Geology Reference
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FINDING EFFECTIVE
DAMPER LOCATIONS
formulation of a general optimization problem
and establishment of a solution procedure. An
empirical procedure to find the optimal locations
of actuators by maximizing an optimal locations
index is proposed (Pantelides, 1990). The modal
responses and earthquake spectra are taken into
consideration. Four distinct design criteria, influ-
encing the active control design, are considered
to study the optimal actuator placement problem
(Rao, 2008). The sensitivities of the four criteria
with respect to different earthquake records were
also explored.
An algorithm for finding optimal active con-
trolled devices locations is recently proposed
(Agranovich, 2010). It is based on LQG design
that is carried out using an artificial white noise
ground motion. According to this algorithm, it is
assumed that active controlled dampers are placed
at each floor. The most effective dampers' locations
are selected according to maximum contribution to
the total energy dissipation. It was demonstrated
numerically that the method yields effective
improvement of structural seismic response by a
limited set of active controlled devices.
For optimal distribution of active controlled
devices it is sometimes required to connect more
than one device per floor, because the peak force
that can be developed in one device is limited.
Connecting active dampers to amplifiers can
significantly reduce the number of devices. Using
less damping units per floor leaves more open
bays that is also a very important issue.
This study is focused on analysis of a 20-story
active controlled structure described in numerical
example. Active devices are located at the floors,
where their positive effect is maximal. In cases,
when the maximum control force value, required
at a certain floor, is higher than the peak force
that may be produced in a single device, lever
arms are used for connection of active dampers.
It allows reduction of dampers and increases the
efficiency of control.
Optimal dampers' location in structures is a prob-
lem that is studied for many years (Wu, 1979,
Chang, 1980, Hahn, 1992) A wide literature review
in this field is given (Liu, 2003). An effective de-
sign method is developed recently (Agranovich,
2010). The method is based on simple and logical
principles, requiring no changes in the control
law. Moreover, it is fast, compared to generic
algorithms that are often used for finding optimal
dampers' placement. The method does not require
defining additional transfer functions or using
mode shapes of undamped structure.
According to this method, an artificial earth-
quake record is modeled and a response of an
undamped structure to this earthquake is ob-
tained. After that dampers are connected to the
structure at all floors and the structural response
to the artificial ground motion is calculated. The
control forces correspond to the optimal control
law requirements and the number of active con-
trolled devices at each floor is obtained according
to a maximum force that can be developed by a
single device. Energy at each floor is calculated
and its portion in the total energy over the entire
structure is obtained. It is further considered that
dampers' cost and energy, required to activate
them, are limited. Hence, dampers are placed
at the most effective positions and their number
is increased until desired reduction in seismic
response is achieved.
An artificial white noise ground acceleration
signal that is used as an earthquake record for
finding optimal dampers' locations is generated
using an algorithm, implemented in MATLAB
routines (Ribakov, 2007). The input parameters
for this algorithm are the desired peak ground
acceleration (PGA), the desired spectrum band-
width (BW) and the earthquake duration (
t
f
).
The algorithm and its program realization allow
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