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Purpose This study aims to analyse the impact of cracks on the free vibration characteristics of various structural beams; hence, a novel damage index is implemented for accurate crack localization. A modified normalized curvature damage factor (MNCDF) has been proposed based on the curvature data of the damaged beam, without relying on the healthy beam, thereby enhancing the reliability of damage detection. Design/methodology/approach The analysis was conducted on Euler–Bernoulli beams subjected to three different boundary conditions: simply supported, clamped–clamped and cantilever beams. The cracked beams are modelled by using the continuous method with a rotational spring at the crack region. The beam is divided into uniform sub-segments, and each segment is connected by rotational springs to account for the localized flexibility of the crack formation. The stiffness of these springs is derived from the principles of fracture mechanics, where continuity and compatibility conditions were applied at the crack location to ensure accurate dynamic behaviour was performed and the vibration characteristics can be extracted accordingly. The MNCDF technique relies on the data of the extracted mode shape curvature for each mode, where a good validation was demonstrated via different frequency modes by using a simplified computational approach. Findings The results showed that the presence of cracks leads to noticeable changes in the vibration behaviour of the structural beam, which become more significant as the number of cracks increases. The MNCDF method has demonstrated high efficiency to identify the sharp variations in the mode shape curvature near the crack locations, which confirms its effectiveness in detecting both single and double cracks, and independently for each vibration mode, which can be considered an advanced step in the field of structural health monitoring. Research limitations/implications The results confirm the validity of the MNCDF with the related papers, to accurately reveal single and double crack locations within beam structure. The validation process has demonstrated that the proposed damage index can accurately identify the crack location across different frequency modes by using a simplified computational approach. Originality/value This research presents a refined damage index that leverages vibration data of the damaged beams without needing to know the modes of the healthy beam. The proposed MNCDF can accurately reveal single and double crack locations within different beam structures based upon any frequency mode. It offers a significant advancement in early-stage structural damage detection and contributes to extend service life of engineering structures.
Namah et al. (Mon,) studied this question.