V.2 No 1

29

Homogeneous 1d resistant line

?We can trace the same property in the phase velocity dependence on frequency. To find it, substitute (34) into (27). We will yield

At 0 , the phase velocity v_f 0, and at (/)² << 1, v_f (T_l/)^1/2 – i.e., to the conventional value of phase velocity in an ideal distributed line. At the same time in an ideal distributed line the phase velocity does not vanish at 0 but remains the value (T_l/)^1/2. In its turn, (40) does not describe the anomalous dispersion of velocity at high frequencies. The typical plot of v_f () is presented in Fig. 6.

Fig. 6. Phase velocity of wave propagation in a distributed elastic line against the frequency

Thus, we see that in (40) the main regularities of resistance affection on vibration process have retained. At the same time, the regularities describing the main parameters _r,    _0r,  R, v_f   have essentially transformed. In them, as a result of limit passing, the summands describing the process at the boundary band have disappeared, and this transformation is irreversible in case of the reverse transition to a lumped line. This property makes impossible the correct description of a lumped line by means of solutions yielded for that distributed.