Vibration-based damage detection in laminated composite plates: a novel approach using superposition of higher-order derivatives of mode shapes

Damage detection in composite structures can prevent sudden failure and catastrophic consequences. However, current detection methods based on mode shape often exhibit limited noise resistance and insufficient capability to detect components with specialized structures. To address these challenges, this paper proposes an innovative damage index based on the superposition of high-order derivatives of appointed-order modal shapes. Through normalization and feature highlighting algorithms, the index value at the damage edge is significantly higher than at other lossless locations. To avoid limitless superposition, a cut-off criterion for this index has been proposed by leveraging the numerical stability of the damage index in the damaged area, thereby indicating the optimal cycle for detection images. The superiority of the proposed method is validated through numerical and experimental results compared with other existing approaches. From the processed results of the numerical simulation, the proposed damage index can accurately highlight damage in different composite structures and can resist interference up to a signal-to-noise ratio of 40 dB. From the processed results of the vibration experiment, this new method correctly detects damage in two types of composite structures, producing clear images with precise damage location identification. Over all, the proposed method demonstrates an effective ability to highlight the damage edges, thereby providing a reliable means of ensuring the safety and integrity of engineering structures during operation.