81

Some features of the forced vibrations modelling

At the same time, the solutions presented here are more general than the corresponding 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 itself takes the form

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

Note that when the solutions transform, the definite multipliers disappear; this makes the reverse transition impossible out of direct using the method being the base for these models calculation.

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

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

in the periodical regime ( < 1)

in the aperiodical regime ( > 1)

and in the critical one ( = 1)