Issue 49

E.U.L. Palechor et alii, Frattura ed Integrità Strutturale, 49 (2019) 614-629; DOI: 10.3221/IGF-ESIS.49.56 627 In the previous figures (Figs. 22 and 23), it can be observed that the greatest peak, or spike, was generated between nodes 8 and 9 which matches to the damage located at 1.5m. The graph also shows a less prominent, but still noticeable, spike between nodes 23 and 24 which is the position of the second damage. Note that such peaks are big enough to be seen compared with the other peaks where no damage exists. Case 2 In Fig. 24, the graph of the data corresponding to the first frequency of the beam vs. mass position is shown along 31 nodes of the beam (discretization made every 20 cm). The added mass used was 24.718 kg, positioned on each node location. Figure 24 : Mass (M) Position vs. First Frequency (f1). In Fig. 24 three curves can be observed, the first (dashed line) represents the FFT peak frequencies; the second (dotted line) represents the corrected frequency using the FFT spectral lines around the peak as a weighted average to calculate the real frequency. The third curve (solid line) represents the interpolation of corrected frequency data (dotted line) by a cubic spline interpolation method. (a) Symlet 6. (b) rbio2.6. Figure 25 : DWT First Frequency (f1) using Symlet 6 and rbio2.6 mother wavelets. a) db5 b)bior6.8 Figure 26 : DWT First Frequency (f1) using db5 6 and bior6.8 mother wavelets. Posição da Massa (Nó nº) 5 10 15 20 25 30 1ª Frequência (Hz) 7.5 8 8.5 9 9.5 1ª Frequência vs. Posição de Massa FFT FREQUENCY CORRECTED FREQUENCY INTERPOLATED CURVE Fundamental Frequency Fundamental Frequency (Hz) Mass Position (node number) WAVELET COEFFICIENT (sym6) damage 1 damage 2 damage 1 damage 2 damage 1 damage 2 damage 1 damage 2