Vibrations problems

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Arnaud Deraemaeker

VIBRATIONS PROBLEMS

Arnaud.Deraemaeker@ulb.be

PEDESTRIAN BRIDGES

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Vibrations problems

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From [Bureau Greisch, 2020]

Footbridge in Durbuy

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From ‘Vibration problems in structures’, H. Bachman, 1995

Vibration source

Main frequencies of excitation from 1.5 to 3 Hz! Harmonics !

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Vibrations problems

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Footbridge in Durbuy

Mode 1 (2 Hz) Mode 2 (4.16 Hz)

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[A. Banas, R. Jankowski Experimental and Numerical Study on Dynamics of Two Footbridges with Different Shapes of Girders, Appl. Sci. 2020, 10, 4505; doi:10.3390/app10134505]

Arch footbridge S8 expressway – Poland

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Vibrations problems

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Mode shapes

Potential resonance (first harmonic)

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Pedestrian induced vibrations

https://www.youtube.com/watch?v=zpGZN8r2QxY

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Vibrations problems

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Pedestrian induced vibrations

https://www.youtube.com/watch?v=gQK21572oSU

HIGH-RISE BUILDINGS

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Vibrations problems

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Freq spectrum of ground acceleration

Santa Cruz Earthquake

Wind and earthquake excitations

Davenport spectrum

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Wind excitation

Zhi Li, J. Fu, Y. He, Z. Liu, J. Wu, R. Rao and C.T. Ng, Structural Responses of a Supertall BuildingSubjected to a Severe Typhoon at Landfall, Appl. Sci. 2020, 10, 2965

303 m high-rise building,Guangzhou China

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Vibrations problems

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Building swaying in the wind

https://www.youtube.com/watch?v=i1sHJRCJPS4

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Building swaying after earthquake

https://www.youtube.com/watch?v=2t2xxKMN-Ic&t=230s

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Vibrations problems

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MACHINE INDUCEDVIBRATIONS

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Force transmitted to the surroundings

Machine induced vibrations

FFT of idle engine acceleration

Main excitation (30 Hz)

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Vibrations problems

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Washing machines

https://www.youtube.com/watch?v=SRbFxgezAX0

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Harvester

[Romaric BIAOU OLAYE]

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Vibrations problems

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Tractor engine

https://www.youtube.com/watch?v=7tJkI7dygfU

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Helicopter ground resonance

https://www.youtube.com/watch?v=ZcdYIkrQVzA

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Vibrations problems

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PRECISION EQUIPMENTAND COMFORT

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Vibrations caused by the surroundings

GSFC Standard (Nasa)

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Vibrations problems

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23https://www.youtube.com/watch?v=1O4PEqeXk5M

Payload comfort in space launchers (satellites)

24https://www.youtube.com/watch?v=5bsuar1vo2g

Comfort in sports cars

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Vibrations problems

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25https://www.youtube.com/watch?v=9MFsymYmwLo

Precision microscope vibration

VIBRATIONS CAUSED BY TRAFFIC

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Vibrations problems

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Vibrations caused by traffic

28https://www.youtube.com/watch?v=ZAa6ehyIZ94

Vibrations caused by traffic

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Vibrations problems

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29https://www.youtube.com/watch?v=ioSyeKusvE8

Vibrations caused by traffic

30https://www.youtube.com/watch?v=ioSyeKusvE8

Vibrations caused by traffic

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Vibrations problems

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VORTEX INDUCED VIBRATIONS

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Vortex Induced Vibrations

Resonance

Critical wind speed

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Vibrations problems

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Vortex Induced Vibrations

https://www.youtube.com/watch?v=8OExYy28moc

https://www.youtube.com/watch?v=-JA6EfdDeckhttps://www.youtube.com/watch?v=YbZE_dgAqkc

34https://www.youtube.com/watch?v=rlpUhgfEZPU

Vortex Induced Vibrations

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Vibrations problems

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Vortex Induced Vibrations

https://www.youtube.com/watch?v=oYegGVgvDb4

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https://www.youtube.com/watch?v=qROefSbKcms

Vortex Induced Vibrations

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Vibrations problems

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https://www.youtube.com/watch?v=J21uZjFVPak

Vortex Induced Vibrations

GALOPPING AND DIVERGENCE

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Vibrations problems

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Variable damping Variable stiffness

Galopping (oscillatory) Divergence (static)

Galopping and divergence

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Galopping

https://www.youtube.com/watch?v=GEGbYRii1d4

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Vibrations problems

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Divergence

[From Vincent Denoël, ULiège]

FLUTTER

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Vibrations problems

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Single mode flutter

44Can be negative and lead to zero damping at critical speed

Single mode flutter

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Vibrations problems

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Can be negative and lead to zero damping at critical speed

Single mode flutter

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Stability for MDOF systems

• Single mode flutter (galopping)• Coupled mode flutter

Frequency matching of twomodes

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Vibrations problems

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47https://www.youtube.com/watch?v=XggxeuFDaDU

Flutter in Tacoma Narrows bridge

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Aeroelastic flutter in aircrafts

https://www.youtube.com/watch?v=pEOmCkZyXzk

Aeroelastic flutter in aircrafts

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Vibrations problems

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VIV vs instabilities

VIV

• Resonance• Amplitude limited by damping

Galopping, flutter

• Instability of a pole• Unlimited amplitude (zero damping)

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Summary

ExcitationFreqTime

ModelM,C,KModal properties

ResponseFreqTime

Acceptable ?Yes

NoNew designRemedial measures

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