SELF

58

S.B. Karavashkin, O.N. Karavashkina

Another important characteristic of a wave process in a complex resistant line is the experimental measurement of vibration velocity of the lumped line end elements or of the distributed line end. Skudrzyk [1] has carried out this investigation. In Fig. 8 we show one of regularities of the rod end vibration velocity against the frequency taken from [1, p.244], and in Fig.9 – the similar theoretical regularity, obtained by way of (9) – (12) time differentiation. The difference between the theoretical and experimental results is only in the regions of lower spikes caused by the aperiodical vibration regime. This last is conditioned by the studied model ideality. With the line resistance appearance, the transition between the periodical and aperiodical regimes smoothes, and damping at the aperiodical band decreases, while at the periodical band it increases. The vibration pattern transformation itself with the resistance appearance is very interesting and can be studied on the basis of exact analytical solutions obtained here. However here we will limit ourselves with the above analysis, as this investigation far exceeds the frames of present task.

 Conclusions

Basing on exact analytical solutions obtained for semi-finite elastic line with resonance subsystems having the form of linear elastic lines with rigidly connected end elements, we have revealed that between the first boundary frequency for the elastic line as a whole and that for the subsystem the resonance peaks arise, and their quantity is equal to the integer part of [(n – 1)/2], where n is the number of elements in the subsystem. These resonance peaks arise at the boundary between the aperiodical and complex aperiodical vibration regimes. And this last regime is typical namely for elastic systems having resonance subsystems. In simple elastic lines its appearance is impossible.

Despite in complex aperiodical regime the measure of inertia of a resonance subsystem is negative, the phase delay of this process does not become leading. It fully accords with Skudrzyk’s conclusion that the negative measure of inertia of resonance subsystem completely corresponds to the conservation law. In this regime, with the steady-state process in the line the standing waves form, and the wave propagation phase velocity turns to infinity for the ideal line.

We also have determined that for interior elements of an elastic line the resonance peaks bifurcate, and it fully corresponds to Skudrzyk’s experimental results. However the reason of bifurcation is not the resonance circuits mismatch, as Skudrzyk supposed, but the features of resonance peaks formation for the input resistance and transfer function of an elastic line, which causes the resonance frequencies for these parameters to be not the same.

The theoretically obtained regularities for vibration velocity of a boundary element of a line are in good agreement with Skudrzyk’s experimental results.