Damper Optimization for Long-Span Suspension Bridges - Design Optimization of Active and Passive Structural Control Systems - page 113

INTRODUCTION bridges (Kawashima & Unjoh, 1994; Symans &

Kelly, 1999; Abe & Fujino, 1998).
In this chapter, principle introductions are con-
ducted in terms of seismic response control, the
analytic hierarchy process (AHP) and first-order
optimization method. Through the parameters
sensitivity analyses of 3-dimensional model for
the Runyang Suspension Bridge (RSB), damper
optimization for seismic control of the RSB under
certain seismic input are realized, on the basis
of the combination of the AHP and first-order
optimization method.

Long-span suspension bridges are always attrac-
tive because of their magnificence, symbolization
and convenience. Currently this bridge type is
becoming prevalent globally with the rapid prog-
ress of design methodologies and construction
technologies. Take China for instance, numerous
suspension bridges have been constructed, such
as the Humen Bridge (main span: 888 m), the
Xiling Bridge (main span: 900 m), the Jiangyin
Bridge (main span: 1385 m) and the Runyang
Bridge (main span: 1490 m). Nevertheless, some
issues existing in long-span suspension bridges
still challenge engineers, as dynamic behavior
subjected to earthquakes. How to ensure an ad-
equate level of safety against earthquakes for both
new and existing long-span suspension bridges is
important (Fan, 1997).
Rigid connections between the main girder
and towers would transmit to foundations inertial
forces generated by the superstructure, magnifying
shear forces and overturning moments at the bot-
tom of towers. In order to reduce seismic forces of
towers, the seismic isolation system forming the
floating system is generally adopted to supplant
rigid connections. It is notable that for such case
the seismic displacement at the end of the main
girder may potentially exceed the threshold (Park
et al., 2005; He et al., 2001). Dampers intended
to control the seismic displacement of long-span
bridges are therefore installed between towers
and the main girder and has been proved to be an
effective approach (He, Agrawal, & Mahmoud,
2001; Erkus, Abe, & Fujino, 2002; Murphy &
Collins, 2004). The application of the seismic
isolation system with dampers is by far the most
practical solution to control the seismic responses
of structures and a number of studies have been
conducted on damper optimization for seismic
response control of buildings (Furuya, Hamazaki,
& Fujita, 1998; Shukla & Datta, 1999; Chen &
Wu, 2001; Aydin, Boduroglu, & Guney, 2007) and

FOUNDATIONS OF
OPTIMIZATION THEORY

Optimization theory is widely used in civil engi-
neering to combat various issues such as sensor
placement for structural health monitoring (Heo,
Wang, & Satpathi, 1997; Meo & Zumpano, 2005),
finite element model updating (Wang, Li, & Miao,
2005), cable force optimization of the cable-stayed
bridges (Zhang & Xiao, 2005), bridge design
(Ming, Hu, & Huang, 2007), acoustic design
(Duhring, Jensen, & Sigmund, 2008), structural
damage identification (Andrzej, Przemyslaw, &
Jan, 2008), et cetera. Generally, the constrained
optimization problem can be expressed as:

= ( )

Minimize J J x (1)

subjected to:

x x x
i

≤ ≤ ( i =1,2,3,…, N )

i

i

g x ( ) ≤ ( j =1,2,3,…, m 1 ) g

j

j

h

≤ ( ) ( k =1,2,3,…, m 2 )

h x

k

w ≤ w x ( ) ≤ w ( l =1,2,3,…, m 3 )

l

l

l