Let us consider the dependence of the displacement and the speed of the left end
in time under the condition
()
0
,
=
V
U
R
(there is no element with the HLS), Fig. 7 (a). The
solutions, which are obtained by the Fourier method and the difference method, are
almost identical. So, the parameters are selected at P=305 Ns:
5
10
5
−
=
s,
3
10
6
,
9
−
=
h
m (coarse grid),
8
,
0
=
.
Figure 7. The oscillation of the left shank end without an HLS element: 1 - the
Fourier method, 2 - the difference method (stove (a) and fine (b) grid)
Figure 7 (b) shows the solutions that are obtained over a short period of time (a
fine grid). In this case we have a high frequency and a small amplitude oscillation.
These oscillations cause high-frequency oscillations of the shank end speed. For
comparison, the oscillation of a rod without HLS element is given (the solution is found
by the Fourier method).
We consider the left shank end oscillation when included an HLS element. The
result of high-frequency oscillations (small amplitude) of the left shank end is speed
fluctuation of a large amplitude and frequency, i.e. we have a high frequency change
of the velocity sign (Fig. 8). So, we have the corresponding oscillations in the resistance
of the working medium and, as a result, the slow oscillation suppression, which does
not correspond to the parameters obtained experimentally.
Figure 8. The velocity (a) and the displacement (b) of the left shank end. The
velocity of the shank end is determined by the formula
(
)
1
1
1
−
−
+
−
=
t
U
U
V
n
N
n
N
n
N
while
=
t
; 1) the Fourier method, 2) - the difference method.
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