Geology Reference
In-Depth Information
For large civil engineering structures it is nec-
essary to install a sufficient number of dampers
to achieve a reduction of the structural response
due to earthquake and the performance of these
dampers depends on their location in the struc-
tures. The selection of few locations out of a large
number of locations for the placement of passive
dampers is typically a nonlinear constrained op-
timization problem. This problem can be solved
either by simple heuristic search approaches or
through integral optimization. The first ones are
simple and they yield a solution which may be
close to the optimal solution, but computationally
expensive, instead the second ones are fast but
solution is complex.
In this chapter heuristic search methods have
been investigated in detail using four different
objective functions and applied to three build-
ing typologies that have been modeled as linear
behavior for simplicity, however these methods
can also be applied nonlinear structures.
an inverse problem approach, under the assump-
tion that the ratio between the mean maximum
interstory drift due to a spectrum compatible
earthquake and the target specified value remains
constant. Gluck, Reinhorn et al. (1996) suggested
a method for the design of supplemental dampers
and stiffness based on optimal control theory using
a linear quadratic regulator (LQR) that minimizes
a performance cost function, but the algorithm is
valid under the assumption of white noise input
and it is effective only for systems where the first
mode effects are predominant.
Takewaki (1997) proposed a stiffness-damping
simultaneous optimization procedure where the
sum of mean square responses to stationary ran-
dom excitations is minimized subjected to the
constraints on total stiffness and damping capac-
ity. It is a two-step optimization method where,
in the first step, the optimal design is found for
a specified value of total stiffness and damping,
while in the second step the procedure is repeated
for a set of total stiffness and damping capacity.
All methods mentioned above, even if they
lead to an optimal damper configuration, are not
practical, because they are not simple enough to
be used routinely by practical engineers. An ideal
method should be practical and capable of control-
ling the number of different damper sizes to be
used. The method should be also efficient, in the
sense that the resulting damper configuration (i.e.,
size and location of added dampers) minimizes
the total amount of added damping necessary to
reach a given performance objective.
A practical method is the one proposed by
Zhang and Soong (1992), who suggested a sequen-
tial procedure to find the optimal placement of
viscoelastic dampers, based on the controllability
index method presented by Cheng and Pantelides
(1988). The procedure consists in adding dampers
one by one to the structure in the story where the
optimal location index is maximum, assuming
that all the dampers have the same size. Since
all dampers have the same size the method is
more practical than other optimization methods,
BACKGROUND
The seismic response of structures subjected to
earthquake excitations may be effectively reduced
by incorporating any of various kinds of available
passive energy dissipation devices (Soong and
Dargush 1997). Numerous are the studies related
to optimal placement and capacity of damping
coefficient for linear multistory buildings.
Tsuji and Nakamura (1996) proposed an
algorithm that finds the optimal story stiffness
distribution and the optimal damper distribution
for a shear building model subjected to a set of
spectrum-compatible earthquakes, but it requires
high computational afford because it is necessary
to run dynamic analysis and include artificial
constraints like the upper bound of the damp-
ing coefficients. Nakamura et al. (1996) found a
method for evaluating an ordered set of stiffness
design variables of an elastic shear type building
with an ordered set of damping coefficients via
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