Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge (Maastricht, NL)

Transcription

1 Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge (Maastricht, NL) Alain FOURNOL Florian GERARD AVLS, bureau d études en dynamiques des structures - Orsay (France) Vincent DE VILLE Yves DUCHENE BE GREISCH - Liège (Belgium) Michel MAILLARD GERB France - Marly-le-Roi (France)

2 Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge (Maastricht, NL) Alain FOURNOL Florian GERARD AVLS, bureau d études en dynamiques des structures. Orsay (France) Vincent DE VILLE Yves DUCHENE BE GREISCH. Liège (Belgium) Michel MAILLARD GERB France. Marly-le-Roi (France)

3 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

4 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

5 1. Conception

6 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

7 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.

8 2. Experimental Dynamic Behaviour of the Footbridge without TMD

9 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) velocimeters were 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 the roving points. The FRFs were FFT computed in the 0 25Hz frequency range with a resolution of 31.2mHz.

10 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 : 2.5 x 10-3 Vertical acceleration (m/s2) mi-travée quart de travée

11 Natural frequencies x 10-4 Horizontal acceleration (m/s2) 7 mi-travée quart de travée

12 Mode Shapes 1 st transversal 0.97 Hz 1 st vertical 1.47 Hz 2 nd vertical 1.66 Hz 3 rd vertical 2.34 Hz 2 nd transversal 2.66 Hz 1 st torsion 3.19 Hz

13 Mode Shapes

14 Mode Shapes

15 Mode Shapes

16 Damping Ratio H1 Excitation of the 1 st horizontal mode at 0.97 Hz Acceleration spectrum [m/s² RMS] - window: Hanning - Resolution: Hz 0.1 max=0.34 m/s² Vert. mid-span 0.05 Vert. mid-span Acceleration [m/s²] max=0.34 m/s² Hori. mid-span max=0.43 m/s² Hori. mid-span max=0.43 m/s² Frequency [Hz] Time [s]

17 Damping Ratio V1 Excitation of the 1 st vertical mode at 1.47 Hz Vert. mid-span Acceleration spectrum [m/s² RMS] - window: Hanning - Resolution: Hz max=0.96 m/s² Vert. mid-span Acceleration [m/s²] max=0.96 m/s² Hori. mid-span max=0.02 m/s² Frequency [Hz] Hori. mid-span max=0.02 m/s² Time [s]

18 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. Acceleration [m/s 2 ] Decrement logarithm method - ζ=0.28 % - f 0 =1.45 Hz - error=5.91 % 1 0 original signal detected min-max identified envelop Frequency Damping Mode Hz 1.2 % ζ Magnification factor Q 42 Mode Hz 0.3 % 167 Mode Hz 0.6 % Time [s] Mode Hz 0.5 % 100 The couples of frequency / damping parameters of the first modes provide a fairly complete characterization of vibration harshness of the structure.

19 Frequencies and damping of some footbridges VERTICAL MODES, WITHOUT_TMD Damping (% critical) Solférino V1 Solférino Tr1 Solférino Tr2 Solférino Tr3 Maastricht V1 Maastricht V2 Maastricht V3 Seoul V2 Melun V1 Melun V2 Suresnes V1 Epinal V1 Epinal V Frequency (Hz)

20 Frequencies and damping of some footbridges HORIZONTAL MODES, WHITOUT TMD Damping (% critical) Maastricht H1 Maastricht H2 Seoul H1 Melun H1 Suresnes H1 Epinal H1 Solférino H Frequency (Hz)

21 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 ] T [ms -2 ] Random walk of 10 persons Random walk of 25 persons Synchronised walk of 25 persons with Flexion H1 mode Synchronised walk of 25 persons with Flexion V1 mode Synchronised walk of 25 persons with Flexion V2 mode Specific excitation of Flexion V1 with 10 persons Specific excitation of Flexion V2 with 10 persons Specific excitation of Flexion V3 with 10 persons Specific excitation of Flexion H1 with 10 persons Specific excitation of Torsion T1 with 10 persons

22 Dynamic Diagnosis of 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.

23 2. Calculations

24 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

25 First results Results of modal analysis : Measurement Calculation Deviation Modal Mass Mode Hz 1.04 Hz 7 % 157 tons Mode Hz 1.50 Hz 2 % 255 tons Mode Hz 1.77 Hz 6 % 232 tons Mode Hz 2.47 Hz 5 % 212 tons

26 First results 1 st horizontal 0.97 Hz 1 st vertical 1.47 Hz 2 nd vertical 1.66 Hz Measured modes : 3 rd vertical 2.34 Hz 2 nd transversal 2.66 Hz 1 st torsion 3.19 Hz 1 st horizontal 1.04 Hz 1 st vertical 1.50 Hz 2 nd vertical 1.77 Hz Calculated modes : 3 rd vertical 2.47 Hz 2 nd horizontal 2.94 Hz 1 st torsion 3.68 Hz

27 3. Design of Tuned Mass Damper

28 TMD Design 2 DOFs Model TMD k m M c Footbridge Mode Vi Mi Ki Ci

29 TMD Design F=2.08Hz F=2.10Hz F=2.12Hz F=2.14Hz F=2.16Hz F=2.18Hz d=8% d=10% d=12% d=13% d=14% d=15% d=17% Parameter : TMD frequency Parameter : TMD damping

30 TMD position ¾ span Midspan ¼ span

31 Design of Tuned Mass Dampers 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) : Number of TMD Unit Mass Tuned Frequency Spring Coefficient Damping Coefficient % Modal Mass Mode 2: vertical flexion order kg 1.31 Hz 0.28 kn/mm 4.1 kn.s/m 1.3 Mode 3: vertical flexion order kg 1.63 Hz 0.32 kn/mm 4.2 kn.s/m 1.3 Mode 4: vertical flexion order kg 2.29 Hz 0.88 kn/mm 10.3 kn.s/m 2.0 A set of 3 TMD units (with a total mass of 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.

32 4. Performance Checking of the TMD

33 Performance Checking of the TMD Testing was carried out after TMD setup : damping ratios were measured. Frequency ζ without TMD ζ with blocked TMDs ζ with free TMDs Flexion H Hz 1.2 % % Flexion V Hz 0.3 % 0.3 % 1.6 % Flexion V Hz 0.6 % 0.6 % 1.7 % Flexion V Hz 0.5 % 0.6 % 2.3 % Torsion T Hz 0.2 à 0.3 % % 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.

34 TMD ¼ span ½ span TMD V1 TMD V2 TMD V3 Excitation of mode V2

35 TMD efficiency on footbridges (sample) VERTICAL MODES, WITH_TMD 3 Damping (% critical) constant mobility 2e-6 m/s/n Solférino V1 Solférino Tr1 Solférino Tr2 Solférino Tr3 Maastricht V1 Maastricht V2 Maastricht V3 Seoul V2 Melun V1 Melun V2 Suresnes V1 Epinal V1 Epinal V2 Maastricht V1b Maastricht V2b Maastricht V3b Solférino Tr2b Solférino Tr3b V/F criteria, M=250t Seoul V2b Frequency (Hz)

36 TMD efficiency on footbridges (sample) HORIZONTAL MODES, WITH TMD Maastricht H1 Damping (% critical) no Horizontal TMD!!! -> side effect Maastricht H2 Seoul H1 Melun H1 Suresnes H1 Epinal H1 Solférino H1 Seoul H1b Solférino H1b Maastricht H1b Frequency (Hz)

37 5. Conclusion

38 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.

39 Experimental Dynamic Behaviour and Pedestrian Excited Vibrations Mitigation at Ceramique Footbridge (Maastricht, NL) Thank you for your attention Alain FOURNOL Florian GERARD AVLS, bureau d études en dynamiques des structures. Orsay (France) Vincent DE VILLE Yves DUCHENE BE GREISCH. Liège (Belgium) Michel MAILLARD GERB France. Marly-le-Roi (France)

40 Performance Checking of the TMD Forced single-degree-of-freedom oscillator with damping 10 3 X F = 2 ω 1 2 ω0 1 k 2 ω + 2ζ ω0 2 X / X stat ζ=0.25% ζ=1% ζ=2% ζ=5% ζ=10% Dynamic amplification ω = ω X F 0 = 1 2kζ 10 0 ζ=100% Static limit Frequency [Hz]

41 Floors Mobilities