V.2 No 1 |
57 |
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On complex resonance vibration
systems calculation |
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Basing
on K () and on results presented in
[22], we can determine the phase velocity vf of the wave propagation
along the ideal line |
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, |
(20) |
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where a
is the distance between the elastic line non-excited elements, and K is the i th
element phase delay in (17). The typical form of the phase velocity dependence on
frequency is shown in Fig. 7. |
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We can
see from Fig. 7 and (20) that in the complex aperiodical regime the phase velocity turns
to infinity, as at these bands K is zero (see Fig. 4). At the same time,
the phase delay vanishing evidences that the standing wave has produced in the line,
despite its limited length. This is the consequence of the steady-state pattern of the
studied wave process. If the line impedance was present, the phase K does not
vanish. Similarly, if along the line the wave process propagated whose spectrum is wider
than one band of complex aperiodical regime, then the resulting phase delay also does not
vanish. Thus, the obtained result is the idealisation too and can be corrected
automatically when solving the practical models having the impedance. Going
on analysing (20), we see that the phase velocity achieves its minimal value in
aperiodical regime, since at these bands K is maximal. At these bands the
phase velocity dependence on frequency is linear, as the phase delay is constant and equal
to . With it,
all bands of aperiodical regime are located on one line coinciding with the linear
regularity, after which the phase velocity would increase in the absence of resonance
substructure. It corroborates additionally the above statement that the resonance peaks of
the subsystem arise in the region between the periodical and aperiodical regimes for the
system as a whole. Furthermore,
it is typical that despite the sections having negative measure of inertia appear, the
transfer function phase retains delaying always, and this also is in full accordance with
the above Skudrzyks statement [1] that the negative measure of inertia of line
elements fully corresponds to the conservation laws. This
negative measure of inertia, which we used to think strongly associated with the mass,
does not mean a negative mass introduction. In this case, there reacts not a separate mass
but a complex system of elastically connected masses being the parts of a general elastic
system. So we have to identify just this reaction with the negative measure of inertia of
the subsystem. We see that the pattern of subsystem reaction to the external action
changes. With it the pattern of process also changes. And the phase with regard to the
external action retains negative. Thus, introducing the idea of negative measure of
inertia, we do not contradict the laws by Newton who considered an accelerated body as an
entire rigid system. |
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