V.2 No 1

33

Homogeneous 1d resistant line

6. Conclusions

Studying the vibrations in a semi-infinite resistant elastic lumped and distributed lines, we have revealed that the resistance effects both on the line vibration pattern as the whole and on the transmission parameters of along-the-line excitation. The resistance effect on vibrations as the whole is revealed at the low and ultralow frequencies, and its effect on the transmission of excitation is considerable at the whole range.

We have ascertained that the progressive vibrations in a resistant line retain also at the over-boundary frequencies. At this band the phase velocity grows approximately linearly, and the group velocity increases when the resistance falls. At large r, the dependence of all parameters of vibration process on frequency transforms into the smooth functions without local extremes or kinks in the domain of critical vibration regime corresponding to the boundary frequency ₀.

Besides, we have revealed that when the vibration propagated in a line, the phase delay never reaches the value corresponding to the first Brillouin zone.

The solutions for a distributed line reflect the salient features of the initial frequency band of solutions for lumped lines. Particularly, the phase velocity vanishes at 0, doing not retaining its finite value, as in an ideal elastic line occurs. At the same time, the solutions for a distributed line do not describe the anomalous dispersion of velocity, which the solutions for a resistant line describe.

When comparing the yielded results with the experimental data on the study of phase velocity of ultrasonic wave in carbonic acid gas, we saw that taking the resistance into account, we can essentially improve the conventional models and promote their better relation to the experimental data.