Exploiting evanescent bending waves for the identification of near-boundary cracks in slender beams

Bending evanescent waves are among the promising approaches for the local damage identifi-cation of slender beams due to the high sensitivity and spatial concentrating nature. However, such local damage usually appears near the boundary of the beam in practices. It is therefore difficult to distinguish the evanescent wave components resulting from the boundary and the crack, leading to confusion in damage identification. In order to tackle this issue, the generalized reflection coefficient of the evanescent wave with respect to the incident propagating wave (GRC-EP) is exploited in the present work, which allows to quantitatively identify the severity of the near-boundary crack. Taking the semi-infinite Timoshenko beam having a crack damage at the fixed end, the generalized reflections of the evanescent and propagating waves at the crack, with respect to a unit incident wave, are derived analytically, showing that the amplitude of the evanescent wave is negatively related to the damage severity. Based on this, the amplitude ratio between the reflected evanescent wave and the incident propagating wave, i.e., the GRC as mentioned, is proposed to be the damage indicator. Referring to the theoretical GRC values, the damage severity can then be identified from the estimated GRCs that are obtained from the inverse algorithm, as long as the acceleration responses are given. Finally, the feasibility of the proposed indicator is verified by taking a slender beam having a local damage at the fixed end as an example. The results show that the proposed GRC-EP is capable to indicate the severity of the near-boundary damage despite the consideration of noise, confirming its potential value in the health monitoring of slender beam structures.

Automated summary

This study proposes a new method to quantitatively evaluate the severity of near-boundary crack damage by utilizing the reflection coefficient of waves. Analytical derivations show that the amplitude of evanescent waves is negatively correlated with the damage severity, making it possible to use the amplitude ratio as a damage indicator. Through an inverse algorithm, estimated amplitude ratios can be compared with theoretical values to determine the severity of the damage. The results verify the potential value of this indicator in the health monitoring of slender beam structures.