Earthquake Engineering Research - HKU Libraries - The University ...

1
459
Uncontrolled
Controlled
Reduction
(%)
179.62
132.89
26.02
920.32
514.17
44.13
195.41
133.64
31.61
1.95
1.74
11.06
9.58
6.27
34.49
1.88
1.47
21.50
M and Q denote the moment and shear force, respectively,
and 45° (horizontal) directions, respectively. In this example, the random earthquake excitation
spectrum is taken as the Kanai-Tajimi power spectral density function with the parameters % g = 0.25,
0) s = 5 rad/s, and S 0 = 0.01 m 2 -rad/s j . For each seismic excitation, five AMD implementation schemes
are investigated. The number of the AMDs, each with mass of 8xl0 4 kg, ranges from 5 to 20. The
AMDs are installed on top of the three towers, at the half heights of the towers, on one or two sides of
mid-span and quarter-span positions of the two main spans. Due to the limited space, only the control
results of one AMD configuration under the earthquake excitation in 45° direction are reported here.
The AMD implementation is designed as follows: one AMD on each tower top and mid-points of Ting
Kau and Tsing Yi main spans both in lateral and longitudinal directions. As a result, a total of ten
AMDs are utilized in this case. Figure 2 shows the reduction of cable tension forces after active control
using the AMDs. Tables 1 and 2 list the displacement and internal force responses and the response
reduction of the TKB after using the AMDs achieved with the proposed control strategy. It is observed
that the seismic response of the TKB can be significantly reduced by using AMDs in conjunction with
the proposed stochastic optimal control method. The reduction of displacement responses is larger than
that of internal forces. Simulation studies also show that the control effectiveness for the deck
displacements and internal forces under transverse seismic excitation is better than that under
longitudinal seismic excitation. It is found that installation of AMDs on top of the bridge towers and at
the middle of main spans can achieve relatively good control effectiveness.
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