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

• We propose a nonlinearity-sensitive approach for the detection of “breathing” cracks. • The energy modulation effect with its physical sense is reported. • The quadratic Teager-Kaiser energy can enhance hidden higher harmonics. • The approach is experimentally validated by non-contact laser measurement. 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.