Geology Reference
In-Depth Information
OPTIMAL DESIGN OF MULTIPLE
TUNED MASS DAMPERS
span bridge made of steel under the threat of wind
resonance. An article written by Morgenstern
(1995) describing the history of the tuned mass
damper in Citicorp Center, New York, points out
how these advantages are important to an existing
structure when most of its structural elements are
not accessible and immediate retrofit is demand-
ed.
To solve the detuning effect of single TMD, a
multiple-TMD (MTMD) comprising of multiple
units of SDOF substructures arranged in parallel
was first proposed by Xu and Igusa (1992). Since
then, numerous studies on the design approach and
control efficiency have been carried out theoreti-
cally. Most of the previous studies did not consider
the stroke problem of the control device. Lin
et
al
. (2010) by expanding the efforts of Wang
et
al
. (2009) for single TMD were among the first
to study the stroke parameter in MTMD design.
Practical Issues of Single TMD
Figure 1(a) implies that minimizing the area of
transfer function can statistically reduce the seis-
mic response of a structure under unpredictable
ground excitations, which usually have wide-
banded frequencies. Therefore, in conventional
design of TMD, structural response-based param-
eters are usually defined as the objective function
in optimization process. When TMD absorbs some
of the vibration energy, the structural vibration is
reduced. Inevitably, significant TMD stroke (dis-
placement relative to the installed place) is the
consequence, as shown in Figure 1(b). Figure 1(b)
also implies that the more the structural response
reduction, the larger the TMD stroke. In practice,
TMD stroke demand for seismic application is
larger than that of the wind application since an
earthquake can induce more energy to structures.
This may not be allowed due to the limitation of
installation space and TMD's components. In
addition, the difference in control performance
of two TMD designs shown in Figure 1(a) results
mainly from the difference in TMD design fre-
quency(
r
f
= 0.953 or 0.972), even though there
is only 2% difference. Results of previous studies
have also shown that any slight change in TMD
design frequency can significantly deteriorate the
control effectiveness. This “detuning effect” is
another issue in real world application since the
natural frequency of a structure is usually evalu-
ated by employing system identification tech-
niques from field measurements contaminated by
machine and environment noises, which always
induce errors to the outcome.
Building-MTMD System Model
The equations of motion of a general
n
-DOF build-
ing equipped with an MTMD of
p
units at the
i
th
floor, as shown in Figure 2, can be expressed as
Mx
t
+
Cx
t
+
Kx
t
=
M r
x t
(3)
( )
( )
( )
( )
f
g
in which
M 0
M M
M
=
p
sp
s
C C
0
p
ps
C
=
T
C
s
K K
0
p
ps
K
=
T
K
s
M 0
0 M
p
M
=
T
f
s
are (
n
+
p
)
×
(
n
+
p
) mass, damping and stiffness
matrices of the entire system.
M
p
,
C
p
,
and
K
p
Search WWH ::
Custom Search