Issue 49

E.U.L. Palechor et alii, Frattura ed Integrità Strutturale, 49 (2019) 614-629; DOI: 10.3221/IGF-ESIS.49.56

Fundamental Frequency FFT FREQUENCY CORRECTED FREQUENCY INTERPOLATED CURVE

Fundamental Frequency (Hz)

Mass Position (node number)

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).

DWT DWT

DWT

10 -5

TDW - FREQUÊNCIA F1

0 1 2 3

-4 -3 -2 -1

damage 2

damage 2

damage 1

damage 1

WAVELET COEFFICIENT  (rbio2.6)

WAVELET COEFFICIENT  (Sym6)

5

10

15

20

25

-4

NÓ nº

5

10

15

20

25

NODE NUMBER NODE NUMBER

NODE NUMBER NÓ nº NODE NUMBER

(b) rbio2.6

(a) Symlet 6

Figure 22 : DWT First Frequency (f1) using Symlet 6 and rbio2.6 mother wavelets.

DWT DWT

DWT DWT

damage 2

damage 2

damage 1

COEFICIENTES WAVELET (bior6.8) WAVELET COEFFICIENT  (bior6.8)

WAVELET COEFFICIENT  (db5)

damage 1

NODE NUMBER NODE NUMBER

NODE NUMBER NODE NUMBER

(b)bior6.8

(a) db5

Figure 23 : DWT First Frequency (f1) using db5 and bior6.8 mother wavelets.

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