Présentation de mon dernier stage à ISTERRE de l'instrumentation et l'analyse vibratoire d'un viaduc

1. PRESENTATION OF INTERNSHIPTITLE: VIBRATORY ANALYSIS OF A CIVIL ENGINEERING STRUCTURE (PONT LE FAYET - CHAMONIX)
ABANOBI EKENE ALEXANDER M2 SIM
GUEGUEN Philippe BAILLET Laurent
1

2. • Brief Introduction to parameters of dynamic behaviour of structures
• Introduction to the particularities of the work at hand
• Comparison of Numerical and Experimental Natural frequencies
• Numerical Mode Shapes
• Field Notes for experimental organisation of sensors
• Flowchart of the experimental signal processing procedure
• Further details into of the experimental data processing procedure
• Experimental results and numerical comparison
• Perspectives & Conclusion
2
 TABLE OF CONTENTS

3. 3
CHARACTERISATION
OFTHELINEAR
DYNAMICBEHAVIOUR
OFASTRUCTURE RESONANCE FREQUENCIES
MODAL SHAPES
DAMPING RATIOS
 Introduction
Alexander ABANOBI M2 SIM
STIFFNESS
YOUNG’S MODULUS

4. 4
Alexander ABANOBI M2 SIM
 Material parameters of the numerical model

5. Position of the elastomer layer (blue) modelising contact between the deck and the support
Figure 2 shows where the thin elastic layer that models the contact between the deck and the bridge supports (pillars)
is located. The area around pillar 29 is shown in the figure.
5
 VISUALISATION OF AN IDENTITY PAIR (THE CONTACT BETWEEN THE DECK
AND THE PILLARS)
Alexander ABANOBI M2 SIM
Default Young’s Modulus 25GPa : Reinforced
Concrete Material

6. 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10
Fréquencespropres
Numérotation des fréquences propres
Variation des composants horizontals de la raideur pour
les paires d'identités pour les 10 premières fréquences
propres. Module d'Young du béton 15GPa
[1e5,1e5,1e13]N/m
[5e5,5e5,1e13]N/m
[1e6,1e6,1e13]N/m
[5e6,5e6,1e13]N/m
[1e7,1e7,1e13]N/m
[5e7,5e7,1e13]N/m
[1e8,1e8,1e13]N/m
[5e8,5e8,1e13]N/m
[1e9,1e9,1e13]N/m
[5e9,5e9,1e13]N/m
[1e10,1e10,1e13]N/m
[5e10,5e10,1e13]N/m
[1e11,1e11,1e13]N/m
[5e11,5e11,1e13]N/m
[1e12,1e12,1e13]N/m
[5e12,5e12,1e13]N/m
[1e13,1e13,1e13]N/m
6
Fig.1: Evolution of the first 10 natural frequencies as a function of the different elastomer stiffness for a cement
Young’s Modulus of 15GPa. This is used as the base case for the interpolation for the other Young Moduli
 Base Case; Young Modulus of concrete, E = 15 GPa

7. 0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
Fréquencespropres
Numérotation des fréquences propres
Variation des composants horizontals
de la raideur pour les paires
d'identités pour les 10 premières
fréquences propres. Module d'Young
du béton 20GPa
[1e5,1e5,1e13]N/m
[5e5,5e5,1e13]N/m
[1e6,1e6,1e13]N/m
[5e6,5e6,1e13]N/m
[1e7,1e7,1e13]N/m
[5e7,5e7,1e13]N/m
[1e8,1e8,1e13]N/m
[5e8,5e8,1e13]N/m
[1e9,1e9,1e13]N/m
[5e9,5e9,1e13]N/m
[1e10,1e10,1e13]N/m
[5e10,5e10,1e13]N/m
[1e11,1e11,1e13]N/m
[5e11,5e11,1e13]N/m
[1e12,1e12,1e13]N/m
[5e12,5e12,1e13]N/m
[1e13,1e13,1e13]N/m
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
Fréquencespropres
Numérotation des fréquences propres
Variation des composants horizontals
de la raideur pour les paires
d'identités pour les 10 premières
fréquences propres. Module d'Young
du béton 20GPa - Interpolée
[1e5,1e5,1e13]N/m
[5e5,5e5,1e13]N/m
[1e6,1e6,1e13]N/m
[5e6,5e6,1e13]N/m
[1e7,1e7,1e13]N/m
[5e7,5e7,1e13]N/m
[1e8,1e8,1e13]N/m
[5e8,5e8,1e13]N/m
[1e9,1e9,1e13]N/m
[5e9,5e9,1e13]N/m
[1e10,1e10,1e13]N/m
[5e10,5e10,1e13]N/m
[1e11,1e11,1e13]N/m
[5e11,5e11,1e13]N/m
[1e12,1e12,1e13]N/m
[5e12,5e12,1e13]N/m
[1e13,1e13,1e13]N/m
7
COEFFICIENTS DE
CORRELATION DES
17 SERIES ENTRE
LES DEUX PLOTS
(NUMERIQUE ET
NUMERIQUE
INTERPOLE)
0.9998
0.9985
0.9839
0.9959
0.9971
0.9967
0.9983
0.9999
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000Fig.2: Evolution of the first 10 natural frequencies as a function of the different
elastomer stiffness for a cement Young’s Modulus of 20GPa : Numerical values.
Fig.3: Evolution of the first 10 natural frequencies as a function of the different
elastomer stiffness for a cement Young’s Modulus of 20GPa : Interpolated Numerical values.
Values for the table are gotten from the diagonal of the matrix
of the pairwise linear correlation coefficients from matlab
 Interpolation : Freqs x √((20/15)); E = 20GPa
Alexander ABANOBI M2 SIM
Relation tested : 𝐸 ∝ 𝑓2

8. 0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
Fréquencespropres
Numérotation des fréquences propres
Variation des composants horizontals
de la raideur pour les paires
d'identités pour les 10 premières
fréquences propres. Module d'Young
du béton 23GPa
[1e5,1e5,1e13]N/m
[5e5,5e5,1e13]N/m
[1e6,1e6,1e13]N/m
[5e6,5e6,1e13]N/m
[1e7,1e7,1e13]N/m
[5e7,5e7,1e13]N/m
[1e8,1e8,1e13]N/m
[5e8,5e8,1e13]N/m
[1e9,1e9,1e13]N/m
[5e9,5e9,1e13]N/m
[1e10,1e10,1e13]N/m
[5e10,5e10,1e13]N/m
[1e11,1e11,1e13]N/m
[5e11,5e11,1e13]N/m
[1e12,1e12,1e13]N/m
[5e12,5e12,1e13]N/m
[1e13,1e13,1e13]N/m
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
Fréquencespropres
Numérotation des fréquences propres
Variation des composants horizontals
de la raideur pour les paires
d'identités pour les 10 premières
fréquences propres. Module d'Young
du béton 23GPa - Interpolée
[1e5,1e5,1e13]N/m
[5e5,5e5,1e13]N/m
[1e6,1e6,1e13]N/m
[5e6,5e6,1e13]N/m
[1e7,1e7,1e13]N/m
[5e7,5e7,1e13]N/m
[1e8,1e8,1e13]N/m
[5e8,5e8,1e13]N/m
[1e9,1e9,1e13]N/m
[5e9,5e9,1e13]N/m
[1e10,1e10,1e13]N/m
[5e10,5e10,1e13]N/m
[1e11,1e11,1e13]N/m
[5e11,5e11,1e13]N/m
[1e12,1e12,1e13]N/m
[5e12,5e12,1e13]N/m
[1e13,1e13,1e13]N/m
8
COEFFICIENTS DE
CORRELATION DES
17 SERIES ENTRE
LES DEUX PLOTS
(NUMERIQUE ET
NUMERIQUE
INTERPOLE)
0.9998
0.9985
0.9839
0.9959
0.9971
0.9967
0.9983
0.9999
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
Fig.4: Evolution of the first 10 natural frequencies as a function of the different
elastomer stiffness for a cement Young’s Modulus of 23GPa : Numerical values.
Fig.5: Evolution of the first 10 natural frequencies as a function of the different
elastomer stiffness for a cement Young’s Modulus of 23GPa : Interpolated Numerical values.
 Interpolation : Freqs x √((23/15)); E = 23GPa
Alexander ABANOBI M2 SIM

9. 9
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
NaturalFrequency(Hz)
Numebering of the Natural Frequencies
Comparison of the Natural Frequencies from the
Numerical Model and those from the Experimental
Model
Experimental Model
Numerical Model
 WORK ON NUMERICAL MODEL
Alexander ABANOBI M2 SIM
Correlation between experimental and numerical modal frequencies

10.  NUMERICAL 3D MODE SHAPES
10
Alexander ABANOBI M2 SIM
3D Numerical Mode shapes of the first 10 modes
Mode 1
Mode 10Mode 9Mode 8Mode 7Mode 6
Mode 5Mode 4Mode 3Mode 2

11. 11
 NUMERICAL 2D MODE SHAPES
Alexander ABANOBI M2 SIM
2D Numerical Mode shapes of the first 10 modes
Mode 1
Mode 10Mode 9Mode 8Mode 7Mode 6
Mode 5Mode 4Mode 3Mode 2

12. 12
Field Notes
Alexander ABANOBI M2 SIM
Field Note showing the position of the sensors and pillars for each series of measurement

13. 13
Presentation of results
Processing Numerical data to get rid of complications related to the numerical model
Normalisation of readings so that every reading is a relative to the last sensor (synchronization)
Fishing out of bad sensors
Windowing : Moving window of 60seconds (60*200 samples) half a minute of overlap (6000 samples) in order to make spectrogrammes that are clean
and clear with less amount of noise : (29 windows in total) and Averaging of each frequency line over the 29 windows. FFT was taken window by
window. Choose the window and then take the FFT of that window
Absolute value of the FFT (Fast Fourier Transfromation)–Transition to the frequency domain
Rotation (about the z-axis) of the axis des données selon les pentes determinées par les coordonnées des pillers prises en comsol
Reorganization of the sequence of the axis from (Z, X, Y) to a more familiar (X, Y, Z)
Loading up of the raw data into Matlab
 ORGANOGRAM FOR EXPERIMENTAL DATA PROCESSING
Alexander ABANOBI M2 SIM

14. 14
Average over these 29 windows reduces samples per sensor to 12,000 and removes noise.
Alexander ABANOBI M2 SIM
Fig. : Graphic showing how the windowing was carried out
 Windowing and Averaging

15. 15
Alexander ABANOBI M2 SIM
• The rotation had to be done carefully and the manner in which the
angles were taken from the COMSOL model had to be a factor in the
manner of the rotation.
• The angles were taken in COMSOL with clockwise angle as positive.
Cosθ -Sinθ 0
Sinθ Cosθ 0
0 0 1
Rotation Matrix about the Z-axis
Rotation schema
 Rotation Method

16. 16
Alexander ABANOBI M2 SIM
Numerical Model of the bridge showing the only data points
 Nature of the numerical model

17. 17
Alexander ABANOBI M2 SIM
3D Experimental bridge model showing the position of sensors and pillars
 Position of Sensors And Pillars

18. 18
Alexander ABANOBI M2 SIM
Numerical Model of the bridge showing the only data points
 Spectrograms

19. 19
Alexander ABANOBI M2 SIM
Numerical Model of the bridge showing the only data points
 Spectrograms

20. 20
Alexander ABANOBI M2 SIM
First mode shape in the X, Y and Z directions
Mode 1 : X direction
Mode 1 : Y direction
Mode 1 : Z direction
 Numerical vs Experimental Mode Shapes (peak-picking)

21. 21
Alexander ABANOBI M2 SIM
8th mode shape in the Y-dircetion
2nd mode shape in the Y-dircetion
 Some higher modes

22. 22
21
22
23
24
25
26
27
28
pillars
Position of pillar 21 to pillar 28. Mode shape 1.
 Position of pillars 21 – pillar 28

23. 23
Alexander ABANOBI M2 SIM
Comparison of the frequency spectrum of the numerical and experimental models with
stiffness (9 9 and 5% damping)
Experimental Frequency Spectrum vs Numerical FRF with damping ratio
5% and stiffness of elastomer layer [1e9, 1e9, 1e13]N/m

24. Experimental Frequency Spectrum vs Numerical FRF with damping ratio
10% and stiffness of elastomer layer [1e9, 1e9, 1e13]N/m
24
Comparison of the frequency spectrum of the numerical and experimental models
with stiffness ([1e9, 1e9, 1e13]N/m and 10% damping)

25. 25
Alexander ABANOBI M2 SIM
Effect of stiffness on the first mode shape
 EFFECT OF STIFFNESS

26. 26
Alexander ABANOBI M2 SIM
A dataset consists of the entire readings taken at once. There was a total of 19
datasets.
 Singular Value Decomposition
First dataset Second dataset Average of all datasets

27. • Correlation parameter used to separate physical modes from non-physical ones. It
assures consistency of a mode shape among the many measures and it not
necessarily a criteria for validity of the mode shape.
• MAC value of less than 80-85% shows the lower limits of the contribution of a
certain frequency to the global shape of the mode.
27
Alexander ABANOBI M2 SIM
 Modal Assurance Criterion (MAC)

28. • The experimental mode shapes modeled the numerical ones to a good
extent but the lesser precision (number of computation points and
sensor accuracy) of the experimental model meant the modes were not
as smooth as the numerical modes.
• Futher work is being done to produce the mode shapes using the SVD
method.
• SVD is a more accurate method of deterimining the mode shapes
followed by the correlation given by the Mac value.
28
Alexander ABANOBI M2 SIM
 Perspectives & Conclusion

29. THANKS FOR LISTENING
29
Alexander ABANOBI M2 SIM