Civil Engineering Reference
In-Depth Information
8.4.5.3.3. Extension to a narrow-band process
As the maxima of a narrow-band process come in the shape of packages, the
Poisson
model for the calculation of W is no longer valid. Instead of applying the
model to the process itself, we could try to apply it to its envelope.
For a
Gaussian process,
the average number of maxima per package is given by:
1
ª
1/ 2
º
ª
º
[8.35]
EN
r
1 exp ʌ/2 įr
¬
¼
«
maxi
»
¬
¼
where the bandwidth parameter G appears.
Thus, we can derive from it a threshold crossing average frequency by the
envelope:
fr/EN
ª
r
º
¼
[8.36]
¬
maxi
and use this frequency as previously.
It will also be possible to adjust semi-empirical formulas inspired by what comes
before, the most sophisticated of which is
Vanmarcke
's formula:
^
ª
º
2
2
W r, N
1
exp
r
/ 2 Ln2
exp
N exp
r
/ 2
«
»
¬
¼
`
ª
1/ 2
1.2
º
ª
º
2
1exp ʌ/2
r
/ 1
exp
r
/ 2
[8.37]
į
«
»
¬
¼
¬
¼
Figure 8.6 shows a comparison between different models and simulation results
carried out with a reduced 0.01 (G = 0.11) damping harmonic oscillator.
Figure 8.7 shows the results of digital simulations concerning the evolution of
the peak factor and the maximum standard deviation as a function of N and G.
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