The paper presents a method to detect, locate and evaluate damage severity of Euler-Bernoulli beams, based on how natural frequencies change due to damages. Previous researches that dealt with this issue focused only on quantitative changes, mainly considering a global stiffness reduction in the damaged area. The authors have contrived a correlation between the strain energy stored in a segment of the beam, which is proportional with the mode shape curvature of a considered vibration mode at that location, and the frequency change for this mode if damage appears on that segment. This reveals that for an element of the beam, the stiffness change of a certain mode for a given damage varies between zero and a maximum, depending solely on the location of that element. Moreover, one has to consider different stiffness changes for a damaged element placed on a certain location, depending on the vibration mode. This rule how frequencies of various modes change due to damage are used to create patterns, based on relative frequency shifts, which characterize damaged beams in respect to defect location and severity. The method was validated by numerous experiments, which proved its accuracy and reliability.

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