Numerical Study of the Stiffness Degradation Caused by Branched Cracks and its Influence on the Natural Frequency Drop
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Abstract
This paper focuses on the accuracy of detecting the location of a complexly shaped damage present in a cantilever beam. The study is carried out by involving the finite element method. At first, we have parametrically described the geometry of a branched crack and designed its discrete model. As a further step, we performed simulations to observe the changes in the static and dynamic behavior of the beam that occur in the presence of damage. Several types of Y-shaped cracks have been taken for these analyses. We have shown the beam has a diminished capacity to store energy and consequently the frequency decreases. The frequency shift phenomenon for the first mode of vibration was found to be in concordance with the changes in the deflection of beam’s free end. We derived on this basis a correction coefficient that considers the beam deflections in the intact and damaged state. This coefficient permits predicting the frequency shift due to a given crack. As the last step, we have successfully compared the frequencies achieved directly using the FEM with those for the intact beam to which the correction coefficient was applied.
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References
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