A Crack Location Index for Crack Detection in Beam-Like Structures Carrying a Roving Mass

Abstract Purpose Vibration-based damage identification methods rely on robust damage indices to detect and localize structural defects. While natural frequency shifts are often cost-effective and easily obtainable, their sensitivity to minor damage and dependence on baseline (intact) data remain key challenges. Existing roving-mass-based methods often suffer from mass-induced modal fluctuations that generate false peaks in frequency-location curves, limiting their reliability for crack localization. This study aims to develop a robust crack location index for beam-like structures that improves crack localization accuracy when a roving mass with rotary inertia traverses a crack, while relying primarily on measured natural frequencies. Methods An analytical expression for natural frequency estimation is derived and validated against results from the Dynamic Stiffness Method, forming the basis for the index formulation. The proposed index integrates measured natural frequencies with analytically available modal properties of an intact Euler-Bernoulli beam, allowing false peaks to be suppressed without requiring baseline frequency measurements. Results Numerical studies demonstrate that the index reliably identifies single and multiple cracks and performs consistently across different boundary conditions, with the combined use of the 2nd and 3rd modes providing the most stable diagnostic signatures. Experimental validation confirms the index’s superiority over the change of natural frequency shift; the results show that the index can pinpoint crack locations with high accuracy without requiring experimental baseline measurements from the undamaged structure. Conclusion The proposed index provides a robust and baseline-free approach for crack localization in beam-like structures. By incorporating intact-beam modal information into post-processing, the method improves damage identifiability.