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INTRODUCTION
and characteristics of triangular adding damping
and stiffness dampers in moment resisting steel
structures is an additional topic that is investigated
(Yousefzadeh, 2011).
Active devices are able to change the control
force, applied to the structure according to the
optimal control requirements. They allow more
effective control, but external energy source is
required for activation of these devices. In other
words, active controlled devices externally acti-
vated and apply control forces to the structure in
order to improve its performance. Active devices
include active tendons, active tuned mass dampers
and actuators.
To reduce the energy, required for activation
of the devices, semi-active dampers are used. In
these devices a relatively small energy amount is
enough to change the dampers properties so that the
energy of structural motion would yield damping
forces that are close to the optimal control force
values. Semi-active devices include active variable
stiffness systems, electro-rheological dampers,
magneto-rheological dampers, semi-active vari-
able friction dampers, shape memory alloys and
piezoelectric materials etc. In order to ensure the
structural safety, reliability and durability, pole
assignment method, optimal control method and
independent model-space control method are
usually used. Modern control strategies are also
developed for active and semi-active systems
(Gu, 2008).
Hybrid applications of active and passive
devices are also known. For example, magneto-
rheological dampers are successfully used as a
part of base isolation systems (Ribakov, 2002).
Selective control is an effective algorithm for
such systems (Ribakov, 2003). A hybrid isolation
system, comprised of a bidirectional roller-pen-
dulum system and augmented by controllable
magnetorheological dampers is proposed to re-
duce the potential for damage to structures and
sensitive equipment (Shook, 2007). Comparison
of neural network control, LQR/clipped opti-
Reduction of structural responses to earthquakes
is a subject that is widely investigated during the
last decades. Structural control is known as one of
the effective ways for enhancing structural seismic
response. Various structural control strategies are
developed and implemented in practice. Structural
control applications are effectively used in new
buildings and also to retrofit existing structures
all over the world.
For example, steel moment frames with fluid
viscous dampers located at the ground floor are
used for seismic retrofitting of a 4-story reinforced
concrete building of the Woodland Hotel located
in Woodland, California. Seismic rehabilitation
of the ten-story MUCTC building in Montreal
was achieved by Pall friction dampers in steel
bracing. Navy Building in San Diego is equipped
with viscoelastic dampers. A tuned mass damper
is used in City Corporation Building in NY City.
An active mass damper is installed in the Nanjing
television tower in China.
For implementation of structural control
algorithms passive, semi-active and active de-
vices are used. Passive devices use the energy of
structural motion to dissipate energy. This group
of devices includes viscous dampers, viscoelastic
dampers, friction dampers, tuned mass dampers,
base isolation devices, etc. (Soong, 1997). They
require no external energy, but the properties of
these devices are constant and the forces across
these devices are not changed according to any
optimal control law.
Modern approaches are developed to improve
the efficiency of passive dampers. Seismic de-
sign of friction dampers based on the desired
structural performance yields effective passive
energy dissipation (Tabeshpour, 2010). A gradient-
based evolutionary optimization methodology
is presented for finding the optimal design of
viscoelastic dampers and their supporting mem-
bers (Fujita, 2010). Finding optimal location
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