting transducer and out-of-plane surface velocities of the beam measured by laser Doppler scanning vibrometry. For identification of the nonlinear response an identification method is used and verified that is readily published. Furthermore, the diffusion of the nonlinear behavior shall be investigated to conclude on its possible measurement by a transducer that is located at some distance to such a damage.


  • Electromechanical impedance
  • Vibration-based
  • Delamination
  • Subsurface crack
  • Damage identification
  • Nonlinear vibration
  • Contact acoustic nonlinearity
  • Transfer frequency response function

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  1. Humer, C., Kralovec, C., Schagerl, M.: Scattering analysis of lamb waves at subsurface cracks in isotropic plates. In: 8th ECCOMAS Thematic Conference on Smart Structures and Materials, pp. 1843–1853. CIMNE, Madrid (2017)

    Google Scholar 

  2. Giurgiutiu, V.: Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd edn. Academic Press, Inc. (2014)

    Google Scholar 

  3. Bhuiyan, M. Y., Shen, Y., Giurgiutiu, V.: Interaction of lamb waves with rivet hole cracks from multiple directions. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. 231(16) (2017). 0954406216686996

    Google Scholar 

  4. Holford, K.M., et al.: A new methodology for automating acoustic emission detection of metallic fatigue fractures in highly demanding aerospace environments: an overview. Prog. Aerosp. Sci. 90, 1–11 (2017).

    CrossRef  Google Scholar 

  5. Ono, K.: Review on structural health evaluation with acoustic emission. Appl. Sci. 8(6), 958 (2018).

    CrossRef  Google Scholar 

  6. Zhao, Y., Schagerl, M., Gschomann, S., Kralovec, C.: In-situ spatial strain monitoring of a single-lap joint using inkjet-printed carbon nanotube embedded thin films. Struct. Health Monit. 18(5–6), 1479–1490 (2018)

    Google Scholar 

  7. Loh, K.J., Hou, T.-C., Lynch, J.P., Kotov, N.A.: Carbon nanotube sensing skins for spatial strain and impact damage identification. J. Nondestr. Eval. 28, 9–25 (2009).

    CrossRef  Google Scholar 

  8. Nonn, S., Schagerl, M., Zhao, Y., Gschomann, S., Kralovec, C.: Application of electrical impedance tomography to an anisotropic carbon fiber-reinforced polymer composite laminate for damage localization. Compos. Sci. Technol. 160, 231–236 (2018)

    CrossRef  Google Scholar 

  9. Tallman, T., Smyl, D.: Structural health and condition monitoring via electrical impedance tomography in self-sensing materials: a review. Smart Mater. Struct. 29(12), 123001 (2020).

    CrossRef  Google Scholar 

  10. Hunt, S.R., Hebden, I.G.: Validation of the Eurofighter Typhoon structural health and usage monitoring system. Smart Mater. Struct. 10(3), 497–503 (2001).

    CrossRef  Google Scholar 

  11. Bergmayr, T., Winklberger, M., Kralovec, C., Schagerl, M.: Structural health monitoring of aerospace sandwich structures via strain measurements along zero-strain trajectories. Eng. Fail. Anal. 126, 105454 (2021)

    CrossRef  Google Scholar 

  12. Crawley, P.: The impedance method for non-destructive inspection. NDT Int. 17(2), 59–65 (1984)

    CrossRef  Google Scholar 

  13. Giurgiutiu, V., Rogers, C.A.: Modeling of the electro-mechanical (E/M) impedance response of a damaged composite beam. Adapt. Struct. Mater. Syst. 59, 39–46 (1999)

    Google Scholar 

  14. Kralovec, C., Schagerl, M.: Electro-mechanical impedance measurements as a possible SHM method for sandwich debonding detection. In: Key Engineering Materials, vol. 742, pp. 763–777. Trans Tech Publications Ltd., Zurich (2017)

    Google Scholar 

  15. Solodov, I.Y.: Nonlinear NDE using contact acoustic nonlinearity (CAN). In: 1994 Proceedings of IEEE Ultrasonics Symposium, vol. 2, pp. 1279–1283. IEEE, Cannes (1994)

    Google Scholar 

  16. Chillara, V.K., Lissenden, C.J.: Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments. Opt. Eng. 55(1), 011002 (2015).

    CrossRef  Google Scholar 

  17. Soleimanpur, R., Ng, C.-T.: Locating delaminations in laminated composite beams using nonlinear guided waves. Eng. Struct. 131, 207–219 (2017).

    CrossRef  Google Scholar 

  18. Worden, K., Farrar, C.R., Haywood, J., Todd, M.: A review of nonlinear dynamics applications to structural health monitoring. Struct. Control. Health Monit. 15(4), 540–567 (2008).

    CrossRef  Google Scholar 

  19. Kralovec, C., Schagerl, M., Erlinger, T.: Model-based evaluation of electro-mechanical impedance measurements for detection and size identification of face layer debondings in sandwich panels. In: Structural Health Monitoring 2017 - Real-Time Material State Awareness and Data-Driven Safety Assurance, pp. 472–479. DEStech Publications Inc., Stanford (2017)

    Google Scholar 

  20. Kralovec, C., Erlinger, T., Gschomann, S., Schagerl, M.: Manufacturing of artificial sub-surface cracks to investigate non-linear features of electro-mechanical impedance measurements. In: Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and Transportation XII, vol. 10599. International Society for Optics and Photonics, Denver (2018)

    Google Scholar 

  21. Kralovec, C., Schagerl, M.: Experimental measurements of vibrations of artificial sub-surface cracks and evaluation of identification potential for the electro-mechanical impedance method. In: Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and Transportation XIII, vol. 10971, p. 109711T. International Society for Optics and Photonics, Denver (2019).

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This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 101006952.

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Correspondence to Christoph Kralovec .

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Kralovec, C., Schagerl, M. (2023). Identification of Contact Acoustic Nonlinearities of Subsurface Cracks Located at Free-Edges. In: Rizzo, P., Milazzo, A. (eds) European Workshop on Structural Health Monitoring. EWSHM 2022. Lecture Notes in Civil Engineering, vol 253. Springer, Cham.

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