A nonlinearity-sensitive approach for detection of “breathing” cracks relying on energy modulation effect

Maosen Cao, Qitian Lu, Zhongqing Su, Maciej Radzieński, Wei Xu, Wiesław Ostachowicz

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)


For a cracked structural component under a single-tone harmonic excitation, the opening-closing motion of the “breathing” crack can lead to higher harmonics in its steady-state responses, which can be efficient indicators for the detection of the crack. Nevertheless, when the opening-closing motion of a “breathing” crack is slight, higher harmonics can become barely visible in frequency spectra and seem to be hidden. As a consequence, the crack can hardly be detected by such hidden higher harmonics. Addressing this problem, this study proposes a nonlinearity-sensitive approach for the detection of “breathing” cracks. In particular, a novel phenomenon of energy modulation effect (EME) is reported, based on which a new concept of quadratic Teager-Kaiser energy (Q-TKE) is formulated. Hidden higher harmonics can be considerably enhanced in Q-TKEs, such that “breathing” cracks can be readily detected. A physical insight into the mechanism of the EME is provided. The approach is numerically verified using the finite element method and experimentally validated through non-contact laser measurement. The results suggest that hidden higher harmonics can be considerably enhanced in the Q-TKEs and become sensitive indicators to manifest the occurrence of the cracks, suitable for the detection of initial fatigue cracks.

Original languageEnglish
Article number116754
JournalJournal of Sound and Vibration
Publication statusPublished - 28 Apr 2022


  • Energy modulation effect
  • Higher harmonics
  • Non-contact laser measurement
  • Quadratic Teager-Kaiser energy
  • “Breathing” crack

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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