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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 IREQ’s cable testbench is used to validate a beam element model of the cable span

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Introduction

(Courtesy of Alcoa 1961)

Example of power line cable damage caused by fatigue

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IntroductionDamage 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 conductor’s variable bending stiffness

• Take into account conductor’s 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 EI=591.3 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

ModePosition of

node 1 measure

d [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%

Comparison between measured and computed position of vibration node 1 for the beam and cable models

« Vibration Node 1 »

The position of node 1 is computed with a difference of a few % with the beam model against ~10% for the cable model

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Time Response with a Forced Excitation

• No numerical damping (Newmark’s integration scheme)

• The vibration shaker is modelled by a vertical harmonic force

Hypotheses

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Time Response with a Forced ExcitationResults

• 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

Lissajous’ curve acceleration vs excitation

Time evolution of antinode position

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Time Response with a Forced Excitation

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

Time evolution of tension

Frequency content of tension

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

Results

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Sensitivity Analysis

Sensitivity to the value of the average bending stiffness

Sensitivity to the value of the excitation force

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%

time time

Pos

ition

of

antin

ode

Pos

ition

of

antin

ode

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Conductor Self-Dampingvv v

v H

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

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

7.E-04

8.E-04

9.E-04

1.E-03

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

distance from span end (m)

pk

-pk

dis

pla

ce

me

nt

(m)

v=0.001

v=0.0001 (minimum and maximum values of the "beat")

Measurements

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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

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6

Ratio "excitation frequency/ fundamental frequency of subspan A"

Rat

io "

anti

no

de

amp

litu

de

of

sub

span

A/a

nti

no

de

amp

litu

de

of

sub

span

B"

M=8kg M=5kg M=0kg

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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 span’s 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 neglectedContinuous change of eigenfrequencies

Difficult to obtain a perfect resonance with the model

Contribution to node vibrations => potential impact on ISWR damping method has to be checked

Interest for experiments on « real» longer spans