PSI - Issue 32

I.O. Glot et al. / Procedia Structural Integrity 32 (2021) 216–223 Shestakov A.P./ Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 6. Localized harmonic signal (left) and its spectrum (right).

Another approach to processing vibrograms can be based on the windowed Fourier transform. The good applicability of this method follows from the analysis of the causes of the appearance of a nonsmooth spectrum. Clearly, using examples of simple signals, these causes are explained below. A graph of a constant harmonic signal and its spectrum are shown in Figure 5. From the figure it follows: one harmonic signal corresponds to one sharp peak in the spectrum. The localized harmonic signal is shown in Figure 6. In this case, one peak is observed in the spectrum, but its width increases. In the case of the appearance of a second localized harmonic signal, the spectrum changes greatly (Fig. 7). Figure 7 shows the cases where the second signal is shifted in phase relative to the first by 0, π / 2 and π , respectively. In the absence of a shift of the second signal relative to the first ( 0  = ), one dominant peak and two adjacent peaks of lesser magnitude are observed in the spectrum. In the case of a shift / 2   = , the dominant peak in the spectrum does not correspond to the given frequency; in addition, a second peak of comparable amplitude appears. At   = , two peaks of practically equal amplitude appear. Unambiguous determination of the natural frequency by the maximum value in this case becomes impossible. Similar spectra were obtained by processing vibrograms measured on the structure (Fig. 4). This suggests that at time intervals corresponding to technological operations, a lot of localized shock impact are implemented, which can be in an arbitrary phase relative to each other. Therefore, the spectrum is a non-smooth function. The most preferable in this case is the analysis of vibrograms using a windowed Fourier. By using this method and decreasing the "window", the probability of two signals being into the "window" is reduced. As a consequence, the spectrum of the windowed Fourier is a smoother function.

Fig. 7. Two localized harmonic signals (left) and their spectra (right), the second signal is phase-shifted relative to the first by 0, π /2 and π .