PSI - Issue 13

I. Shardakov et al. / Procedia Structural Integrity 13 (2018) 1342–1346 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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of the lateral surface (Fig. 2b) leads to the excitation of vibrations with a dominance of flexural-torsional eigenmodes. Registration of vibrograms of displacement along the normal to surface at local points of the sample was carried out by the laser vibrometer 3. The registration points were chosen so that they could fix the dominant eigenmodes.

a

b

c

Fig. 1. (a) Excitation of longitudinal vibrations; (b) excitation of flexural vibrations; (c) pulse shape

Let us demonstrate the performance of the algorithm of experimental data processing for the case of excitation of longitudinal vibrations. The algorithm consists of several stages. At the first stage, the time interval for the excitation of free vibration is determined from the results of measuring the velocity vibrogram (Fig. 2a). In this case, it is the interval from 15 ms to 50 ms. For the vibrogram of the velocity, a Fourier image is built in the selected range (Fig. 2b), which allows evaluating the value of the eigenfrequencies for the dominant (longitudinal) vibration eigenmode, which is equal to exp 4882 Hz long f  . At the second stage the band-pass filtering of the obtained Fourier image is performed in the neighborhood of the eigenfrequency exp 4882 Hz long f  . The vibrogram obtained after filtering is shown in Fig. 3a, and the corresponding Fourier image is shown in Fig. 3b. The third stage is associated with determining the evolution of the amplitude of the decaying natural vibrations at frequency exp 4882 Hz long f  . It is evaluated using the points of local extrema of the vibrogram. In Fig. 4a, these points are marked with crosses. The dependence of the amplitude on time in the logarithmic scale is shown in Fig. 4b. It also shows a linear approximation of this relation. The logarithmic decrement is calculated based on the linear approximation. It is equal to e 3 xp 33.38 10 long     .

a

b

Fig. 2. (a) Longitudinal vibrations: vibrogram; (b) corresponding Fourier image

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b

Fig. 3. (a) Vibrogram of a signal filtered in the vicinity of the eigenfrequency exp

long f 

; (b) corresponding Fourier image

4882 Hz

a

b

Fig. 4. (a) Vibrogram of the filtered signal; (b) amplitude evolution and its linear approximation in the logarithmic scale