Embed Size (px)
Citation preview
Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge (Maastricht, NL)
Alain FOURNOL – Florian GERARDAVLS, bureau d’études en dynamiques des structures - Orsay (France)
Vincent DE VILLE – Yves DUCHENEBE GREISCH - Liège (Belgium)
Michel MAILLARDGERB France - Marly-le-Roi (France)
Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at
Ceramique Footbridge (Maastricht, NL)
Alain FOURNOL – Florian GERARDAVLS, bureau d’études en dynamiques des structures. Orsay (France)
Vincent DE VILLE – Yves DUCHENEBE GREISCH. Liège (Belgium)
Michel MAILLARD
GERB France. Marly-le-Roi (France)
Presentation
Context :• Design practice of footbridges with intensive use of lightweight materials and long spans
Study case :• New Ceramic footbridge• Link upon the river Meuse (Maas) in the city of Maastricht, NL
Table of contents
1. Conception
2. Experimental Dynamic Behaviour of the Footbridge without TMD
3. Sizing of TMDs
4. Experimental Dynamic Behaviour of the Footbridge with TMD
5. Conclusions – Perspectives
1. Conception
Conception
• Œuvre of René Greisch
• Total length : 261 m entirely made of steel
• The 164m main span is a bowstring bridge with a central boxed arch, a box-girder and 14-inclined full locked cables
Conception
• A new modern ward of high qualitative architecture
• The bridge has been opened end 2003 and was awarded the 2004 Dutch steel prize.
© photo- daylight.com
• In order to anticipate for low structural damping, and thus mitigate the pedestrian induced vibration, it was decided at early stage of design to allow installation of Tuned Mass Dampers.
2. Experimental Dynamic Behaviour of the Footbridge without TMD
Experimental Modal Analysis• using residual vibration levels, an Operating Deformation Shape (ODS) measurement was
conducted using natural excitation (microseismic excitation, air motion).
• ODS are performed by measuring Frequency Response Functions (FRF) between each point of a mesh and a fixed reference point.These FRFs contain phase and amplitude relationship between all points of the mesh.
• A reference vibration transducer was placed at 45 degrees in the vertical – transversal plane.Two roving bi-dimensional (Vertical – Transversal) velocimeterswere then successively moved on the 44 points representing the structure.
• Thus a total of 44 Frequency Response Functions (FRFs)were computed between the reference point and theroving points.
• The FRFs were FFT computed in the0–25Hz frequency range with aresolution of 31.2mHz.
Natural Frequencies• Natural frequencies emerge from residual vibration levels (excitation: residual wind or microseismic excitation). The
picture below shows the acceleration frequency content calculated from a 10 minutes acquisition of residual vibrations.
• The first natural frequencies are found at :– 0.97 Hz in the horizontal direction,– and 1.47 Hz, 1.66 Hz and 2.34 Hz in the vertical direction :
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
x 10-3
mi-travéequart de travée
Vertical acceleration (m/s2)
Natural frequencies
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
x 10-4
mi-travéequart de travée
Horizontal acceleration (m/s2)
Mode Shapes1st transversal 0.97 Hz
1st vertical 1.47 Hz
2nd vertical 1.66 Hz
3rd vertical 2.34 Hz
2nd transversal 2.66 Hz
1st torsion 3.19 Hz
Mode Shapes
Mode Shapes
Mode Shapes
DampingRatio H1
Excitation of the
1st horizontal mode
at 0.97 Hz
0 20 40 60 80 100-2
-1
0
1
2Acceleration [m/s²]
Ver
t. m
id-s
pan
max=0.34 m/s²
0 20 40 60 80 100-2
-1
0
1
2
Time [s]
Hor
i. m
id-s
pan
max=0.43 m/s²
0 2 4 6 8 100
0.05
0.1Acceleration spectrum [m/s² RMS] - window: Hanning - Resolution: 0.013 Hz
Ver
t. m
id-s
pan
max=0.34 m/s²
0 2 4 6 8 100
0.05
0.1
Frequency [Hz]
Hor
i. m
id-s
pan
max=0.43 m/s²
DampingRatio V1
Excitation of the
1st vertical mode
at 1.47 Hz
0 2 4 6 8 100
0.05
0.1
0.15
0.2
Acceleration spectrum [m/s² RMS] - window: Hanning - Resolution: 0.013 Hz
Ver
t. m
id-s
pan
max=0.96 m/s²
0 2 4 6 8 100
0.05
0.1
0.15
0.2
Frequency [Hz]
Hor
i. m
id-s
pan
max=0.02 m/s²
0 50 100 150-2
-1
0
1
2Acceleration [m/s²]
Ver
t. m
id-s
pan
max=0.96 m/s²
0 50 100 150-2
-1
0
1
2
Time [s]
Hor
i. m
id-s
pan
max=0.02 m/s²
Damping Ratios• Vibration amplitude decreases after harmonic excitation (10 to 15-persons group
bending knees simultaneously) is stopped.
• Several methods are usually used for damping estimation :– Logarithm decrement if only one mode is visible– Hilbert transform method or Prony-Pisarenko algorithm if several modes co-exist.
• The couples of frequency / damping parameters of the first modes provide a fairly complete characterization of vibration harshness of the structure.
Frequency Dampingζ
Magnification factor Q
Mode 1 0.97 Hz 1.2 %
Mode 2 1.47 Hz 0.3 % 167
Mode 3 1.66 Hz 0.6 % 83
0.5 %
42
Mode 4 2.34 Hz 1000 50 100 150 200
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time [s]
Acc
eler
atio
n [m
/s2 ]
Decrement logarithm method - ζ=0.28 % - f0=1.45 Hz - error=5.91 %
original signaldetected min-maxidentified envelop
Frequencies and damping of some footbridgesVERTICAL MODES, WITHOUT_TMD
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
Frequency (Hz)
Dam
ping
(% c
ritic
al)
Solférino V1Solférino Tr1Solférino Tr2Solférino Tr3Maastricht V1Maastricht V2Maastricht V3Seoul V2Melun V1Melun V2Suresnes V1Epinal V1Epinal V2
Frequencies and damping of some footbridgesHORIZONTAL MODES, WHITOUT TMD
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
Frequency (Hz)
Dam
ping
(% c
ritic
al) Maastricht H1
Maastricht H2Seoul H1Melun H1Suresnes H1Epinal H1Solférino H1
Acceleration levels• Some of these values (corresponding to case of vandalism) exceed the acceptance criteria
usually accepted for footbridges (both for low frequency motion, typically 0-3Hz) : – 0.2 m.s-2 in horizontal directions,– 0.7 m.s-2 in the vertical direction.
• The measurements confirm that these levels may be easily reached on the structure.
Mid-span Quarter-span
Z [ms-2] T [ms-2] Z [ms-2]
-
-
Synchronised walk of 25 persons with Flexion H1 mode 0.28 0.09 - -
Synchronised walk of 25 persons with Flexion V1 mode 0.56 0.02 - -
Specific excitation of Flexion V2 with 10 persons 0.43 0.04 0.92 0.05
Specific excitation of Flexion V3 with 10 persons 1.69 0.04 1.64 0.10
Specific excitation of Flexion H1 with 10 persons 0.44 0.46 - -
Synchronised walk of 25 persons with Flexion V2 mode 0.62 0.04 - -
Specific excitation of Flexion V1 with 10 persons 1.42 0.06 0.92 0.08
T [ms-2]
1.52
Random walk of 10 persons 0.12 0.02 -
Random walk of 25 persons 0.18 0.02 -
0.15Specific excitation of Torsion T1 with 10 persons 2.02 0.20
Dynamic Diagnosisof the Structure
• HORIZONTAL DIRECTION : Damping of the first horizontal mode is satisfactory (1.2%)
• VERTICAL DIRECTION : the frequency / damping couple is clearly unfavourable :
– The three first natural frequencies in the vertical direction are inside the frequency range of pedestrian excitation (walking fundamental frequency is mainly between 1.5 Hz and 2.5 Hz).
– The related damping ratios are very low, from 0.3% to 0.6%: a damping ratio of 0.3% induces a magnification factor of roughly 160 at resonance (compared to static response).
• ⇒ DECISION : add damping with TMDs to the first three vertical modes, since :
– Their frequencies are located inside the walking frequency range : 1.47 Hz, 1.66 Hz, 2.34 Hz– Their damping is very low : 0.3%, 0.6 %, 0.5%.– Vertical acceptance criteria was easily approached with only 25 persons randomly walking,– Their frequencies are mainly represented in the measured response spectrum during random
walking.
2. Calculations
Dynamic Model
• Dynamic model using Finelg, by Greisch
• Material : Concrete and steel
• Elements : beams and shells
• Rayleigh Damping Model
• Improvement of the accuracy of the model :by making softer links (spring connection) between beams and posts
First results
• Results of modal analysis :
Measurement Calculation Deviation
1.04 Hz 7 %
Mode 2 1.47 Hz 1.50 Hz 2 % 255 tons
Mode 3 1.66 Hz 1.77 Hz 6 % 232 tons
5 %2.47 Hz
Modal Mass
Mode 1 0.97 Hz 157 tons
Mode 4 2.34 Hz 212 tons
First results
Measuredmodes :
Calculatedmodes :
1st horizontal 0.97 Hz
1st vertical 1.47 Hz
2nd vertical 1.66 Hz
3rd vertical 2.34 Hz
2nd transversal 2.66 Hz
1st torsion 3.19 Hz
1st horizontal1.04 Hz
1st vertical1.50 Hz
2nd vertical1.77 Hz
3rd vertical2.47 Hz
2nd horizontal2.94 Hz
1st torsion3.68 Hz
3. Design of Tuned Mass Damper
TMD Design
• 2 DOFs Model
Ki
M
k
m
c
Mi
Ci
TMD
Footbridge Mode Vi
TMD Design
1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.60
0.1
0.2
0.3
0.4
0.5
0.6
F=2.08HzF=2.10HzF=2.12HzF=2.14HzF=2.16HzF=2.18Hz
1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.60
0.1
0.2
0.3
0.4
0.5
0.6d=8%d=10%d=12%d=13%d=14%d=15%d=17%
• Parameter : TMD frequency Parameter : TMD damping
TMD position
Midspan
¼ span
¾ span
Design of Tuned Mass Dampers
Number of TMD
Unit Mass
TunedFrequency
SpringCoefficient
DampingCoefficient
Mode 2: vertical flexion – order 1 1 3 300 kg
3 000 kg
0.28 kN/mm
4 240 kg
1.34.1 kN.s/m1.31 Hz
1.63 Hz 4.2 kN.s/m
Mode 4: vertical flexion – order 3 1 2.29 Hz 0.88 kN/mm 10.3 kN.s/m 2.0
Mode 3: vertical flexion – order 2 1 0.32 kN/mm 1.3
% Modal Mass
• Optimisation of the TMD parameters (mass, frequency, damping ratio) was carried out using analytical equations of 2-DOF mass-spring systems (see Mechanical Vibrations, Den Hartog, 1956) :
• A set of 3 TMD units (with a total mass of 10 540 kg) was installed at mid-span and quarter span, in order to damp the three first vertical modes of the structure, using the available space.
• The TMDs were designed and built by GERB Company in France.
4. Performance Checking of the TMD
• Testing was carried out after TMD setup : damping ratios were measured.
• The structural damping of the first vertical modes was about 3 to 5 times larger with TMD than without TMD.
• Notice that the installed TMDs increase damping of the first horizontal mode further on.
Performance Checkingof the TMD
Frequency ζ without TMD ζ with blocked TMDs
Flexion H1 0.97 Hz 1.2 % -
0.3 %
Flexion V2 1.66 Hz 0.6 % 0.6 % 1.7 %
Flexion V3 2.34 Hz 0.5 % 0.6 % 2.3 %
Torsion T1 3.19 Hz 0.2 à 0.3 % - 0.4 %
2.4 %
Flexion V1 1.47 Hz 0.3 % 1.6 %
ζ with free TMDs
TMD
• Excitation of mode V2
¼ span
½ span
TMD V1
TMD V2
TMD V3
TMD efficiency on footbridges (sample)VERTICAL MODES, WITH_TMD
0
0.5
1
1.5
2
2.5
3
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
Frequency (Hz)
Dam
ping
(% c
ritic
al)
Solférino V1Solférino Tr1Solférino Tr2Solférino Tr3Maastricht V1Maastricht V2Maastricht V3Seoul V2Melun V1Melun V2Suresnes V1Epinal V1Epinal V2Maastricht V1bMaastricht V2bMaastricht V3bSolférino Tr2bSolférino Tr3bV/F criteria, M=250tSeoul V2b
constant mobility 2e-6 m/s/N
TMD efficiency on footbridges (sample)HORIZONTAL MODES, WITH TMD
0
0.5
1
1.5
2
2.5
3
3.5
4
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
Frequency (Hz)
Dam
ping
(% c
ritic
al)
Maastricht H1Maastricht H2Seoul H1Melun H1Suresnes H1Epinal H1Solférino H1Seoul H1bSolférino H1bMaastricht H1b
no Horizontal TMD !!!-> side effect
5. Conclusion
Conclusion(case of TMD installation on an existing footbridge)
• It was shown that the application of TMDs efficiently brings damping to an underdamped structure. Here, the TMD mass was particularly low (1.3 to 2 % of modal mass), however damping was noticeably increased (x3 to x5).
• Owners usually ask for a maximum acceleration level guarantee. This is uneasy, since the excitation is not under our control (pedestrians)
• it is difficult to accurately predict (by computing) the future damping, although its should be a contractual goal for this type of project
• The prediction of TMDs effect on Footbridge’s damping needs further investigations.
Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge
(Maastricht, NL)
Alain FOURNOL – Florian GERARDAVLS, bureau d’études en dynamiques des structures. Orsay (France)
Vincent DE VILLE – Yves DUCHENEBE GREISCH. Liège (Belgium)
Michel MAILLARDGERB France. Marly-le-Roi (France)
Thank you for your attention
Performance Checkingof the TMD
• Forced single-degree-of-freedom oscillator with damping
2
0
2
20
2
21
1
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛−
=
ωωζ
ωω
kFX
ζωω
kFX
21
0 =⇒=
0 2 4 6 8 1010
-1
100
101
102
103
X /
Xst
at
Frequency [Hz]
ζ=0.25%
ζ=1%ζ=2%ζ=5%ζ=10%
ζ=100% Static limit
Dynamic amplification
Floors Mobilities
