Geology Reference
In-Depth Information
Parameter Identification
of the Bare Building
tribution of the 2% MTMD mass ratio was 1.69%
to the first group and 0.31% to the second group,
which was obtained by minimizing the mean
square roof acceleration under the condition of
two single TMDs controlling two structural modes.
With the given masses, the optimal parameters of
the first-mode MTMD and second-mode TMD
with
α
= 0 are first obtained based on the design
theory stated earlier. The optimal parameters are
presented in Table 2.
The mass block of each MTMD unit was a
steel cuboid with four bearing wheels and was
placed in a metal box of 93 cm in length. Inside
the box, there were two parallel guiding rails. Two
compression coil springs were used to generate
the resilient force of each MTMD unit. Based on
the optimum masses and designed stiffness coef-
ficient in Table 2, mass blocks and springs were
made. The simulation 3D view of the finished
MTMD device is shown in Figure 5. The installed
location of this MTMD was on the roof at which
the maximum of the first mode shape located
(Ueng
et al.
, 2008).
According to the design parameters in Table
2, each MTMD unit of the first-mode MTMD is
supposed to give a supplemental damping device
with optimal
c
s
0
. However, measurements of the
free vibration of the SDOF mass-spring system
of the fabricated MTMD unit showed that due to
contact friction, an equivalent damping coefficient
of 71.0 N·s / m, exceeding the demand optimum
damping coefficient, 27.8 N·s/m, in the case of
α
= 0
, was observed. Consequently, no addi-
tional supplementary damping was installed. The
After the setup of the bare building, a shaking
table test was conducted first. The excitation used
for the test was the ground acceleration recorded
during the 1999 Chi-Chi earthquake on the campus
of National Chung Hsing University (NCHU) in
Taiwan along the E-W direction. The original PGA
(360 gal) was scaled down to 30 gal to ensure
that the building remained linear and the strokes
of MTMD units were within the allowable range.
After collecting and processing the acceleration
measurements, the SRIM (System Realization
using Information Matrix) system identification
technique (Juang, 1997; Lin
et al.
, 2005) was
employed using the second floor (2F), third floor
(3F), and roof (RF) accelerations as output and
the base acceleration as input. The identified
modal frequencies, damping ratios, and mode
shapes are presented in Table 1. It can be seen
that the first modal damping of the steel building
is normal (around 2%) but the second and third
modal damping ratios are extremely low (0.21
and 0.17%, respectively).
Design and Fabrication of MTMD
The given mass of the MTMD was 360 kg
µ
=
(
)
2%
consisting of five units. Due to the light
damping in higher modes of the building, the
MTMD units were divided into two groups: four
units were tuned to the first structural mode and
one unit to the second structural mode. The dis-
Table 1. Identified modal parameters of the 3-story experimental building
Modal frequency (Hz)
Modal damping ratio (%)
Mode shape
1 08
3 24
5 02
.
.
.
1 95
0 21
0 17
.
.
.
0 4933
.
0 3576
.
0 1362
.
F
F
RF
2
3
0 9791
.
0 1695
.
−
0 1586
.
1 2383
.
−
0 3088
.
0 0783
.
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