SELF

20

S.B. Karavashkin and O.N. Karavashkina

It is convenient to transform (7) into an algebraic form, noting (11):

Now substituting (5) and (13) into (14), after the transformation we yield the sought solution in the form

where 

_r , _0r are the delay phases of the resistant line:

and A, B, C, D are auxiliary parameters:

Comparing (15) with (14), we see that the resistance affects the solution in two ways. It effects on the vibration pattern on the whole and on the link-to-link excitation transmission. The multiplier ( ⁴m² + r^{2 2})^1/4 effects on the amplitude as the whole. Its influence is especially considerable at the low and ultralow frequencies, when r^{2 2} is comparable with ⁴m². It is quite limited band, out of which in practical calculations we can neglect r^{2 2} in comparison with ⁴m².

The parameter _0r  also effects on the vibration phase on the whole. According to (18) and taking into account (19) and (20), this influence is also limited by low and ultralow frequencies. At  r << m, the vibration phase _0r can be approximately calculated as

Despite so limited influence of these parameters, we have to take them into consideration when studying the ultralow-band vibrations and broad-range excitations, since the presence of phase _0r causes the dependence of initial phase of vibration process on the frequency, because of hyperbolic dependence of this phase on frequency in (23).