Issue 48

R. S. Y. R. C. Silva et alii, Frattura ed Integrità Strutturale, 48 (2019) 693-705; DOI: 10.3221/IGF-ESIS.48.65 699 effectiveness and applicability of the methodology proposed in Section 3 of this paper. Fig. 7 shows details of two of the damage cases studied in this research. (a) (b) (c) (d) Figure 7 : Damage cases: (a) Damage artificially introduced; (b) Damage D1; (c) Damage D2; (d)Plan view of the damage positions. Damage D1 consists of a half cut along the height of the external beam. Damage D2 is a complete cut of 1cm width along the height of the beam. Damages D1 and D2 represent reductions, in different measure, of the cross section area of the bridge beam corresponding to 8% and 16%, respectively. Tab. 1 presents the experimental natural frequencies obtained from the ARTeMIS software [16]. Mode Intact Case D1 1º 10.25 9.96 2º 14.16 14.06 3º 27.29 27.63 4 º 35.98 35.32 Table 1: Experimental natural frequencies (Hz). The damage detection was done by taking into account only the damaged mode shape in case D1. The data of five points corresponding to the first experimental mode shape of each line of the bridge (Fig. 3) were exported to MATLAB and then Cubic-Spline interpolation was used to increase the number of data from 5 points to 1,000 points. After interpolations, the Tikhonov regularization technique was applied to the interpolated mode shapes. As explained in the flowchart in Fig. 1, the last but one step of the proposed methodology is the application of CWT. The results of CWT application are presented in Figs. 8 and 9, respectively, for the Daubechies5 (Db5) and the Coiflet4 (Coif4) mother wavelets. Figs. 8 and 9 show the CWT results of damage case D1 adopting, respectively, the Daubechies and Coiflet wavelets. Notice that in this case just a single crack is present. In Fig. 8 and 9, the left and right plots, respectively, represent the CWT analysis in 3D and 2D. In these figures it can be observed that the wavelet coefficients in the damaged region achieved very large amplitudes due to the singularities in the sign (mode shape data) caused by the presence of the damage D1.