Geology Reference
In-Depth Information
Figure 2. Earthquake: acceleration measurement and spectrum
must combine some of the most typical ones by
for example, taking the mean of their frequency
components. The spectrum of this average earth-
quake is representative in intensity and frequency
as it covers the base terms of the earthquakes to
be assumed to act on the building.
1
2
∫
T
W
(
ω
)
=
µ
(
ω
)
Ã
(
ω
)
dVol
(7)
el
k
max
k
max
k
Vol
where
ε
(ω
k
) denotes the vector of the strain com-
ponents and
σ
(ω
k
) the vector of the stress compo-
nents at the frequency ω
k
. The summed response
Building Response
k
max
∑
W
=
W
(
ω
)
(8)
el tot
,
el
k
The ground's seismic time-dependent displace-
ment causes the dynamic response of the structure.
We decompose the impact (here interpreted as
exciting force) into its frequency components
(Figure2b)
k
=
0
represents the energy input over the frequency
range if ω
kmax
=
k
max
ω
0
stands for a frequency
larger than the maximum Eigen frequency to be
considered. An optimization of the building's
capability to withstand earthquake excitation may
be done by minimizing this response or any other
appropriate measure.
∑
i
ω
t
F
=
F e
ω
=
k
ω
0
(6)
k
k
k
k
ω
0
being a reasonable base frequency, and check
the impact of each frequency on the dynamic
system. As one result, we have the response and
the elastic energy of the volume of the structure
About Compensators
Compensators are often used to reduce the dynamic
response of oscillating systems. Most of the basic
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