Issue 49

E.U.L. Palechor et alii, Frattura ed Integrità Strutturale, 49 (2019) 614-629; DOI: 10.3221/IGF-ESIS.49.56 626 Figure 21 : Mass (M) Position vs. First Frequency (f1). In Fig. 21, the first graph (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 the corrected frequency (dotted line) by a cubic spline interpolation method which, according to Palechor. [29], is the method that best fits the signals used to locate damages in the steel beams. Figs. 22 and 23 show the graphs corresponding to DWT applied to the previous signal considering the use of the four mother wavelet functions (rbio2.6, bior6.8, sym6, db5). (a) Symlet 6 (b) rbio2.6 Figure 22 : DWT First Frequency (f1) using Symlet 6 and rbio2.6 mother wavelets. (a) db5 (b)bior6.8 Figure 23 : DWT First Frequency (f1) using db5 and bior6.8 mother wavelets. Mass Position (node number) Fundamental Frequency FFT FREQUENCY CORRECTED FREQUENCY INTERPOLATED CURVE Fundamental Frequency (Hz) damage 1 damage 2 WAVELET COEFFICIENT  (Sym6) NODE NUMBER DWT NÓ nº 5 10 15 20 25 -4 NODE NUMBER NÓ nº 5 10 15 20 25 10 -5 -4 -3 -2 -1 0 1 2 3 TDW - FREQUÊNCIA F1 damage 1 damage 2 DWT WAVELET COEFFICIENT  (rbio2.6) NODE NUMBER DWT NODE NUMBER damage 1 damage 2 DWT WAVELET COEFFICIENT  (db5) NODE NUMBER NODE NUMBER DWT COEFICIENTES WAVELET (bior6.8) damage 1 damage 2 DWT WAVELET COEFFICIENT  (bior6.8) NODE NUMBER NODE NUMBER DWT