VIBRATIONS OF A SHORT SPAN, COMPARISON BETWEEN MODELIZATION AND MEASUREMENTS PERFORMED ON A LABORATORY TEST SPAN

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VIBRATIONS OF A SHORT SPAN, COMPARISON BETWEEN
MODELIZATION AND MEASUREMENTS PERFORMED ON A
LABORATORY TEST SPAN

• S. Guérard (ULg)
• J.L. Lilien (ULg)
• P. Van Dyke (IREQ)

8th International Symposium on Cable Dynamics
(ISCD 2009) September 20-23 2009, Paris
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Introduction

• The present work is a sequel to paper 44, ISCD2009

Data collected on IREQs cable testbench is used
to validate a beam element model of the cable span
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Introduction
Example of power line cable damage caused by
fatigue

(Courtesy of Alcoa 1961)
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Introduction

• Damage occurs at points where the motion of the
  conductor is constrained against transverse
  vibrations.
• E.g.
• suspension clamp,
• spacer,
• air warning marker,
• spacer,
• damper,

Need to model the shape of the conductor near
those Concentrated masses
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Objectives

• Reproduce mode shapes
• Reproduce the shape of the conductor in the
  vicinity of span ends
• Take into account conductors variable bending
  stiffness
• Take into account conductors self damping
  characteristics

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Key result with the model

• The impact of tension fluctuations on the model
  of the 63.5m span is not negligible

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Model description

• The finite element code Samcef V13.0 and its non
  linear module Mecano has been used
• with non linear beam element (T022)
• An average bending stiffness value of
  EI591.3 N.m² is considered

One of the models used 331 nodes along the 63.5m
span, with mesh refinement near the span
extremities
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Shape of eigen modes
Comparison between measured and computed position
of vibration node 1 for the beam and cable models
Mode Position of node 1 measured m Position of node 1 beam model m Difference Position of node 1 cable model m Difference
19 3.65 3.68 3 3.34 8.5
40 1.83 1.856 1.5 1.63 11
53 1.39 1.40 0.4 1.22 12.4
The position of node 1 is computed with a
difference of a few with the beam model against
10 for the cable model
 Vibration Node 1 
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Time Response with a Forced Excitation
Hypotheses

• No numerical damping (Newmarks integration
  scheme)
• The vibration shaker is modelled by a vertical
  harmonic force

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Time Response with a Forced Excitation
Results

• Eigenfrequencies are shifted with the
  introduction of the shaker
• Even after a frequency adjustment, beats can be
  seen in the time evolution of antinode
• The phase between excitation and acceleration is
  not constant

Time evolution of antinode position
Lissajous curve acceleration vs excitation
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Time Response with a Forced Excitation
Time evolution of tension
Results

• The presence of vibrations generates a continual
  tension fluctuation which reaches up to 3 of the
  conductor average tension and 0.5 RTS

Frequency content of tension

• A frequency content analysis of the tension shows
  an important component at twice the excitation
  frequency gt an anti-symmetrical mode is excited

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Sensitivity Analysis
Sensitivity to the value of the average bending
stiffness
Sensitivity to the value of the excitation force
Position of antinode
Position of antinode
time
time
A bending stiffness change of 10 leads to an
amplitude change comprised between 1 to 6
Changes of 10 in the amplitude of the excitation
force leads to an amplitude change of the order
of 5
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Conductor Self-Damping
Using a visco-elastic model for the beam material
It appears that the most adequate value of
parameter v is comprised between 0.001 and 0.0001
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Reproduction of Observed Phenomena When In-Span
Line Equipment is Introduced
For certain frequencies, higher amplitudes were
observed on subspan A
Equipment
Subspan A
Subspan B
These higher amplitudes on subspan A are met
for excitation frequencies equal to a multiple of
the fundamental frequency of subspan A (see
graph in the next slide)
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Reproduction of Observed Phenomena When In-Span
Line Equipment is Introduced
Higher amplitudes on subspan A are met for
excitation frequencies which correspond to a
multiple of the fundamental frequency of subspan A
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Conclusions

• The model allowed to show that higher amplitudes
  on the short portion of the span occur when the
  excitation frequency is a multiple of the short
  spans fundamental frequency

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Conclusions

• The shape of a conductor vibrating at its
  vibration modes in the vicinity of the span end
  is correctly reproduced
• tension fluctuations cannot be neglected

Continuous change of eigenfrequencies Difficult
to obtain a perfect resonance with the
model Contribution to node vibrations gt
potential impact on ISWR damping method has to be
checked Interest for experiments on  real
longer spans