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Table 3. Optimal TMD/MTMD(7) parameters for Case 1 and Case 2 irregular building-MTMD systems
(structural damping ratio = 2%)
Damping
ratio,
ξ
s
0
Controlled
mode (Mass
ratio)
Number
of MTMD
units,
p
Location ratio,
d
s
k
/
r
Frequency ratio,
r
f
k
Building
Parameters
Case
1
0.86
9.2%
0.948
λ
λ
ω
e
=
=
0 3
1 0
.
.
first mode
(2%)
1
0.71, 0.76, 0.81, 0.86,
0.91, 0.96, 1.01
0.826, 0.864, 0.901, 0.939,
0.982, 1.032, 1.098
7
2.5%
1
0.86
8.2%
0.958
λ
λ
ω
e
=
=
0 3
1 0
.
.
first mode
(1.59%)
0.71, 0.76, 0.81, 0.86,
0.91, 0.96, 1.01
0.846, 0.881, 0.915, 0.950,
0.988, 1.033, 1.091
7
2.2%
2
1
-1.16
4.9%
1.324
second mode
(0.41%)
-1.206, -1.191, -1.176,
-1.161, -1.146, -1.131,
-1.116
1.230, 1.266, 1.297, 1.328,
1.359, 1.393, 1.435
7
1.2%
amplitude but the entire trace of the acceleration
responses are significantly reduced due to the
installation of MTMD, in particular for the Case
2 MTMD system in controlling two structural
modes.
sider SSI parameters,
h
ω
≈
60
and
λ
h
=2
T
u
π
=
2
π ω
is the fundamental period
in second suggested by Sikaroudi and Chandler
(1992) were used. In addition, the value
σ
=1.5
corresponding to soft soil (
V
s
≅
280 m/s) was
used to represent the site conditions of the Kobe
earthquake. The value
σ
= ∞
representing the
fixed-base condition was also investigated for
comparison. Figure 11 presents the peak floor
translational acceleration of the irregular building
versus
T
u
under the Kobe earthquake. Comparing
the curves with and without the SSI effect, it is
found that the building response would generally
be overestimated if the SSI effect is ignored. These
figures also show that the TMD and MTMD
control effectiveness is strongly dependent upon
the frequency content of the earthquake. Moreover,
the SSI effect decreases the TMD and MTMD
effectiveness since the detuning effect occurs. If
the SSI effect is not considered, the vibration
control effectiveness will be overestimated. The
time history accelerations illustrated in Figure 12
are the dynamic responses of floor translation for
the building of
T
u
= 0.4 sec in Case 1 (or Case 2)
without and with MTMD(7) considering SSI ef-
fect. It is clearly shown that not only the peak
where
T
u
(
/
)
x
FUTURE RESEARCH DIRECTIONS
Since a TMD/MTMD is a frequency-sensitive
device, the accuracy of dynamic properties of
primary structures is a key issue in designing this
type of device. Although this could be achieved
by employing system identification techniques
directly based on the vibration measurements of
the structures, using a more precise mathematical
model to simulate the controlled system is still
worthy for the prediction of the TMD/MTMD
vibration control effectiveness. The authors sug-
gest that a more accurate system model, such
as an SSI model of multi-story, nonlinear TC
building under bi-directional ground motions or
vertical ground motion and so on, be developed
in the future. Another direction is to develop a
different TMD/MTMD mechanism to solve the
stroke problem, which may completely change
the original behavior of a TMD/MTMD system.
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