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Takewaki (1997a, 1997b, 1998) opened a new
approach of smart passive damper placement
techniques with a series of algorithms based on the
concepts of inverse problem and optimal criteria
based design approaches. The problem pioneered
by Takewaki was to find the optimal damper place-
ment to minimize the sum of the amplitudes of
the transfer functions evaluated at the undamped
fundamental natural frequency of the structural
system. A constraint was imposed on the sum of
the damping coefficients of the added dampers.
This was a single criterion approach because only
the damping coefficients of the added dampers
were considered as a design variable, whereas
the story stiffness was pre-specified.
Subsequently, Takewaki (1999) came up with
an approach of stiffness-damping simultaneous
optimization for displacement-acceleration simul-
taneous control. The structural system considered
was a shear building model and both stiffness and
damping coefficients of the added dampers were
considered as design variables. This is a two-
step design method. In the first step, a design is
obtained by satisfying the optimality conditions
for a specified set of total story stiffness capacity
and total damper capacity. In the second step, a
series of optimal designs is obtained sequentially
for various stiffness and damping capacity levels.
Deformation is reduced in both the steps while
acceleration is reduced only in the second step.
This is a very significant work as it considers
acceleration also as a quantity that needs to be
controlled. To the authors' knowledge most of
the earlier works were mainly concentrated on
drift reduction as the primary objective, whereas
this was the first work which explicitly aimed
to minimize both displacement and acceleration
responses through minimization of the weighted
sum of mean-square inter-story drifts and a mean
square top floor absolute acceleration. Takewaki
also showed that increases in total stiffness ca-
pacity and total damper capacity are effective
in reducing the inter-story drift, but increase of
only the total damper capacity reduces the floor
acceleration.
Takewaki and Yoshitomi (1998), Takewaki and
Uetani (1999) and Takewaki (2000) described a
systematic procedure for determining the optimal
positioning of dampers in planar moment resist-
ing frames by minimizing the dynamic compli-
ance subjected to a constraint on the sum of the
damping coefficients of the dampers. Dynamic
compliance is defined as the sum of the transfer
function amplitudes of inter-story drifts evaluated
at the undamped fundamental natural frequency.
The systematic procedure developed is called the
steepest direction search algorithm. This again is
a significant advancement because most of the
earlier researchers were only considering shear
building models. Takewaki consolidated all his
work on optimal damper positioning in the form
of a textbook (Takewaki 2009). In addition to the
works mentioned above, the topic illustrates the
procedures by which the steepest direction search
algorithm could be extended to three dimensional
systems. This topic also describes the procedures
by which the effect of soil structure interaction
could be incorporated in optimal positioning of
dampers and gives an overview of the design of
shear buildings with uncertainties using the prin-
ciple of critical excitation. Some additional useful
references on this are Takewaki and Nakamura
(1995, 1997), and Takewaki (2000a, 2000b).
Gluck et al (1996) pioneered and adapted the
optimal control theory using a quadratic regula-
tor to design and place control devices based on
their deformations and velocities. They considered
linear passive viscous and visco-elastic devices,
represented them by a fully effective Kelvin model
using a full state static feedback. This work holds
a significant place in the literature, as it adapted
the well established active control theories for
passive devices. Wu et al. (1997) applied the
sequential search algorithm (SSA) developed
by Zhang and Soong (1992) to 3-D torsionally-
coupled structures and carried out an investigation
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