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al. (1997) provided a single-degree-of-freedom
model of the one which Villaverde et al. offered.
Rana and Soong (1998) studied about TMD
systems with steady-state harmonic excitation
and used time-history analysis to find optimum
parameters of TMD. Pourzeynali & Datta (2002)
studied control of flutter of suspension bridge
deck using TMD system. Cao and Li (2004)
studied the application of active TMD system to
control flexible structures, particularly, tall build-
ings. Pourzeynali and Esteki (2009) performed a
comprehensive research study on optimization
of the TMD parameters to suppress the verti-
cal vibration of suspension bridges subjected to
earthquake excitations.
The TMDs are undoubtedly reliable, simple
and they do not require external power source, so
their construction cost is low (Pinkaew & Fujino,
2001); but, inasmuch as the parameters of TMD
system are constant, if there is any changes in load-
ing conditions, then this system may not be able
to control the vibrations properly. Therefore, the
need to a system which is capable to be changed
with different conditions is fully felt.
The semi-active tuned mass dampers (STMDs)
can compensate the limitation of the passive
and active systems. Various studies confirm the
efficiency of STMDs and show that the applica-
tion of TMDs is much better when they behave
as STMDs, especially in wind and earthquake
excitations. Therefore, modeling procedure of the
STMD system automatically includes modeling
of the TMD system which uses the passive fluid
viscous damper. The theory of TMD system has
been used for the first time by Frahm (1909) to
reduce the movement of a structure subjected
to monotonic harmonic forces reviewed above.
Hrovat et al. (1983) used STMDs for the control
of tall buildings against wind pressure. Kelly and
Hasegawa (1992) have proposed STMD with con-
trollable dynamic characteristics. Abe and Igusa
(1996) developed analytical theory for optimum
control algorithms for semi-active absorbers.
Hidaka et al. (1999) investigated the operation of
various dynamic absorbers which use ER liquid.
Agrawal and Yang (2000) proposed particular
tools namely semi-active algorithms to protect
unstable structures which are subjected to near
field earthquakes. Pinkaew and Fujino (2001)
studied controlling effects of STMDs with differ-
ent dampers for single-degree-of-freedom systems
which are subjected to harmonic excitations. Lin
et al. (2005) suggested a new semi-active con-
trol system that used variable damping and MR
damping. Mulligan et al. (2006; & 2007) studied
spectral analysis and the probabilistic design of
STMDs. In these systems, the stiffness or the
damping ratio of the control device changes pro-
portional to the relative displacement or relative
velocity, by receiving information from sensors
in every second (Mulligan, 2007). Therefore, they
do not require large power supply and they do
not add additional energy to the main structure
and guarantee stability of the system. In order to
regulate the stiffness or the damping ratio of the
STMD, fuzzy systems can be used. Pourzeynali
and Datta (2005) studied application of STMD
system to control the suspension bridge flutter
using fuzzy logic.
In the present study, the STMD system is
considered with variable damping produced
by a semi-active fluid viscous damper. Fluid
viscous damper, which is used in TMD system,
is a device to absorb part of the input energy in
buildings and reduce possible structural damage
during the earthquake excitations. A passive fluid
viscous damper is similar to the shock absorber
in automobiles. The configuration of this damper
includes a hydraulic cylinder filled with a damp-
ing fluid like silicone or oil and a piston head
with a small orifice. As the damper strokes, the
damping fluid flows through the orifice at high
speed from one side to the other, and produces a
damping pressure which creates a damping force.
A semi-active fluid damper can be achieved by
adding an external bypass loop which contains
a controllable valve to a passive fluid damper.
The behavior of the semi-active fluid damper is
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