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Martinez-Rodrigo and Romero (2003) de-
scribed a simple numerical methodology that leads
to an optimum retrofitting option with nonlinear
fluid viscous dampers. Subsequently, Lavan and
Levy (2005) presented a methodology for the
optimal design of supplemental viscous damp-
ers for regular and irregular building models by
minimizing the added damping subjected to a
constraint on energy based global damage index
for an ensemble of realistic ground motions. A
gradient based optimization scheme was used
in this study, which tried to address the effect of
strength irregularity caused by different story stiff-
ness. This work was definitely an improvement
as compared to most of the studies documented
earlier because it considered nonlinearity in the
parent frame. Lavan and Levy (2004, 2006a) also
presented a methodology for the optimal design of
supplemental viscous dampers in which the parent
frame remains elastic. The problem of minimizing
the added damping was achieved by solving an
equivalent optimization problem subjected to a
constraint on the maximum inter-story drift for a
frame excited by an ensemble of ground motion
records. The other significant contribution of these
two works is that they achieved the optimum design
for an ensemble of realistic ground motions rather
than for a stationary or non-stationary stochastic
excitation as used in majority of the other meth-
ods recorded in this section. Again, Lavan and
Levy (2006b) extended this methodology into
the optimal design of viscous dampers for 3D
irregular framed structures. In this study too, an
ensemble of realistic ground motions was used
and the parent frame is assumed to be linear. The
added damping was minimized and subjected to
a constraint on inter-story drifts on floor edges. A
gradient based optimization algorithm was used
and a variational approach was adopted for the
derivation of the gradient of the constraint.
In the last decade, there have been several
studies on optimal damper positioning. Aydin et
al (2007) presented an alternative to Takewaki's
method by considering the transfer function
amplitude of base shear evaluated at the fun-
damental frequency as the objective function.
Planar building frames with a soft storey were
investigated in this study. The efficiency of the
proposed method was illustrated by a comparison
with Takewaki's method. Ajeet and Shirkhande
(2007) showed that the efficiency of optimally
placed dampers is maximised in symmetric build-
ings and its efficiency reduces as plan irregularity
increases. Cimellaro (2007) addressed the issue of
simultaneous optimal distribution of stiffness and
damping for retrofitting structures by optimizing
a generalized objective function that combines
absolute acceleration, displacement and base shear
transfer function. This method basically modified
the method proposed by Takewaki (1997). In order
to highlight the efficiency of the proposed method
a comparison with the methods of Takewaki (1997)
and Aydin et al (2007) was carried out. Lavan et
al (2008) developed a non-iterative optimization
procedure for seismic weakening and damping of
inelastic structures. The procedure determines the
optimal location and amount of weakened struc-
tural components and added damping devices in
inelastic structures. The methodology proposed
assumes proportional changes in strength and
stiffness which is a limitation. Cimellaro et al.
(2009) extended the above proposed methodol-
ogy into a more generic design strategy in which
uncoupled changes of strength and stiffness are
allowed for the control of buildings experiencing
inelastic deformations during seismic response.
More recently, Lavan and Dargush (2009)
examined a multi-objective seismic design opti-
mization in which the maximum interstorey drift
and maximum acceleration were considered as the
primary control parameters. The multi-objective
problem was formulated in Pareto optimal sense
(Pareto 1927) and a genetic algorithm based ap-
proach was adopted to identify the Pareto front.
The end result of this multi-objective optimization
is a family of Pareto front solutions providing the
decision makers with an opportunity to understand
the tradeoff between the drift and acceleration.
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