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By Farzad Ebrahimi

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Mechanical Systems and Signal Processing, Vol. 23, No. 3, 415-431, ISSN: 0888-3270. Michael A. Koplow, Abhijit Bhattacharyya and Brian P. Mann. (2006). Closed form solutions for the dynamic response of Euler–Bernoulli beams with step changes in cross section. 1-2, 214-225, ISSN: 0022-460X. , Biswas M. M. (1991). Damage detection from change in curvature mode shapes. 145, 321-332, ISSN: 0022460X. K & Biswas M. (1994). Damage detection in structures using change in flexibility. 169, 3-17, ISSN: 0022-460X.

02 as the first two modal damping ratios. Figure 7 shows comparison on the acceleration response at the 1/4 span of the beam for different crack depth. The crack is assumed to be at the mid-span of the beam. From this figure, one can see that the crack depth has significant effect on the dynamic response of the beam. 3 . 5L of the beam. From this figure, one can see that the response changes with the crack location. These studies show that the effect of the crack on the dynamic response is significant, so it is feasible to identify crack from measured structural dynamic responses.

The proposed model, in general, gives better results than the model in Sinha et al. Vibration Analysis of Beams with and without Cracks Using the Composite Element Model 29 since the latter crack model is a linear approximation of the theoretical crack model of Christides and Barr. 2 Free vibration analysis for a cantilever beam with multiple cracks The last beam above is studied again with a new crack introduced. The first crack is at 595mm from the left end with a fixed crack depth of 12mm while the second crack is at 800mm from the left end with the crack depth varying from 4mm to 12mm in step of 4mm.

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