V.2 No 1

55

On complex resonance vibration systems calculation

We see from (17) and (18) that both parameters K and _input have the amplitude K , _input and phase _K , _input parts, and for different bands of _g variation they differ. In Figures 4 and 5 the typical form of these parameters is shown for the case when the resonance subsystems contained 10 elastically connected bodies each. To visualise, under each plot we give the scale of regimes corresponding to the conditions (17) and (18). It is seen clearly that all these regularities consist of sequentially alternating regions of the above regimes. All the resonance peaks locate at frequencies higher than critical for an elastic system as a whole, i.e. higher than the frequency before which we can consider the system, disregarding the substructure of its elements. With variation from zero to the first maximum, the input resistance falls from F₀/2s _g to zero. But practically, at this entire band the transfer function modulus is equal to unity. At frequencies exceeding the boundary frequency for the system as a whole, in simple models the aperiodical regime of antiphase damping vibrations is usually expected, but when taking the substructure into account, we see a resonance peaks succession. Each peak for the parameter K is formed at the joints of aperiodical and complex aperiodical vibration regimes, and for _input – at the joints of complex aperiodical and periodical vibration regimes. The number of these peaks depends on the subsystem size and is equal to the integer part of the value [(n – 1)/2]. This last is determined by the denominator of the first expression of (7).