A novel method for single and multiple damage detection in beams using relative natural frequency changes

Abstract Concentrated damage such as cracks is one of the most common types of damage in beams. It is essential to detect such damage early to avoid structural failure. Vibration-based damage detection methods that employ changes in structural dynamic parameters such as natural frequencies have been extensively studied, and it is commonly acknowledged that natural frequencies depicting structural global dynamic properties are incompetent to portray local damage. Differing from extant work, this study presents a concept of relative natural frequency change (RNFC) curves for local damage characterization and especially ascertains the relationship between RNFC curves and mode shapes, leading to an explicit equation of RNFC. With RNFC curves and measured values of RNFCs, a two-step method for localizing and quantifying damage is created: a novel probabilistic damage indicator is developed using Bayesian data fusion for localizing single and multiple damage; moreover, a damage severity factor defined as the stiffness reduction ratio of the damaged element is formulated to quantify damage. The proposed method features localization, quantification, and evolution monitoring of damage, relying solely on natural frequencies. The efficacy of the method is verified numerically and then validated experimentally on cracked beams. The numerical and experimental results demonstrate the capability of the method to localize single and multiple damage and to estimate damage severity. This mechanism of characterizing damage relying solely on natural frequencies provides the foundation for developing practical local damage detection and monitoring technologies for beam-type structures.