SELF

22

S.B. Karavashkin and O.N. Karavashkina

Despite in a resistant line only the periodical vibration regime can be realised, in the plots we clearly see that at small  r at the sub-critical band, 2_r varies as arc sine and the damping is absent, because R = 1. At the overcritical band, the phase is constant and equal practically to , but the damping arises. The antiphase vibration damping at the neighbouring elements of a line causes it. At the point of critical regime, which in Fig. 1 and Fig. 2 relates to the frequency f₀ = 31,8Hz (where f₀ is the boundary frequency), we see the kink of characteristics. In other words, at small  r   a resistant line exactly replicates all features of the periodical, critical and aperiodical regimes of a related ideal line. The only distinction is, for a resistant line all features of vibration regimes are described by the unified analytical functions, not by a system like (25). When calculating the elastic systems having small r, it enables us to use the ideal line model in which the conditions causing the line to the pass- or stop-band vibrations have been differentiated more clearly for a wave process.

With the resistance growth, at the subcritical band the plot 2_r() differs from arc sine more and more. At the overcritical band 2_r also is not equal to , but asymptotically tends to this value. This is why the aperiodical regime is impossible in a resistant line. But the worsening of damping properties caused by the disturbance of antiphase vibrations of the neighbouring elements does not diminish the damping introduced by R²(). It even increases, when the dissipative properties of a line grow. The more r grows the more damping has an effect on the subcritical band, and the transition typical for the critical regime smoothes, leading R²() to the asymptotic form at large r. We can see alike transformations also in 2_r(). The transition typical for the critical regime is also smoothed in this last regularity, and at large r the regularity 2_r() takes a form of a smooth function. At the same time, the delay phase  2_r exceeds in case of neither ideal nor resistant line, and at r 0  it will not reach it on all the range.