Skip to main content
SpringerLink
Log in

Nonlinear Resonant Acoustic Spectroscopy

  • Living reference work entry
  • First Online:
Book cover Handbook of Advanced Non-Destructive Evaluation

  • 236 Accesses

Abstract

Ultrasound nondestructive evaluation methods are popular since they are noninvasive, can be done by a trained technician, and can be used in situ. Pulse echo measurements with a single transducer and more advanced material examination using phased arrays allow for the detection of cracks and cavities in homogeneous materials. However, some types of damage remain invisible to traditional ultrasound nondestructive testing (NDT). Early stage fatigue damage, closed cracks, or delaminations in composites are typically difficult to discern. This chapter deals with the assessment of nonlinear wave distortion due to the presence of damage. In nonlinear elastic materials, resonance frequencies depend on the excitation amplitude. Nonlinear reverberation spectroscopy (NRS) exploits this small frequency shift in the ringing of a sample that was harmonically excited at resonance. Two successful applications are described. First, NRS was used to quantify thermal damage of carbon fiber reinforced polymers (CFRP) samples. The nonlinear parameters are much more sensitive to the microdamage than linear properties, such as a change of the Young’s modulus or the damping coefficient. Moreover, the NRS results correlate well with optically gathered crack density values, and they can be modeled using a hysteretic elastic constitutive equation. The second example is the detection of early fatigue damage. A single closed crack in a steel sample can be exposed and even located when combining the NRS results with a finite element modal analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Aleshin V, Van Den Abeele K (2005) Micro-potential model for stress-strain hysteresis of micro-cracked materials. J Mech Phys Solids 53(4):795–824

    Article  MathSciNet  Google Scholar 

  • Aleshin V, Van Den Abeele K (2007) Microcontact-based theory for acoustics in microdamaged materials. J Mech Phys Solids 55(2):366–390

    Article  Google Scholar 

  • Aleshin V, Van Den Abeele K (2009) Preisach analysis of the hertz-mindlin system. J Mech Phys Solids 57(4):657–672

    Article  Google Scholar 

  • Antonets V, Donskoy D, Sutin A (1986) Nonlinear vibro-diagnostics of flaws in multilayered structures. Mech Compos Mater 15(5):934–937

    Google Scholar 

  • Bentahar M, El Aqra H, El Guerjouma R, Griffa M, Scalerandi M (2006) Hysteretic elasticity in damaged concrete: quantitative analysis of slow and fast dynamics. Phys Rev B 73(1):14,116

    Article  Google Scholar 

  • Blanch J, Robertsson J, Symes W (1995) Modeling of a constant-Q – methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique. Geophysics 60(1):176–184

    Article  Google Scholar 

  • Buck O, Morris W, Richardson J (1978) Acoustic harmonic generation at unbonded interfaces and fatigue cracks. Appl Phys Lett 33(5):371–373

    Article  Google Scholar 

  • Courtney C, Drinkwater B, Neild S, Wilcox P (2008) Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis. NDT & E Int 41(3):223–234

    Article  Google Scholar 

  • Darling T, TenCate J, Brown D, Clausen B, Vogel S (2004) Neutron diffraction study of the contribution of grain contacts to nonlinear stress-strain behavior. Geophys Res Lett 31:L16,604

    Article  Google Scholar 

  • Géradin M, Rixen D (1994) Mechanical vibrations: theory and application to structural dynamics, vol 25. Wiley, New York

    Google Scholar 

  • Gliozzi A, Griffa M, Scalerandi M (2006) Efficiency of time-reversed acoustics for nonlinear damage detection in solids. J Acoust Soc Am 120:2506

    Article  Google Scholar 

  • Guyer R, Johnson P (1999) Nonlinear mesoscopic elasticity: evidence for a new class of materials. Phys Today 52:30–36

    Article  Google Scholar 

  • Guyer RA, Johnson PA (2009) Nonlinear mesoscopic elasticity: the complex behaviour of rocks, soil, concrete. Wiley, New York

    Book  Google Scholar 

  • Guyer R, McCall K, Boitnott G (1995) Hysteresis, discrete memory, and nonlinear wave propagation in rock: a new paradigm. Phys Rev Lett 74(17):3491–3494

    Article  Google Scholar 

  • Guyer R, McCall K, Van Den Abeele K (1998) Slow elastic dynamics in a resonant bar of rock. Geophys Res Lett 25(10):1585–1588

    Article  Google Scholar 

  • Hamilton M (1986) Fundamentals and applications of nonlinear acoustics, in nonlinear wave propagation in mechanics. The American Society of Mechanical Engineers, New York

    Google Scholar 

  • Haupert S, Guerard S, Peyrin F, Mitton D, Laugier P (2014) Non destructive characterization of cortical bone micro-damage by nonlinear resonant ultrasound spectroscopy. PLoS One 9(1):e83,599

    Article  Google Scholar 

  • Hyllengren F (2001) Tech. Rep. No. TEK01-0022, C.S.M. Materialteknik, Linköping

    Google Scholar 

  • Jin J, Moreno MG, Riviere J, Shokouhi P (2017) Impact-based nonlinear acoustic testing for characterizing distributed damage in concrete. J Nondestruct Eval 36(3):51

    Article  Google Scholar 

  • Johnson P, Sutin A (2005) Slow dynamics and anomalous nonlinear fast dynamics in diverse solids. J Acoust Soc Am 117:124

    Article  Google Scholar 

  • Johnson P, Zinszner B, Rasolofosaon P (1996) Resonance and elastic nonlinear phenomena in rock. J Geophys Res 101(B5):11,553–11,564

    Article  Google Scholar 

  • Johnson P, Zinszner B, Rasolofosaon P, Cohen-Tenoudji F, Van Den Abeele K (2004) Dynamic measurements of the nonlinear elastic parameter α in rock under varying conditions. J Geophys Res 109(B2):B02,202

    Article  Google Scholar 

  • Kawashima K, Murase M, Yamada R, Matsushima M, Uematsu M, Fujita F (2006) Nonlinear ultrasonic imaging of imperfectly bonded interfaces. Ultrasonics 44:e1329–e1333

    Article  Google Scholar 

  • Kazakov V, Sutin A, Johnson P (2002) Sensitive imaging of an elastic nonlinear wave-scattering source in a solid. Appl Phys Lett 81:646

    Article  Google Scholar 

  • Kim J, Jacobs L, Qu J (2011) Nonlinear ultrasonic techniques for nondestructive damage assessment in metallic materials. In: Fu-Kuo Chang (ed) 8th International workshop on structural health monitoring 2011: condition-based maintenance and intelligent structures. Department of Aeronautics and Astronautics, Stanford University, DEStech Publications, Incorporated

    Google Scholar 

  • Korotkov A, Sutin A (1994) Modulation of ultrasound by vibrations in metal constructions with cracks. Acoust Lett 18(4):59–62

    Google Scholar 

  • Landau LD, Lifshitz EM (1959) Theory of elasticity. Pergamon, Tarrytown

    MATH  Google Scholar 

  • Lawn D, Brian R (1998) Nonlinear stress-strain curves for solids containing closed cracks with friction. J Mech Phys Solids 46(1):85–113

    Article  Google Scholar 

  • Lesnicki KJ, Kim JY, Kurtis KE, Jacobs LJ (2011) Characterization of asr damage in concrete using nonlinear impact resonance acoustic spectroscopy technique. NDT & E Int 44(8):721–727

    Article  Google Scholar 

  • Mason W (1969) Internal friction mechanism that produces an attenuation in the earth’s crust proportional to the frequency. J Geophys Res 74(20):4963–4966

    Article  Google Scholar 

  • Matzkanin G (1999) Heat damage in graphite epoxy composites: degradation, measurement and detection. J Nondestruct Test Ultrason (Germany) 4(3). https://www.ndt.net/article/v04n03/ntiac/ntiac.htm

  • Mavko G (1979) Frictional attenuation: an inherent amplitude dependence. J Geophys Res 84(B9):4769–4775

    Article  Google Scholar 

  • McCall K, Guyer R (1994) Equation of state and wave propagation in hysteretic nonlinear elastic materials. J Geophys Res 99(B12):23

    Article  Google Scholar 

  • Mix PE (2005) Introduction to nondestructive testing: a training guide, 2nd edn. Wiley, Hoboken

    Google Scholar 

  • Morris W, Buck O, Inman R (1979) Acoustic harmonic generation due to fatigue damage in high-strength aluminum. J Appl Phys 50(11):6737–6741

    Article  Google Scholar 

  • Muller M, Renaud G (2011) Nonlinear acoustics for non-invasive assessment of bone micro-damage. In: Bone quantitative ultrasound. Springer, Dordrecht, pp 381–408

    Google Scholar 

  • Nagy P (1998) Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 36(1–5):375–381

    Article  Google Scholar 

  • Nazarov V, Radostin A (2015) Nonlinear acoustic waves in micro-inhomogeneous solids. Wiley, Hoboken

    Google Scholar 

  • Pecorari C (2003) Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact. J Acoust Soc Am 113:3065

    Article  Google Scholar 

  • Pecorari C (2004) Adhesion and nonlinear scattering by rough surfaces in contact: beyond the phenomenology of the preisach-mayergoyz framework. J Acoust Soc Am 116:1938–1947

    Article  Google Scholar 

  • Rayleigh B (1896) The theory of sound. Macmillan, London

    MATH  Google Scholar 

  • Schmerr LW (2016) Probability of detection and reliability. Springer International Publishing, Cham, pp 685–695

    Google Scholar 

  • Sharma M, Tutuncu A (1994) Grain contact adhesion hysteresis: a mechanism for attenuation of seismic waves. Geophys Res Lett 21(21):2323–2326

    Article  Google Scholar 

  • Shkolnik I (1993) Nondestructive testing of concretes: new aspects. Nondestruct Test Eval 10(6):351–358

    Article  Google Scholar 

  • Solodov I, Busse G (2007) Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials. Appl Phys Lett 91(251):910

    Google Scholar 

  • Sutin A, Donskoy D (1998) Vibro-acoustic modulation nondestructive evaluation technique. In: Proceedings of SPIE, vol 3397. International Society for Optics and Photonics, p 226

    Google Scholar 

  • Sutin A, Delclos C, Lenclud M (1995) Investigations of the second harmonic generation due to cracks in large carbon electrodes. In: Proceeding of the 2nd international symposium on acoustical and vibratory surveillance methods and diagnostic techniques, Senlis, pp 725–735

    Google Scholar 

  • Sutin A, Johnson P, TenCate J (2003) Development of nonlinear time reversed acoustics (nltra) for applications to crack detection in solids. In: Proceedings of the word congress of ultrasonics, pp 7–10

    Google Scholar 

  • Taylor R (2011) Fiber composite aircraft-capability and safety. http://www.atsb.gov.au/media/27758/ar2007021.pdf

  • Ten Cate J, Shankland T (1996) Slow dynamics in the nonlinear elastic response of Berea sandstone. Geophys Res Lett 23(21):3019–3022

    Article  Google Scholar 

  • Van Damme B, Van Den Abeele K (2014) The application of nonlinear reverberation spectroscopy for the detection of localized fatigue damage. J Nondestruct Eval 33(2):263–268

    Google Scholar 

  • Van Den Abeele K, De Visscher J (2000) Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques. Cem Concr Res 30(9):1453–1464

    Article  Google Scholar 

  • Van Den Abeele K, Johnson P, Guyer R, McCall K (1997) On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation. J Acoust Soc Am 101:1885–1898

    Article  Google Scholar 

  • Van Den Abeele K, Carmeliet J, TenCate J, Johnson P (2000a) Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part II: single-mode nonlinear resonance acoustic spectroscopy. Res Nondestruct Eval 12(1):31–42

    Article  Google Scholar 

  • Van Den Abeele K, Johnson P, Sutin A (2000b) Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part I: nonlinear wave modulation spectroscopy (NWMS). Res Nondestruct Eval 12(1):17–30

    Article  Google Scholar 

  • Van Den Abeele K, Carmeliet J, Johnson P, Zinszner B (2002) Influence of water saturation on the nonlinear elastic mesoscopic response in earth materials and the implications to the mechanism of nonlinearity. J Geophys Res 107(6):2121

    Article  Google Scholar 

  • Van Den Abeele K, Carmeliet J, Van De Velde K (2004a) Inferring the degradation of pultruded composites from dynamic nonlinear resonance measurements. Polym Compos 22(4):555–567

    Article  Google Scholar 

  • Van Den Abeele K, Schubert F, Aleshin V, Windels F, Carmeliet J (2004b) Resonant bar simulations in media with localized damage. Ultrasonics 42(1–9):1017–1024

    Article  Google Scholar 

  • Van Den Abeele K, Katkowski T, Wilkie-Chancellier N, Desadeleer W (2006) Laboratory experiments using nonlinear elastic wave spectroscopy (NEWS): a precursor to health monitoring applications in aeronautics, cultural heritage, and civil engineering. In: Universality of nonclassical nonlinearity, Springer, New York, pp 389–409

    Google Scholar 

  • Van Den Abeele K, Le Bas P, Van Damme B, Katkowski T (2009) Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: experimental and theoretical study. J Acoust Soc Am 126:963

    Article  Google Scholar 

  • Vanaverbeke S, Van Den Abeele K (2006) Multiscale approach for simulating nonlinear wave propagation in materials with localized microdamage. In: AIP conference proceedings, vol 838, p 91

    Google Scholar 

  • Walsh J (1966) Seismic wave attenuation in rock due to friction. J Geophys Res 71(10):2591–2599

    Article  Google Scholar 

  • Zagrai A, Donskoy D, Chudnovsky A, Golovin E (2008) Micro-and macroscale damage detection using the nonlinear acoustic vibro-modulation technique. Res Nondestruct Eval 19(2):104–128

    Article  Google Scholar 

  • Zhang J (2016) Defect detection, classification, and characterization using ultrasound. In: Structural health monitoring (SHM) in aerospace structures. Elsevier, Amsterdam, pp 307–323

    Google Scholar 

  • Zumpano G, Meo M (2007) A new nonlinear elastic time reversal acoustic method for the identification and localisation of stress corrosion cracking in welded plate-like structures-a simulation study. Int J Solids Struct 44(11–12):3666–3684

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Empa, Swiss Federal Laboratories for Materials Science and Technology, Dubendorf, Switzerland

    Bart Van Damme

  2. Physics, Kulak Kortrijk Campus, Kortrijk, Belgium

    Koen Van Den Abeele

Authors
  1. Bart Van Damme
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Koen Van Den Abeele
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bart Van Damme .

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of Akron, Akron, OH, USA

    Nathan Ida

  2. Center for Nondestructive Evaluation, Iowa State University Center for Nondestructive Evaluation, Ames, IA, USA

    Norbert Meyendorf

Section Editor information

  1. Department of Electrical and Computer Engineering, University of Akron, Akron, USA

    Ida Nathan

  2. Center for Nondestructive Evaluation, Iowa State University, Ames, IA, USA

    Norbert Meyendorf

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Van Damme, B., Van Den Abeele, K. (2018). Nonlinear Resonant Acoustic Spectroscopy. In: Ida, N., Meyendorf, N. (eds) Handbook of Advanced Non-Destructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-30050-4_23-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30050-4_23-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30050-4

  • Online ISBN: 978-3-319-30050-4

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation