1. /171 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

2. /172 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

3. /173 Introduction (Courtesy of Alcoa 1961) Example of power line cable damage caused by fatigue

4. /174 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

5. /175 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

6. /176 Key result with the model The impact of tension fluctuations on the model of the 63.5m span is not negligible

7. /177 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

8. /178 Shape of eigen modes Mode Position of node 1 measure d [m] Position of node 1 beam model [m] Difference % Position of node 1 cable model [m] Difference % 193.653.683%3.348.5% 401.831.8561.5%1.6311% 531.391.400.4%1.2212.4% 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

9. /179 Time Response with a Forced Excitation No numerical damping (Newmark’s integration scheme) The vibration shaker is modelled by a vertical harmonic force Hypotheses

10. /1710 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 Lissajous’ curve acceleration vs excitation Time evolution of antinode position

11. /1711 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

12. /1712 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 Position of antinode

13. /1713 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

14. /1714 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)

15. /1715 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

16. /1716 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

17. /1717 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 => potential impact on ISWR damping method has to be checked Interest for experiments on « real» longer spans