Nonlinear Acoustic Measurements for NDE Applications: Waves Versus Vibrations

  • Igor SolodovEmail author
Part of the Springer Series in Measurement Science and Technology book series (SSMST)


Majority of acoustic instruments widely used in industry and technology for non-destructive evaluation (NDE) make use of a linear elastic response of materials. The nonlinear approach to ultrasonic NDE is concerned with nonlinear material response, which is inherently related to the frequency changes of the input signal, and is a new technology for monitoring of deterioration in material properties and diagnostics of damage. The application field now includes both the nonlinear wave and nonlinear vibration modes. The former is based on the assumption and is applicable to the case studies of the distributed material nonlinearity. It profits from accumulation of the wave nonlinear response along the propagation distance and relies on the higher harmonic signals. A strong nonlinear response of non-bonded interfaces in planar defects introduces the nonlinearity localized in the defect area where the vibration nonlinearity steps up. The concept of local defect resonance (LDR) combined with its nonlinearity identifies a nonlinear inclusion as a nonlinear oscillator and brings about different dynamic and frequency scenarios in vibration nonlinear phenomena. The LDR-induced trapping of the nonlinearity generates a defect-selective nonlinearity and conditions for efficient and even noncontact nonlinear diagnostic imaging of damage.



A part of the results in this Chapter has been obtained in the framework of the project KR 2131/12-1 funded by the Deutsche Forschungsgemeinschaft (DFG) whose support is gratefully acknowledged.


  1. 1.
    L.K. Zarembo, V.A. Krasilnikov, Vvedenie v nelineinuyu akustiku (Introduction to Nonlinear Acoustics) (Nauka, Moskva, 1966)Google Scholar
  2. 2.
    M.A. Breazeale, J. Ford, J. Appl. Phys. 36, 3488 (1965)ADSCrossRefGoogle Scholar
  3. 3.
    A.A. Gedroitz, V.A. Krasilnikov, Sov. Phys. JETP 16, 1122 (1963)ADSGoogle Scholar
  4. 4.
    W.T. Yost, J.H. Cantrell, Rev. Progr. Quant. Nondestr. Eval. 9, 1669 (1990)CrossRefGoogle Scholar
  5. 5.
    J.H. Cantrell, W.T. Yost, W.T.J., Appl. Phys. 81, 2957 (1997)Google Scholar
  6. 6.
    K.S. Len, F.M. Severin, IYu. Solodov, Sov. Phys. Acoust. 37, 610 (1991)Google Scholar
  7. 7.
    I. Solodov, N. Krohn, G. Busse, Ultrasonics 40, 621 (2002)CrossRefGoogle Scholar
  8. 8.
    I.Yu. Solodov, Ultrasonics 36, 383 (1998)CrossRefGoogle Scholar
  9. 9.
    I. Solodov, J. Bai, S. Bekgulyan, G. Busse, Appl. Phys. Lett. 99, 211911 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    I. Solodov, J. Bai, G. Busse, J. Appl. Phys. 113, 223512 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    I. Solodov, G. Busse, Appl. Phys. Lett. 102, 061905 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    J. Hettler, M. Tabatabaeipour, S. Delrue, K.V.D. Abeele, J. Nondestr. Eval. 36, 2 (2017)CrossRefGoogle Scholar
  13. 13.
    M. Rahammer, M. Kreutzbruck, NDT E Internat. 86, 83 (2017)CrossRefGoogle Scholar
  14. 14.
    G.P.M. Fierro, D. Ginzburg, F. Ciampa, M. Meo, J. Nondestr. Eval. 36, 4 (2017)CrossRefGoogle Scholar
  15. 15.
    L. Pieczonka, L. Zietek, A. Klepka, W.J. Staszewski, F. Aymerich, T. Uhl, Damage imaging in composites using nonlinear vibro-acoustic wave modulations. Struct. Contr. Health Monit. 25, 2e2063 (2018)CrossRefGoogle Scholar
  16. 16.
    J. Segers, M. Kersemans, S. Hedayatrasa, J.A.C. Tellez, W. Van Paepegem, NDT E Internat. 98, 130 (2018)CrossRefGoogle Scholar
  17. 17.
    B. Roy, T. Bose, K. Debnath, J. Sound Vibr. 443, 703 (2019)ADSCrossRefGoogle Scholar
  18. 18.
    Ch. Andreades, P. Mahmoodi, F. Ciampa, Characterisation of smart CFRP composites with embedded PZT transducers for nonlinear ultrasonic applications. Comp. Struct. (2018). Scholar
  19. 19.
    F. Ciampa, G. Scarselli, M. Meo, J. Acoust. Soc. Am. 141, 2364 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    I. Solodov, J. Nondestr. Eval. 33, 252 (2014)CrossRefGoogle Scholar
  21. 21.
    R.N. Thurston, in Physical acoustics, vol. 1, chap. 1. (Academic, New York, 1964)Google Scholar
  22. 22.
    J. Na, M. Breazeale, J. Acoust. Soc. Am. 95, 3213 (1994)ADSCrossRefGoogle Scholar
  23. 23.
    K. Van Den Abeele, M. Breazeale, J. Acoust. Soc. Am. 99, 1430 (1996)ADSCrossRefGoogle Scholar
  24. 24.
    Ch. Kube, A. Arquelles, J. Acoust. Soc. Am. 142, EL224 (2017)Google Scholar
  25. 25.
    D. Gerlich, M. Breazeale, J. Appl. Phys. 67, 3278 (1990)ADSCrossRefGoogle Scholar
  26. 26.
    K. Naugolnykh, L. Ostrovskii, Nonlinear Wave Processes in Acoustics. (Cambridge University Press, 1998)Google Scholar
  27. 27.
    R. Beyer, J. Acoust. Soc. Am. 32, 719 (1960)ADSCrossRefGoogle Scholar
  28. 28.
    E.M. Ballad, B.A. Korshak, V.G. Mozhaev, I. Solodov, Moscow Univ. Bull. Phys. 3, 44 (2001)Google Scholar
  29. 29.
    M. Breazeale, D. Thompson, Appl. Phys. Lett. 3, 77 (1963)ADSCrossRefGoogle Scholar
  30. 30.
    K. Matlack, J.-Y. Kim, L. Jacobs, J. Qu, J. Nondestr. Eval. 34, 273 (2015)CrossRefGoogle Scholar
  31. 31.
    V.E. Nazarov, Akust. Zh. 37, 150 (1991)Google Scholar
  32. 32.
    P. Hess, A. Lomonosov, A.P. Mayer, Ultrasonics 54, 39 (2014)CrossRefGoogle Scholar
  33. 33.
    V.A. Krasilnikov, V.E. Ljamov, I. Solodov, Izv. AN SSSR Phys. 35, 944 (1971)Google Scholar
  34. 34.
    Y. Shui, I. Solodov, J. Appl. Phys. 64, 6155 (1988)ADSCrossRefGoogle Scholar
  35. 35.
    Y. Zheng, R. Maev, I. Solodov, Can. J. Phys. 77, 927 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    A.V. Porubov, Lokalizacija nelinejnyh voln deformacii (Localisation of Nonlinear Deformation Waves) (Fizmatgiz, Moscow, 2009)Google Scholar
  37. 37.
    B.A. Konyukhov, G.M. Shalashov, J. Appl. Math. Theor. Phys. 4, 125 (1974)Google Scholar
  38. 38.
    I. Solodov, D. Sci. Dissertation, Moscow State University, 1987Google Scholar
  39. 39.
    I.B. Yakovkin, D.V. Petrov, Difrakcija sveta na poverkhnostnykh akusticheskikh volnakh (Light Diffraction on Surface Acoustic Waves) (Nauka, Novosibirsk, 1979)Google Scholar
  40. 40.
    Y. Shui, I. Yu. Solodov, in Proceedings II WESTPA. (Polytech. Institute Hong Kong, 1985), pp 188Google Scholar
  41. 41.
    A.P. Brysev, V.A. Krasilnikov, A.A. Podgornov, IYu. Solodov, Fiz. Tverd. Tela 26, 2204 (1984)Google Scholar
  42. 42.
    I.Yu. Solodov, C. Wu, Acoust. Phys. 39, 476 (1993)ADSGoogle Scholar
  43. 43.
    K. Sel Len, F.M. Severin, I.Yu. Solodov, Sov. Phys. Acoust. 37, 610 (1991)Google Scholar
  44. 44.
    R. Maev, I. Solodov, Rev. Progr. Quant. Nondestr. Eval. 19, 1409 (2000)CrossRefGoogle Scholar
  45. 45.
    R. Maev, I. Solodov, IEEE Ultrason. Symp. Proc. 707 (1998)Google Scholar
  46. 46.
    I. Yu. Solodov, A.F. Asainov, K. Sel Len, Ultrasonics 31, 91 (1993)Google Scholar
  47. 47.
    I. Solodov, B.A. Korshak, Phys. Rev. Lett. 88, 014303 (2002)ADSCrossRefGoogle Scholar
  48. 48.
    J.D. Achenbach, O.K. Parikh, Rev. Progr. Quant. Nondestr. Eval. 10B, 1837 (1991)Google Scholar
  49. 49.
    C. Bermes, J.Y. Kim, J. Qu, L.J. Jacobs, Appl. Phys. Lett. 90, 021901 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    T.-H. Lee, I.-M. Choi, K.-Y Jhang, Mod. Phys. Lett., B. 22(11), 1135 (2018)Google Scholar
  51. 51.
    J. Zhao, V.K. Chillara, B. Ren, H. Cho, J. Qiu, C.J. Lissenden, J. Appl. Phys. 119, 064902 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    I. Solodov, D. Segur, M. Kreutzbruck, Res. Nondestr. Eval. 30, 1 (2019)CrossRefGoogle Scholar
  53. 53.
    I. Solodov, D. Segur, M. Kreutzbruck, in Proceedings of 12th ECNDT, Gothenburg, (2018)Google Scholar
  54. 54.
    L.D. Landau, E.M. Lifshitz, Mechanics (Pergamon Press Ltd., Oxford-London-Paris, 1960)zbMATHGoogle Scholar
  55. 55.
    N.W. McLachlan, Theory and Applications of Mathieu Functions (University Press, Oxford, 1951)Google Scholar
  56. 56.
    N. Minorsky, Nonlinear Oscillations (D. Van Nostrand Co., Inc., Princeton, 1962)zbMATHGoogle Scholar
  57. 57.
    F.K. Kneubuehl, Oscillations and Waves (Springer, Berlin, 1997)CrossRefGoogle Scholar
  58. 58.
    I. Solodov, M. Rahammer, N. Gulnizkij, M. Kreutzbruck, J. Nondestr. Eval. 35, 47 (2016)CrossRefGoogle Scholar
  59. 59.
    I. Solodov, D. Döring, G. Busse, Appl. Optics 48, C33 (2009)ADSCrossRefGoogle Scholar
  60. 60.
    W. Post, M. Kersemans, I. Solodov, K. Van Den Abeele, S.J. Garsia, S. van der Zwaag, Compos. Part A: Appl. Sci. Manuf. 101, 243 (2017)CrossRefGoogle Scholar
  61. 61.

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Institute for Polymer Technology, University of StuttgartStuttgartGermany

Personalised recommendations