Geology Reference
In-Depth Information
. kg m
2
. The aniso-
tropic shear stiffness in
y
and
z
direction are
k
y
=
5 96 10
6
of inertia of
I
x
=
×
⋅
=
. m
and
L
eff
3
=
m
,
respectively, the constant cross -sectional area of
A
1
L
eff
1
=
. m
,
L
eff
2
20 8
20 0
8 64 10
5
.
×
kN/m
and
2
2
2
=
. m
are too large for practical applications. Therefore
TLCGD1 and TLCGD2 are split into 6, and
TLCGD3 is split into 4 smaller units keeping the
effective fluid column lengths unchanged, thus
rendering altogether 16 TLCGD. The final opti-
mization is done by numerical fine-tuning in the
frequency domain in state space, Eq.(28), the
weighed sum of the generalized coordinates is
given in Figure 3b in the relevant frequency win-
dow. The function
fminsearch
of the Matlab op-
timization toolbox renders the optimal parameters
quite fast when starting the search with the Den
Hartog parameters.
=
. m
,
A
2
12 98
=
. m
,
A
3
12 50
10 00
k
z
=
7 80 10
5
.
kN/m
, and the torsional stiffness
×
1 38 10
8
. kNm/rad
. The center of stiff-
ness is eccentrically located at
C
is
k
t
=
×
=
(
)
, , 0
with
e
y
=
4m
,
e
z
=
3m
. With three dynamic
degrees of freedom for each floor assigned the
model is described by 90 DOF. A model reduction
is performed by applying a modal truncation to
include the first twelve modes, with an assigned
constant modal damping coefficient of 1% and
the natural (undamped) frequencies are 0.348,
0.384, 1.042, 1.151, 1.343, 1.734, 1.915, 2.421,
2.673, 3.102, 3.425 and 3.774Hz, respectively.
The modal analysis of the structure revealed that
three relevant centers of velocity are outside the
floor plan, therefore three plane TLCGD are in-
stalled in the building. The maximum modal
displacements for these modes occur in the 30th
floor (top floor) and the 10th floor, respectively,
indicating the best positions for the TLCGD. The
alignments of the absorber is parallel to the build-
ing floor plan with maximum distance from the
floor's modal center of velocity, see Figure 3a.
With a selected fluid mass of
m
f
1
e e
K
y
z
APPLICATION TO BASE ISOLATION
SYSTEM
Base isolation has become an increasingly applied
technique in structural design to protect civil
engineering structures with natural frequencies,
say above about 1Hz against earthquakes. Base
isolation techniques are used to decouple the
structure from ground motions using a mechani-
cal low pass filter. The decoupling is achieved
by inserting a layer of low horizontal and high
vertical stiffness between structure and founda-
tion. Isolated this way, a structure has a mode of
vibration, commonly referred to as base isolation
mode, with a natural frequency much lower than
the fixed base structure and certainly lower than
the predominant frequencies of the expected
ground motion. The most common laminated
isolation elements consist of alternating layers of
steel and rubber which need additional damping
usually provided by lead core plugs, hydraulic
or mechanical dampers. This type of isolation
system has a limited lifetime since the lead core
or rubber may melt due to overheating during
the earthquake or the aftershocks. Therefore a
=
270 10
×
kg
3
3
250 10
3
50 10
= ×
kg
,
β
= 4
and
κ
= =
0 8.
, the absorber in a
first step were tuned using Den Hartog's formula,
Eq.(25). For the selected structural modes the
effective modal damping coefficients are increased
from 1% to 7.08%, 6.47% and 3.77% respec-
tively. The optimal absorber frequencies, damping
ratios and appropriate gas pressure heads (with
gas volume and effective fluid column length kept
properly assigned as in the first Den Hartog tun-
ing) are given by
f
A
1
m
f
2
=
×
kg
and
m
f
3
=
. Hz
,
f
A
2
0 33
=
. Hz
,
0 37
f
A
3
=
. Hz
,
ζ
A
1
1 03
=
. %
,
ζ
A
2
12 09
=
. %
,
10 93
ζ
A
3
=
. %
,
h
0 1
4 62
=
. m
,
h
0 2
35 47
=
. m
39 14
h
0 3
=
. m
. With an effective length of
30 00
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