Civil Engineering Reference
In-Depth Information
In the present case of a shock oscillator, the relationship can be found
analytically by considering the periodic regime set for the free oscillator (without
any stimulation) instead of the dampened oscillator, which is illustrated in Figure
8.23.
Figure 8.23.
Periodic regime/ratio for the 1-dof, free and non-dampened shock oscillator
The idea involves writing that these sequences correspond to the response of a
Z
0
-resonance pulsation and H-damping coefficient linear oscillator, to random noise,
the intensity of which is different from the initial random noise by an S(Z
0
) factor:
2
2
2
dx/dt
2İȦ dx/dt Ȧ xSȦ t
*
[8.63]
0
0
0
the
pulsation
Z
0
being
random
(H can be considered as constant and thus as
deterministic).
As far as the random process is concerned, we will be able to represent the X(t)
response process using two slow time variation processes: the X
max
(t) amplitude and
the \(t) phase shift which characterize the sequences, and a fast time variation
process that represents the 4(t) phase of the oscillation within a sequence. The :(t)
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