Optimal Passive Damper Positioning Techniques: State-of-the-Art - Design Optimization of Active and Passive Structural Control Systems - page 94

Both linear and nonlinear parent structural frames
were considered in the study. The nonlinear par-
ent frame was idealized as a yielding shear frame
which also takes into account the new retrofitting
techniques based on weakening and damping
described in Lavan et al (2008). The other most
important contribution of this work was the con-
sideration of 'cost of the damper' as an external
constraint. Paola and Navarra (2009) discussed
the stochastic responses of MDOF structures with
nonlinear viscous dampers to a seismic excitation.
Although not described here in detail, some
other related studies include: Takewaki et al
(2010), Viola and Guidi (2009), Cimellaro and
Retamales (2007), Wongprasert and Symans
(2004), Xu et al (2003, 2004), Tan et al (2005)
and Xi Lin (1999) and interested readers should
refer to these.
All the above mentioned studies investigated
different optimal positioning techniques; but some
of the assumptions adopted remain common to
all. Reviewing these assumptions we identify the
following limitations:

and Dargush (2009), majority of all other
studies discussed above assumed the par-
ent frame to remain elastic during a seis-
mic action. Even in the aforementioned
studies, although yielding in the parent
frame was considered, the model was not
adequately set up to reflect reality. Most of
them adopted a yielding shear story frame
idealization, but if a frame is designed to
a seismic code based on capacity design
principles, yielding tends to happen in the
beams to avoid the formation of a soft sto-
rey failure mechanism which might result
in a global collapse. As the shear story
frame models do not consider columns or
beams separately, they fail to capture the
realistic yielding behavior. Hence, consid-
ering the majority of the documented past
research, we can say that linearity of the
parent frame is an inherent assumption
in the existing optimal positioning tech-
niques. In Section 5, we discuss in detail
the consequences of this assumption on the
optimality criteria and substantiate it with
a numerical sensitivity study. • Inherent assumption of Rayleigh's vis-

cous damping model for representing
in-structure damping of parent frame.
Almost all studies recorded above assume
the Rayleigh viscous model for repre-
senting in-structure damping. Reviewing
the available literature on damping we
have strong concerns regarding the use
of this model for representing in-structure
damping of the parent frame (Adhikari
2000, Adhikari and Woodhouse 2003,
Woodhouse 1998, Brenal 1994, Leger and
Duassault 1992, Hall 2006, Charney 2008,
Zareian and Medina 2010). In the next sec-
tion, we further substantiate our concern
through a numerical sensitivity study.

EFFECT OF IN-STRUCTURE
DAMPING MODELS ON OPTIMAL
DISTRIBUTION OF DAMPERS

Takewaki (2009) has shown that the optimal
distribution of added dampers is sensitive to the
in-structure damping inherent in the structure.
The sensitivity study emphasized the fact that the
distribution of the capacity of the added dampers
changes with the extent of in-structure damping.
This means if the in-structure damping model fails
to capture the realistic damping in the system,
then what seems optimal in analysis might not be
optimal in reality. This signifies the necessity of
the use of a more realistic model of in-structure
damping imperative.

• Inherent assumption of linear elastic

behavior of the parent frame. Except
for Lavan and Levy (2005), Lavan et al
(2008), Cimellaro et al (2008), and Lavan