Wind Induced Vibration of Cable Stay Bridges Induced Vibration of Cable Stay Bridges Workshop, April 25-27, 2006 Review of Bridge Cable Vibrations in Japan The practical Cases of Aerodynamic

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  • 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

    D140mmL150m 40 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 VibrationT 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

    D140mmL150m 40 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

    =0

    wind tunnel testswind tunnel tests((=0=0, , =45=45) )

  • Artificial rivulet (WR)

    wind

    Cable diam.:50mm

    Artificial rivulet

    cable length:1100mm

    Width:3.6mmthickness: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.] ( )

    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.] ( )

    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.] ( )

    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.] ( )C

    D

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

    for yawed for yawed circular cylindercircular cylinder((=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.] ( )

    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.] ( )

    L f (L

    ift fo

    rce

    ampl

    itude

    ) [N

    ]

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

    for yawed for yawed circular cylindercircular cylinder((=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 (=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 (=45, V=1m/s)

    Visualized intermittently Karman vortices

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

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

    (AX)

    ((*=40*=40 --5050, where , where *: 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 (=170mm)

    ((VV=8m/s, =8m/s, =45=45))

  • Critical Reynolds Number

    Re=UD/

    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 forc