Geology Reference
In-Depth Information
3.
Simplified Sequential Search Algorithm
(SSSA):
This iterative approach does not
explicitly minimise an objective function, but
seeks to optimise the dampers' contribution
by sequentially placing them where they can
be expected to generate the greatest resist-
ing force (Lopez-Garcia, 2001). The total
damping to be provided is divided between
the number of equally-sized discrete devices.
Device placement is governed by an optimal
location index
γ
i
given by
is altered in a way that maximises the rate of
change of the objective function towards its
minimum value. This is achieved by comput-
ing an optimality index for each floor
j
given
by the differential of the objective function
with respect to the damping at floor
j
+ 1,
normalised by the differential with respect
to the damping at floor 1, i.e.:
n
ˆ
∑
δ
i
i
=
1
,
j
+
1
γ
=
(4)
j
n
ˆ
∑
γ
=
α δ
+
α δ
(3)
δ
i
i
i
1
2
i
i
=
1
,
1
where
δ
i
is the interstory drift at story
i
,
δ
i
the interstory velocity and the coefficients
α
1
and
α
2
can be chosen according to the
dissipater type. For a purely viscous damper
(as in our study)
α
1
= 0 and
α
2
= 1, so that
γ
i
is simply equal to the interstory velocity. A
time history analysis of the bare frame is
performed and a device added to the story
giving the highest
γ
i
value. The process is
repeated until all the devices have been
distributed. To reduce the dependence on
one time history, we suggest that the process
should be based on a set of spectrum-
compatible accelerograms (three in our
analyses), with the damper added to the floor
that most frequently gives the highest
γ
i
value.
4.
Takewaki Method:
The aim of the Takewaki
(1997) method is to minimise an objective
function given by the sum of the amplitudes
of the interstory drifts of the transfer function,
evaluated at the undamped natural frequency
of the structure, subject to a constraint on
the total amount of added viscous damping.
Initially the added damping is uniformly
distributed and the optimum distribution is
then achieved using a gradient-based search
algorithm, that is, the damping distribution
where
δ
i
is the peak interstory drift of the
transfer function at floor
i
,
n
is the number
of floors and the subscripts such as
,j
+1
indicate
differentiation with respect to the damping
at that level. Thus, floors with large values
of
γ
j
are those where a change in the damping
will cause the most rapid change in the
objective function. The change in damping
distribution is therefore weighted according
to the
γ
j
values. An optimal solution is
achieved when the damping distribution is
such that all
γ
j
values tend to unity, implying
that changing the damping at one floor is no
more beneficial than doing so at any other
floor.
5.
Lavan Method:
The Levy and Lavan (2006)
fully stressed analysis/redesign procedure
uses a single 'active' ground motion, selected
based on its high displacement or energy
demands. A response analysis is performed
using this ground motion, and the objec-
tive function, or performance index,
p
i
is
calculated as the value of a chosen response
parameter at story
i
normalised by an al-
lowable value. In this study the parameter
chosen is the interstory drift
δ
i
:
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