Wind Induced Vibration of Cable Stay Bridges Workshop, April 25-27, 2006

Review of Bridge Cable Vibrations in Japan

The practical Cases of Aerodynamic Vibration of Stayed Cables

Masaru MATSUMOTOKyoto UniversityKyoto, JAPAN

Recent experiencesRecent experiencesfor cable vibrationsfor cable vibrations

Cable Aerodynamic Vibration

In various countries, it has been observed. Probably, all countries where cable stayed bridges have been constructed, might have those experiences.

Belgium, China, Denmark, France, German, Holland, Japan, Nepal, USA and others

Practical wind-induced cable vibration of cable-stayed bridges

Karman vortex excitation

Wake galloping

Rain-wind induced vibration

Dry-state galloping

Rain-Wind Induced Vibrations

Rain-wind induced vibration

Rainy and windy day

Wind velocity 5m/s – 15m/s (mostly)

PE-lapped cables

Low turbulent wind

Aerodynamic Behavior of Inclined Cables of Cable Stayed Bridges

Aratsu Bridge

Aerodynamic Behavior of Inclined Cables of Cable Stayed Bridges

Tenpozan Bridge

Aerodynamic Behavior of Inclined Cables of Cable Stayed Bridges

Erasmus Bridge

RainRain--Wind Induced VibrationWind Induced Vibration

D

L

α

D≈140mmL≈150mα ≈40º strong wind with rain caused by typhoon

Vibration characteristics of rain-wind induced Vibration

Velocity-restricted response, mostly

Like galloping vibration(?)

Beat phenomena, mostly

but in some cases sinusoidal vibration with single mode

Observed Wind-Induced Cable Vibration

Characteristics of the windCharacteristics of the wind--induced vibration based on induced vibration based on

the field observationthe field observation

V-A diagram of prototype cable-responses

V-A diagram of stay cables of Fred-Hartman bridge by J.A.Main, N.P.jones

Observed Wind-induced Cable Vibration�T Brdg)

Meiko-Nishi Bridge

Wavelet Analysis of Meiko-West Bridge

Characteristics of Inclined Cable AerodynamicsBased on the Observed Data at Prototype Cables

Beat PhenomenaBeat Phenomena(4th and 5th mode)

V/fD=19.9

RainRain--Wind Induced VibrationWind Induced Vibration

D

L

α

D≈140mmL≈150mα ≈40º strong wind with rain caused by typhoon

Formation of upper water rivulet

Wind velocity

Wind direction to bridge axis

Vertical angle of cable

Cable surface material (PE)

Rivulet Position on Cable Surface

Extremely sensitive on the cable aerodynamics, if water rivulet locates at particular position. (basing upon the wind tunnel tests)

Wind tunnel tests

Top view of wind tunnel

Wind

Wind tunnel walls

β

α =0º

wind tunnel testswind tunnel tests((αα=0=0°°, , ββ=45=45°°) )

Artificial rivulet (WR)

wind

Cable diam.:50mm

Artificial rivulet

cable length:1100mm

Width:3.6mm�����thickness:1.6mm

The detail stationary lift and dragThe detail stationary lift and dragforce coefficient subject to rivulet position force coefficient subject to rivulet position

(WR)(WR)

-0.3-0.2-0.1

00.10.20.30.40.5

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180upper rivulet position [deg.] (θ )

C L

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.] (θ )

CD

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.] (θ )

C L0

0.10.20.30.40.50.60.70.8

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.] (θ )C

D

for nonfor non--yawed yawed circular cylindercircular cylinder((ββ=0=0°°))

for yawed for yawed circular cylindercircular cylinder((ββ=45=45°°))

Rivulet position effect on unsteady lift force and Strouhal number induced by Karman vortex

shedding (WR)

0

0.050.1

0.150.2

0.25

0.30.35

0.4

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.] (θ )

L f (L

ift fo

rce

ampl

itude

) [N

]

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.] (θ )

L f (L

ift fo

rce

ampl

itude

) [N

]

for nonfor non--yawed yawed circular cylindercircular cylinder((ββ=0=0°°))

for yawed for yawed circular cylindercircular cylinder((ββ=45=45°°))

0.1

0.12

0.14

0.16

0.18

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180upper rivulet position [deg.]

S t0.15

0.17

0.19

0.21

0.23

0.25

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

upper rivulet position [deg.]

S t

Movement of water rivulet during cable vibration(MHI)

Significantly complicated behavior and non-uniformly distribution along cable axis

Absolute condition of rivulet movement for vibration ?

Observed water rivulet movement on prototype Observed water rivulet movement on prototype scale cable model during rainscale cable model during rain--wind induced wind induced

vibrationvibration (MHI)(MHI)

V=10m/s

Observed water rivulet movement on prototype scale cable model during rain-wind induced vibration (MHI)

Characteristics of vibration and rivulet motion (Cosenteno et al) (MR)

Time history of rivulet position and cable motion

rivulet positioncable motion

The time history of cable vibration and rivulet movement (MR)

0 5 10 15 20Time [s]

Cab

le m

otio

n

0 5 10 15 20Time [s]

Riv

ulet

mot

ion

0 5 10 15 20Time [s]

Cab

le m

otio

n

0 5 10 15 20Time [s]

Riv

ulet

mot

ion

(large cable amplitude)(large cable amplitude) (small cable amplitude)

Rivulet movement

Rivulet movement behaves non-uniformlyand non-stationary along cable axis even

stationary cross-flow vibration.

Experimental set up (three end conditions)Experimental set up (three end conditions)(without rivulet) (yawing angle=45deg) (without rivulet) (yawing angle=45deg)

(AX)(AX)

three end conditions1.without wall2.without wall and with end plates3.with walls installed windows (φ=170mm)

wind tunnel(without wall)

wind

walls and windows

Time history and the wavelet analysis of the unsteady Time history and the wavelet analysis of the unsteady crosscross--flow displacement (flow displacement (unsteady gallopingunsteady galloping))

0 10 20 30 40 50-0.01

-0.005

0

0.005

0.01

Time [sec]

Dis

plac

emen

t [m

]

18 18.2 18.4 18.6 18.8 19-4

-2

0

2

4 x 10-3

Time [sec]

Dis

plac

emen

t [m

]

40 40.2 40.4 40.6 40.8 41-4

-2

0

2

4 x 10-3

Time [sec]

Dis

plac

emen

t [m

]

free cablefree cable--end condition (without end condition (without wall, without endwall, without end--plates)plates)

((VV=5.0m/s, =5.0m/s, ff00=2.87Hz, =2.87Hz, ffkk=8.6Hz)=8.6Hz)0 10 20 30 40 50-0.01

-0.005

0

0.005

0.01

Time [s]

Dis

plac

emen

t [m

]

The Role of Karman Vortex

Mitigation of Karman Vortex ��������������▼

▼

Galloping

Dry-State Galloping

Dry-state galloping

Sever vibration without rainAxial FlowCritical Reynolds number

Visualized axial flow by light strings for a proto-type cable

(AX)

wind

Visualized Flow Field around an Visualized Flow Field around an Inclined Cable Inclined Cable (AX)(AX)

Visualized axial flow by flags in a wake

of yawed cable (β=45°, V=1m/s)

Visualized intermittently Karman vortices

and axial vortices by fluid paraffinof yawed cable (β=45°, V=1m/s)

Axial flow velocity -approaching wind velocity diagram of a proto-type stay-cable

(AX)

((ββ*=40*=40°° --5050°°, where , where ββ*: equivalent yawing angle)*: equivalent yawing angle)

0 2 4 6 80

2

4

6

8

Mean wind velocity [m/s]

Va

[m/s

]

Axial flow velocityAxial flow velocity (Va) in a wake (Va) in a wake (AX)(AX)

0 4 8 12 16 20 240

0.2

0.4

0.6

0.8

1

1.2

X/ D

Va/V Wind

X

Y

Hot wire

(1) without wall (2) without wall and with end plates

(3) with walls installedwindows (φ=170mm)

((VV=8m/s, =8m/s, ββ=45=45°°))

Critical Reynolds Number

Re=UD/ν

ν�1.5x10-5

D=0.15m

if Recr=(3-5)x105, then U=30m/s-50m/s.

Reynolds number effectsReynolds number effects on circular on circular cylinder aerodynamics (cylinder aerodynamics (ScheweSchewe) ) (RE)(RE)

(a) r.m.s. of the lift fluctuations

(b) Strouhal number of the lift fluctuatioSr=fD/u∞

(c) drag coefficient

Reynolds number effectsReynolds number effects on inclined cable on inclined cable aerodynamics (NRCC) aerodynamics (NRCC) (RE)(RE)

lift force coefficientdrag force coefficient

Cable Model with Surface Roughness(β=45°) (Styrene Foam)

Cable Model with Surface Roughness (β=0°)

Static forces�with surface roughness�(RE)

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

Reynolds Number (*105)

Stea

dy w

ind

forc

e co

effic

ient

CD

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 2-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Reynolds Number (*105)

Stea

dy w

ind

forc

e co

effic

ient

CL

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

Reynolds Number (*105)

Fluc

tuat

ing

win

d fo

rce

coef

ficie

nt CL

′

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

Reynolds Number (*105)

Fluc

tuat

ing

win

d fo

rce

coef

ficie

nt CL

′

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

Reynolds Number (*105)

Stea

dy w

ind

forc

e co

effic

ient

CD

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 2-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Reynolds Number (*105)

Stea

dy w

ind

forc

e co

effic

ient

CL

Wind Velocity (m/s)0 3 6 9 12 15 18

β=0˚

CL CD CL’Decrease of drag

stationary liftDecay of Karman vortex intensity

Critical Re. number range

Increase of dragNon-app. of stationary lift

β=45˚

Super critical Re. number range

Flow field�with surface roughness�β=0 �̊(RE)

0 0.5 1 1.5 2-50-40-30-20-10

01020304050

Reynolds Number (*105)

Diff

eren

ce o

f win

d ve

loci

ty (%

)

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 2-50-40-30-20-10

01020304050

Reynolds Number (*105)

Diff

eren

ce o

f win

d ve

loci

ty (%

)

Wind Velocity (m/s)0 3 6 9 12 15 18

0 0.5 1 1.5 2-50-40-30-20-10

01020304050

Reynolds Number (*105)

Diff

eren

ce o

f win

d ve

loci

ty (%

)

Wind Velocity (m/s)0 3 6 9 12 15 18

wind

(a)(�) (�)

0 0.5 1 1.5 2-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Reynolds Number (*105)

Stea

dy w

ind

forc

e co

effic

ient

CL

Wind Velocity (m/s)0 3 6 9 12 15 18

(a)

(c)

(b�

Velocity difference at critical Re number range where Karman vortex is suppressed

Non-symmetry flow field

Appearance of Stationary lift

At critical Re. number range (RE) Decrease of drag

Velocity-difference btw up and down sides

Stationary lift

wind

Relative angle of attack due to vib.

Amplified velocity at down side

exciting force

The Role of Karman Vortex

Mitigation of Karman Vortex ��������������▼

▼

Galloping

Higashi-Kobe Bridge (l=485m)Galloping at Recr?

The Aerodynamic Countermeasures for Cable

Vibration Control

Axial protuberances(Higashi Kobe Bridge)

Dimples(Tatara Bridge)

A cableA cable--stayed bridge stayed bridge with curved girderwith curved girder

Reference Inclined CableLength

approximately 200mCable Surface material

lapped by PEVibration Frequency

1.0 Hz (2nd mode) ?

Climate ConditionWind velocity

18-19m/s (mean wind velocity)Wind direction to cable

about 20-45degree ?Rain

stopped during sever vibration

Violent cable vibration (Violent cable vibration (DryDry--State GallopingState Galloping? without rain)? without rain)

(Typhoon, 2004)(Typhoon, 2004)

without rain (courtesy of Mr. H. Yoshikawa)

Scruton Scruton NumberNumber effect on effect on drydry--state gallopingstate gallopingon inclined cables (Saito et al)on inclined cables (Saito et al)

ββ; horizontal yaw angle; horizontal yaw angleθθ; vertical angle; vertical angleφφ; cable wind relative angle; cable wind relative angle

Dry-state Galloping

Less sensitive to ScrutonNumber ?

St=2mδ/(ρD2)

DamperDamper--damages due to cable damages due to cable vibrationvibration

Damage due to cable vibration

Damping device

Spacer as vibration control

Cable surface and cable wire(?)

In particular case, bridge girder

The rubber damping device

cable

cable socket

rubber damper device

Damages of Cable and damper

Rubber cover prevented to detect the inside details

Damper-damages due tocable vibration

CableCable--damages due to cable damages due to cable vibrationvibration

Periodical Inspection of Damping Devices

The damping devices of stay cables should be periodically inspected, in particular immediately after sever storm or sever gale.

Vibration ControlStructural countermeasures

Aerodynamic countermeasures

The Structural Countermeasures for Cable Vibration Control

The Structural Countermeasures for Cable Vibration Control

The Structural and Aerodynamic Countermeasures for Cable

Vibration Control

Cable-vibration control devices of Normandy Bridge

The Aerodynamic Countermeasures for Cable

Vibration Control

Axial protuberances(Higashi Kobe Bridge)

Dimples(Tatara Bridge)

Large-scale Cable Model in the Field

A large-scale cable model in natural wind

A rigid cable model in wind tunnel

A prototype cable in natural wind

Field Testlocation of observation

Shionomisaki

KyotoTokyo The Shionomisaki Wind Effect

Laboratory of the Disaster Prevention Research Institute,

Kyoto University

Field Testlarge-scale cable model

Tower23.5m

Cable setup

WW

NN

SS

EE

Accelerometer

30m lengthcable model

45°

Typhoon Pabuk (T0111) August 21, 2001 12:21~12:41

Mean Wind Velocity13.2m/s (20 min.)13.2m/s (20 min.)

Mean Wind Direction126 deg. (ESE126 deg. (ESE--SE)SE)

Maximum Wind Speed35.3m/s35.3m/s

Rainfall37mm/h37mm/h

N

S

EWWind direction

Tower side Ground side

Power Spectrum of Acceleration & Displacement of First mode

0 5 10 15 200

1

2

3

4

Frequency [Hz]

P.S.

D. [

(m/s

2 )2 /Hz]

0 5 10 15 200

1

2

3

4

Frequency [Hz]

P.S.

D. [

(m/s

2 )2 /Hz]

0 200 400 600 800 1000 1200- 1

- 0.8- 0.6- 0.4- 0.2

00.20.40.60.8

1

Time [sec.]

Disp

lace

men

t [m

]

0 200 400 600 800 1000 1200- 1

- 0.8- 0.6- 0.4- 0.2

00.20.40.60.8

1

Time [sec.]

Disp

lace

men

t [m

]

Out Plane Acceleration In Plane Acceleration

In Plane Amplitude of First ModeOut Plane Amplitude of First Mode

First ModeV/fD≅120

1.36m

680 681 682 683 684 685 686 687 688 689 690- 1

- 0.8- 0.6- 0.4- 0.2

00.20.40.60.8

1O

ut-p

lane

dis

plac

emen

t [m

]

Time [sec]

600 650 700 750 8000

10

20

30

Time [sec]

Win

d ve

loci

ty [m

/s]

600 650 700 750 8000

30

60

90

Inte

nsity

[%]

Wind velocity and intensity

Wind velocity

Intensity

Max responseMax response

SummaryStay-cables can be easily excited by the cooperation of wind and rain or only wind, if certain conditions would be satisfied.

Periodical inspection of damping devices are definitely required.

Thank you very much for your kind attention.

Higashi Kobe Bridge (l=485m)

Cable vibration at high wind velocity(Galloping caused by Recr?)