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20 April 2012 Robust method to identify damages in beams based on frequency shift analysis
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The paper presents a method to assess damages in beams, based on how natural frequencies of bending vibration modes change due to damages. 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. For a certain mode, damages placed on inflection points of the mode shape curvature, where the strain energy is null, will not produce changes in frequency, while damages placed on maxima will produce the highest changes in frequency. For other locations of damage, the frequency shift will be proportional with the mode shape curvature of the vibration mode at that location. We worked out a general relation, which gives the frequency shift of all bending modes, with one coefficient depending on the support type. To evaluate damages, we determine analytically the relative frequency shift as ratio between the frequency change and the natural frequency of the undamaged beam, for the first ten vibration modes, considering various damage depths and locations. Comparison of results with that obtained by measurements on the real beam permits detection, location and assessment of damages in beams with high accuracy. The method was validated by experiments.
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Gilbert-Rainer Gillich and Zeno-Iosif Praisach "Robust method to identify damages in beams based on frequency shift analysis", Proc. SPIE 8348, Health Monitoring of Structural and Biological Systems 2012, 83481D (20 April 2012);

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