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Contents

• Introduction
• Cable Damping Experimental Setup
• Experimental Results
• Conclusions

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• Introduction

• Cable

• Cables are efficient structural elements that
  are used in
• cable-stayed bridges, suspension bridges and
  other cable
• structures.
• Steel cables are flexible and have low inherent
  damping,
• resulting in high susceptibility to vibration.
• Vibration can result in premature cable or
  connection
• failure and/or breakdown of the cable
  corrosion protection
• systems, reducing the life of the cable
  structure.
• Numerous passive and active cable damping
  studies have
• been performed and full-scale applications
  realized.

4

• Semiactive damping system

- Johnson et al. (1999, 2000) verification of
the efficacy of a semiactive damper
for a taut/sagged cable model - Christenson
(2001) experimental verification of the
performance of an MR damper in mitigating
cable responses by using a
medium-scale cable - Ni et al. (2002), Ko et al.
(2002), Duan et al. (2002) field
comparative tests of cable vibration control
using MR dampers (the worlds first
time implementation of MR-based
smart damping technology in civil
engineering structures)
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• Objectives

• To experimentally verify the performance of the
  MR
• damper-based control systems for suppressing
  vibration of
• real-scaled stay cables using various
  semiactive control
• algorithms

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• Cable Damping Experimental Setup

• Schematic of smart cable damping experiment

spectrum analyzer
shaker
flat-sag cable
digital controller
MR dampers
shaker force
Where,
damper force
displacement at damper location
evaluation displacement
control signal
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• Cable

parameters values
L 44.7 m
m 89.86 N/m
T 500 KN
1.34 m
13.4 m

8.37
2.53 Hz
Real-scaled cable at HICT
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• Cable model

• Transverse motion of cable could be modeled by
• the motion of a taut string because of small
  sag
• (0.1 sag-to-span ratio with tension of 500
  kN).

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where
transverse deflection of the cable
transverse damper force at location
transverse shaker force at location
angle of inclination
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• MR damper

• MR controllable friction damper
• (RD-1097-01 from Lord Corporation)
• Maximum force level ?100 N
• Maximum voltage 1.4 V

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• MR damper installation

• Twin damper setup
• Location 1.34m
• from bottom support
• Measurement Damper force,
• displacement, and
• acceleration

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• Cable exciting system (Kim et al. 2002)

(1)
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• Controller

• The controller is constructed by the Matlab
  Real-Time
• Workshop executed in real time using MS Visual
  C.
• The measured responses are acquired from
  displacement
• and acceleration sensors at damper location and
  converted
• into digital data by NI DAQ Card-6062E.

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• Control algorithms
• to calculate the command voltage
  input

• Passive-mode cases
• - passive-off (v0V),
• - passive-on (v 1.4V)
• - other passive-modes (v 0.6V, 1.0V, 1.1V,
  1.2V, 1.3V)

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• Semiactive control cases (Jansen and Dyke 2000)
• - Clipped-optimal control algorithm
• where, Vmax1.4V, Fd ci the desired
  control force, and
• Fd the measured control
  force
• - Control based on Lyapunov stability theory
• where, z the state vector, and
• P the matrix to be found
  using the Lyapunov
• equation

(2)
(3)
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- Maximum energy dissipation algorithm
where, vd the velocity at the
damper location - Modulated homogeneous friction
algorithm
(4)
(5)
P?i(t) ?i(t-s),
where s min x?0 ?i(t-x)0
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• Experimental Results

• Displacement in free vibration

Displacement (m)
Time (sec)
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• Damping ratios for verification of performances

• The amplitude-dependent damping ratios are
  calculated by
• the Hilbert transform-based identification
  method
• (Duan et al. 2002)

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• Damping ratios in the passive-mode cases

Damping ratio ()
Amplitude (mm) at the location of 10.2 m away
from the bottom support
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• Damping ratios in the semiactive control cases

Damping ratio ()
Amplitude (mm) at the location of 10.2 m away
from the bottom support
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• Conclusions

• The performance of MR damper-based control
  systems
• for suppressing vibration of stay cables is
  experimentally
• verified.

• Semiactive control systems significantly improve
  the
• mitigation of stay cable vibration over the
  uncontrolled
• and the passive-off cases.

• The control based on Lyapunov stability and the
  clipped-
• optimal control show slightly better
  performance than
• the passive-on case.

• The Modulated homogeneous friction algorithm
  shows
• nearly the same performance as the passive-on
  case.