V.2 No 1

81

Some features of the forced vibrations modelling

At the same time, these solutions are covering for the related solutions in [2]. Thus, for the periodical regime at k = 1, the first expression of (50) takes the following form:

which corresponds to the second expression of the given system at i = 1, k = 1. And the second expression takes the form

which relates to the periodic solution for a finite free-ends line in [1].

Notice that when the solutions transform, some multipliers disappear; this makes the reverse transition impossible, if not using the method being the base for these models calculation.

3.2. Semi-finite line with the free start

The external force affection on the line interior elements considerably changes the vibration pattern in a semi-finite elastic line, too. To prove it, consider the solution for a semi-finite elastic line with a free start; its analogue was considered in [2]. Its general form is shown in Fig. 3.

The modelling system of equations has the following form:

The system (57) has the following form of solution:

for the periodical regime ( < 1)

for the aperiodical regime ( > 1)

and for the critical regime ( = 1)