SELF

24

S.B. Karavashkin and O.N. Karavashkina

To find v_f , note that the wavelength in an elastic lumped line can be presented as

where a is the distance between the unexcited elements of line. With (26), the conventional expression for the phase velocity will take the form

Substituting (17) into (27), we yield the sought regularity whose pattern is presented in Fig. 3.

Fig. 3. The phase velocity v of wave propagation in the line against the frequency f of external force affecting the line

We see that in the subcritical band at small r, the phase velocity in the beginning of frequency band increases rapidly from zero to some local maximum. After it, the velocity slowly falls, and after the critical frequency it grows again practically linearly. It evidences that in a resistant line, in all the range, the progressive pattern of wave propagation takes place. At the ultralow-frequency and overcritical band a normal (positive) phase velocity dispersion takes place. While at the intermediate band, an anomalous (negative) dispersion occurs. With growing resistance the anomalous dispersion band narrows, and at large r the dependence v_f () becomes a monotonously growing function characterising the normal dispersion at the whole range.