PSI - Issue 5

J. V. Araújo dos Santos et al. / Procedia Structural Integrity 5 (2017) 1198–1204 J. V. Araújo dos Santos et al. / Structural Integrity Procedia 00 (2017) 000 – 000

1202

5

~ ( ) ( ) x x r 

r

r

DCD x

( )

  

(10)

3. Results

The study of the influence of the shearing amount on the quality of the damage identification is presented in this section. For brevity sake, it is reported an analysis considering only the first modal rotation field.

3.1. Qualitative analysis of the results

We observe in Figure 2 differences in peak values of the damage indicators DCD and MCD with different shearing amounts. The modal curvatures used for the computation of MCD were obtained by first applying backward finite differences to numerical modal displacement w ( x ), followed by numerical differentiation using central finite differences. A noticeable feature of Figure 2 is that shearing amounts larger than the width of the damage, which is equal to 5 mm, produce important attenuations in the peak values of MCD. We also notice that the area defined by MCD undergoes a shift to the right, relatively to the real damage position. Furthermore, this shift is independent of the stiffness reduction describing the damage. This shows that we need to find a better correlation of the decrease in bending stiffness than simply the values of the damage indicators.

(a)

(b)

(c)

(d)

Fig. 2. Damage indicators for (a) first; (b) second; (c) third; d) fourth damage cases.