V.2 No 1

21

Homogeneous 1d resistant line

3. Analysis of excitation transmission process in a resistant elastic line

The parameters R and _r have the main effect on the resistant elastic line vibrations. To analyse them, conveniently use the transfer function of a link G_r by the analogy with electric filters:

where G_r is the transfer function for resistant elastic lines.

According to (24), the transmission coefficient of each link is proportional to R² and the delay caused by each link – to 2_r. This process is inherent in the whole frequency range from zero to infinity. At the same time, according to (7)–(9), the transfer function of a link G₀ for an ideal line is different in all three bands of   variation:

In accordance with (11) and (17), both parameters, _r and , depend on frequency nonlinearly. At r 0 we have _r , R 1 and G_r G₀. It means that an ideal line reflects the processes occurring in real lines as some approximate model, despite in the general solutions three frequency bands appear. The plots 2_r()  and R²(), shown in Fig. 1 and Fig. 2 corroborate it.

Fig. 1. Delay phase, caused by a member of an elastic line, against the frequency

Fig. 2. Attenuation degree R² caused by a member of line, against the frequency of external affection f , at different resistances r