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into the effect of ground motion characteristics
on optimal distribution.
Shukla and Datta (1999) reconfirmed the ef-
ficiency of the SSA method through a parametric
study using visco-elastic dampers. Frequency
domain approach was employed for determining
the responses to both broad and narrow band
ground motions. The study shows that the optimal
placement of dampers is sensitive to the nature
of excitation force. This is an important observa-
tion because it implies that what is optimal in one
specific ground motion need not be optimal in a
different ground motion. This opens up a whole
lot of concern on the use of the term 'optimality'
because of the high inherent uncertainty in the
ground motions. One approach to address this
uncertainty is to use the principle of critical excita-
tion (Takewaki 2007). As it falls beyond the scope
of the present chapter we will not further discuss
on this aspect; interested readers should refer to
other relevant works such as Takewaki (2000a-d,
2001a-g, 2004a-b, 2005, 2007), Ahmadi (1979),
Drenick (1970, 1973, 1977a-b), Drenick and Park
(1975), Iyengar (1970, 1972, 1989), Iyengar and
Manohar (1985, 1987); to name a few.
Moreschi (2000) and Singh and Moreschi
(2001, 2002) introduced a gradient based approach
and also employed genetic algorithm approaches
as an alternative to address the problem of optimal
placement of dampers. The performance index to
be minimized was defined as a function of the sys-
tem response obtained by considering a stochastic
description of the input motion defined by Kanai-
Tajimi spectral density function. The application
of genetic algorithm is especially suitable where
the performance index is not a continuous function
of the design variables. The basic assumption in
the study was that the parent frame remains linear.
State space approach was used for the analysis.
Numerical results were reported for both shear
and torsional building models.
Garcia (2001), and Garcia and Soong (2002)
developed the simplified sequential search algo-
rithm method (SSSA) which is basically a simpli-
fied form of the SSA method originally developed
by Soong. In order to show the efficiency of the
proposed method a comparison of the proposed
SSSA with other methods was presented. The other
methods used for comparison were the optimal
design using optimal control theory (Gluck et al
1996) and the optimal design using the minimum
transfer functions (Takewaki 1997). It was shown
that the optimal distribution of dampers obtained
is sensitive to ground accelerations. In this study
too, the parent frame was assumed to remain linear.
Palazzo et al (2004) presented a new approach to
optimally locate dampers by assessing the power
balance of structures subjected to seismic actions
described by a response spectrum. Modal state
space approach was used for response evaluation
and optimization.
Trombetti and Silvestri (2004, 2006, 2007)
developed an efficient mass proportional damp-
ing (MPD) system and showed its utility. In this
scheme, the dampers are placed in such a way
that they are connected to a fixed point and are
sized to be proportional to each storey mass. The
scheme is based on the mass proportional damp-
ing component of the Rayleigh viscous damping
matrices. Shear building model was used for the
study, and it is assumed that the first mode of
vibration controls the dynamic response. In an
earlier work (Trombetti et al. 2003), they had
proved that within the class of Rayleigh damping,
the first modal damping ratio of the mass propor-
tional damping system is always higher than the
first modal damping ratio of stiffness proportional
damping system and other Rayleigh damping
systems. They compared their scheme with the
algorithm proposed by Takewaki (1997) to show
its efficiency. Later, Takewaki (2009) agreed that
the MPD scheme is efficient, but expressed his
concern regarding its practical application. From
an implementation perspective, we also wish to
emphasis here that the MPD scheme would be
impracticable unless there is a fixed point associ-
ated with every degree of freedom to which the
dampers could be attached.
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