Nonlinear Resonant Acoustic Spectroscopy

  • Bart Van DammeEmail author
  • Koen Van Den Abeele
Reference work entry


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.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Empa, Swiss Federal Laboratories for Materials Science and TechnologyDubendorfSwitzerland
  2. 2.Physics, Kulak Kortrijk CampusKortrijkBelgium

Section editors and affiliations

  • Ida Nathan
    • 1
  • Norbert Meyendorf
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of AkronAkronUSA
  2. 2.Center for Nondestructive EvaluationIowa State UniversityAmesUSA

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