Damper Optimization for Long-Span Suspension Bridges - Design Optimization of Active and Passive Structural Control Systems - page 119

the isolation system with dampers is usually ap-
plied to restrain the large girder displacement.
The following is about how to achieve the most
satisfied seismic control effect by optimizing the
damping coefficient C and damper placement in
the two towers.

of the tower), D 2 (the along-span displacement at
the top of the tower), M 2 (the moment at mid-span
of the crossbeam below), D 3 (the displacement
of the damper), and F 3 (the force of the damper).
These evaluation parameters are also adopted for
damper optimization of the RSB.
Furthermore, it is notable that traveling wave
effect is considered when conducting the seismic
analysis of the RSB. However, traveling wave
effect is merely a simple form of multi-support
seismic excitation where incoherence effect and
site-response effect should also be considered.
In addition, traveling wave effect is significantly
dependent on the apparent wave velocity, the
seismic input direction and some other factors
which are uncertain. Therefore it is recommend-
able to conduct analysis of uniform seismic input,
traveling wave effect and multi-support seismic
excitation, and a comprehensive investigation is
adopted for optimization (Figure 6). However,
in this chapter only optimization under traveling
wave effect is conducted for simplification, as
shown in shadow part of Figure 6.
It is notable that other factors can be added
for assessment if necessary, such as lateral seismic
input, multiple-point seismic input, shear force
at the base of the tower, displacement response
at the middle of the deck and displacement re-
sponse at the top of the tower, etc.

Parameter Sensitivity
Analysis of Dampers

Parameter sensitivity analysis of dampers is
adequate because it can reveal the correlation be-
tween dampers and structural responses, therefore
is conducive to the damper optimization. Various
damping coefficients C are employed to conduct
the parameter sensitivity study of dampers. The
value of C ranges from 1×10 3 to 20×10 3 kN·s/m,
and α is 1.0, according to the linear damper.
The relationships between damping coefficient
C and the girder displacement, tower moment,
damper force and displacement are shown in
Figure 5. Obviously, the girder displacement,
tower moment and damper displacement de-
crease with the rise of C, while the damper force
varies inversely. Dampers can therefore reduce
structural response significantly if C is selected
appropriately.

Optimization Model Based on AHP

Determining Assessment
Functions Based on First-
Order Optimization Method

When carrying out an optimization based on the
AHP, a correct optimization model including the
selection of evaluation parameters and the deter-
mination of their weighting factors is significant
for the accuracy of the analysis results since it is
a decision-aiding method. To simplify calcula-
tions, only one kind of seismic input (longitudinal
+ vertical input) which could lead to the most
adverse internal responses is employed.
Six evaluation parameters are usually consid-
ered when performing a assessment of seismic con-
trol effect for long-span suspension bridges (Wang,
Li, & Guo, 2006), and they are: D 1 (displacement
at the end of the girder), M 1 (moment at the base

The optimization model and procedure has been
established, with reference to the idea of the
AHP. The next step is to ascertain the optimiza-
tion criteria (Optimization J 1 -J 4 in Figure 6) for
dampers. However this is a complicated case for
that six evaluation parameters and their weighting
factors are not an easy task to be determined. In
this case, four assessment functions for seismic
control are formulated as the object functions
during the optimization, which are as follows: