Amplifying Nonlinear Ultrasonic Signatures for Fatigue Damage Detection Via a Graded Elastic Meta-Enhancer

Abstract Fatigue cracks pose a significant threat to engineering structures owing to their inconspicuous nature and difficulty in detection. However, for the nascent stage of fatigue crack growth, the nonlinear attributes are faint and challenging to discern and characterize, thereby compromising the practical effectiveness of the detection methodology. Consequently, the amplification of these subtle nonlinear features becomes imperative to improve the detection efficiency. In recent developments, elastic metamaterials, comprising artificially engineered structures, have demonstrated considerable potential in controlling wave modes and frequencies. Leveraging the metamaterial concept, this paper proposes an elastic meta-enhancer (ME), featuring special wave dispersion properties to facilitate effective wave collection for second higher harmonic through a graded array of resonators attached to an elastic plate, showcasing the improvement of sensitivity in detecting cracks. The amalgamation of resonance and spatial grading within surface arrays of structures enable meta-units to demonstrate broadband wave trapping, resulting in substantial amplification of out-of-plane displacement within the host plate medium at resonator positions, where the second higher harmonic component accumulates. Harnessing the interplay of these effects—deceleration in the resonators and amplification in the host beam—the numerical findings demonstrate that, given a sufficiently prolonged excitation time, the elastic ME can amplify the faint magnitude of the second higher harmonic produced by fatigue cracks within the host plate structure. The paper concludes with a summary, concluding remarks, and recommendations for future research directions.