Delong Zuo and Nicholas P. Jones Johns Hopkins … Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006 Understanding the Mechanism of Rain-Wind-Induced

2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006

Understanding the Mechanism of Rain-Wind-Induced Vibrations in the Context of Dry Cable Vibrations Observed in the Field

and in the Wind Tunnel

Delong Zuoand

Nicholas P. Jones

Johns Hopkins University


Motivation


Outline

Full-scale measurementFull-scale measurement systemCharacterization and categorization of observed stay cable vibrations

Wind tunnel testing of sectional models


The Fred Hartman Bridge

Over the Houston ship channel in Houston, Texas384 m main span, 54 m clearanceTwin-deck, each 24 m wideDouble-diamond shaped towers 192 cables (59 m to 198 m long) in four inclined planes


Full-Scale Measurement System

South Tower North Tower

AS13-AS24 AS1-AS12 AN24-AN13 AN12-AN1

Major measurementStays

AccelerationDisplacementDamper force

DeckAcceleration

MeteorologicalWindRainfallBarometric Pressure

AnemometerBi-axial accelerometerUni-axial accelerometer


Data Acquisition SetupData Acquisition Setup

Monitoring:record summary statistics to disk every 10 minutesChange to Triggered mode when thresholds are exceeded

Triggered: stream data for all channels to disk at 40 Hz for 5 minutes (More than 64000 records recorded.)


Oops…Or…Ouch!


General Characteristics: Multi-Modal Participation

0 60 120 180 240 300-50

0

50

In-p

lane

dis

p. (c

m)

0 60 120 180 240 300-50

0

50

Lat

eral

dis

p. (c

m)

Time (s)

Time (s)

Freq

uenc

y (H

z)

Spectrogram of In-Plane Displacement

Mod

e nu

mbe

r

15

10

15

20

25

30

0 60 120 180 2400

5

10

15

20

Time (s)

Freq

uenc

y (H

z)Spectrogram of Lateral Displacement

Mod

e nu

mbe

r

15

10

15

20

25

30

0 60 120 180 2400

5

10

15

20


General Characteristics: Two-Dimensional Vibration

-50 -25 0 25 50-50

-25

0

25

50

In-p

lane

Dis

plac

emen

t (cm

)

Lateral Displacement (cm)

Original

-50 -25 0 25 50-50

-25

0

25

50

In-p

lane

Dis

plac

emen

t (cm

)


Mode 2

-50 -25 0 25 50-50

-25

0

25

50

In-p

lane

Dis

plac

emen

t (cm

)


Mode 3

-50 -25 0 25 50-50

-25

0

25

50

In-p

lane

Dis

plac

emen

t (cm

)


Reconstructed


Frequency Estimation: The Hilbert Transform

0 60 120 180 240 300-50

0

50

In-p

lane

dis

p. (c

m)

0 60 120 180 240 300-50

0

50

Lat

eral

dis

p. (c

m)

0 60 120 180 240 300-50

0

50

Am

plitu

de (c

m)

In-planeLateral

0 60 120 180 240 3001.21.221.241.261.281.3

Freq

uenc

y (H

z)

Time (s)

In-planeLateral


Z (Out-of-Plane)

X (In-Plane)

Spatial Coordinate System

α

α: Inclination AngleU

β =0° β =180°β

β: Yaw Angle

X (In-Plane)Z (Lateral)

β*

β*: Effective Attack Angle

B

C

A

O

ΟΑ: Major AmplitudeOB: Minor Amplitudeϕ: Major Axis Angle

Major AxisMinor Axis

φ

A

B


Observed Types of Vibrations

(Kármán-) Vortex-induced vibration (VIV)Rain-wind induced vibration (RWIV)Large-amplitude dry cable vibrationDeck-induced vibrationVibrations not categorized


Vortex-Induced Vibration: Example Record

Time (s)

Freq

uenc

y (H

z)

Spectrogram of In-Plane Displacement

Mod

e nu

mbe

r

1

5

10

15

20

25

0 60 120 180 2400

5

10

15

20

Time (s)

Freq

uenc

y (H

z)Spectrogram of Lateral Displacement

Mod

e nu

mbe

r

1

5

10

15

20

25

0 60 120 180 2400

5

10

15

20

0 60 120 180 240 300-2

0

2

In-p

lane

dis

p (c

m)

0 60 120 180 240 300-2

0

2

Lat

eral

dis

p (c

m)

Time (s)


Significant Modes and Wind Profile

Cable Modes

Wind Profile

UDeck

UTower≈ 1.35 UDeck

sSUND

=


Vortex-Induced Vibration: Dependence on Wind (1)

0

30

60

90

120

150

180

0 2 4 6 8 10

Wind speed, U (m/s)

Yaw

ang

le, β

(°)

Mode 5Mode 6Mode 7Mode 8Mode 9Mode 101 D

0

30

60

90

120

150

180

0 2.5 5 7.5 10

Reduced velocity, V r

Yaw

ang

le, β

(°)


α

U

β =0°ββ* AA

BB

CC

DD

Stay AS23: L=182.5 m; α=23.31°; D=0.194 m; f1=0.64 Hz

Reduced velocity:

for circular cylinder normal to flow

Diameter of circles represents amplitude of vibration

1D=Diameter of cable

1r

i

UVf D S

= =⋅

5rV =



Stay AS23: L=182.5 m; α=23.31°; D=0.194 m; f1=0.64 Hz

Reduced velocity normal to vertical cable plane:

Reduced velocity normal to cable axis in the π plane:

,n ri

U SinVf D

β⋅=

⋅

,**n r

i

U SinVf D

β⋅=

⋅

α

U

β =0°ββ* AA

BB

CC

DD

0

30

60

90

120

150

180

0 2.5 5 7.5 10

Reduced velocity normal to vertical cable plane, V n,r

Yaw

ang

le, β

(°)


0

30

60

90

120

150

180

0 2.5 5 7.5 10

Reduced velocity normal cable axis in π plane, V* n,r

Yaw

ang

le, β

(°)




Stay AS23: L=182.5 m; α=23.31°; D=0.194 m; f1=0.64 Hz

ϕ*: Angle between vertical cable plane and the plane perpendicular to the π plane

-45

-30

-15

0

15

30

45

0 30 60 90 120 150 180

Yaw angle, β (°)

Maj

or a

xis a

ngle

, ϕ (

°)

Mode 5Mode 6Mode 7Mode 8Mode 9Mode 101D

ϕ*

α

U

β =0°ββ* AA

BB

CC

DD


Rain-Wind-Induced Vibration: Previous Beliefs

Occurs only with (light to moderate) rainfallOccurs in relatively smooth windPreferred wind speed in the range of about 6-17 m/sStays declining in the direction of wind are more susceptible (i.e., 0°<β<90°). (Being debated)Large amplitude, up to several diameters of stayOccurs in the lower modes (1-3 Hz)Movement/position of water rivulets critical for the onset of vibration

Wind θ

βU


RWIV: Preferred Wind Speed and Direction

Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz

Stay AS16: L=87.3 m; α=45.92°; D=0.141 m; f1=1.24 Hz

Open circles=simultaneous occurrence of wind and rain

Solid red circles=Large amplitude vibrations with simultaneous occurrence of wind and rain

α

U

β =0°ββ* AA

BB

CC

DD

0

30

60

90

120

150

180

0 5 10 15 20

Wind speed, U (m/s)

Yaw

ang

le, β

(°)

R e (×105)0 0.5 1 1.5 2 2.5

0

30

60

90

120

150

180

0 5 10 15 20

Wind speed, U (m/s)Y

aw a

ngle

, β (°

)

0 0.5 1 1.5R e (×105)

AS24AS24 AS16AS16


RWIV: Effects of Turbulence and Rate of Rainfall

Stay AS16: L=87.3 m; α=45.92°; D=0.141 m; f1=1.24 Hz

Turbulence intensity is based on one-minute values

Open circles=simultaneous occurrence of wind and rain

Solid red circles=Large amplitude vibrations with simultaneous occurrence of wind and rain

0

30

60

90

120

150

180

0 2.5 5 7.5 10 12.5 15 17.5 20

Turbulence intensity, I u (%)

Yaw

ang

le, β

(°)

0

30

60

90

120

150

180

0 5 10 15 20 25 30 35 40

Rainfall rate, R r (cm/h)

Yaw

ang

le, β

(°)


RWIV: Dependence on Wind (1)

0

30

60

90

120

150

180

0 20 40 60 80


Yaw

ang

le, β

(°)

Mode 2Mode 3Mode 4Mode 5Mode 61 D

Super-harmonics

Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz

Reduced velocity:r

i

UVf D

=⋅

0

30

60

90

120

150

180

0 5 10 15 20

Wind Speed, U (m/s)

Atta

ck A

ngle

β (°

)


01

2 / 2 /

0 0

( ) ( ) ( cos sin )

2

( )sin ; ( )cos

j j j jj

j

j j j j

F t F t T b b t a t

j jT

a F t tdt b F t tdtπ ω π ω

ω ω

πω ω

ω ωω ωπ π

∞

=

= + = + +

= =

= =

∑

∫ ∫ α

U

β =0°ββ* AA

BB

CC

DD



-60

-30

0

30

60

0 30 60 90 120 150 180

Yaw angle, β (°)

Maj

or a

xis a

ngle

, ϕ (°

)


ϕ*

0

30

60

90

120

150

180

0 20 40 60 80

Reduced velocity normal to π plane, V* n,r

Yaw

ang

le, β

(°)


Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz

Reduced velocity normal to cable axis in the π plane:

ϕ*: Angle between vertical cable plane and the plane normal to the π plane

,**n r

i

U SinVf D

β⋅=

⋅

α

U

β =0°ββ* AA

BB

CC

DD



Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 HzStay AS23: L=182.5 m; α=23.31°; D=0.194 m; f1=0.64 HzStay AS22: L=168.4 m; α=24.13°; D=0.168 m; f1=0.69 HzStay AS5 : L=137.0 m; α=32.21°; D=0.168 m; f1=0.80 HzStay AS16: L=87.3 m; α=45.92°; D=0.141 m; f1=1.24 HzStay AS9 : L=87.0 m; α=48.95°; D=0.141 m; f1=1.24 Hz

0

30

60

90

120

150

180

0 20 40 60 80


Yaw

ang

le, β

(°)

AS24: Mode 2AS24: Mode 3AS24: Mode 5AS23: Mode 3AS22: Mode 3AS16: Mode 2AS9: Mode 2AS5: Mode 3

-60

-30

0

30

60

0 30 60 90 120 150 180

Yaw angle, β (°)

Maj

or a

xis a

ngle

, ϕ (

°)

AS24: Mode 2AS24: Mode 3AS24: Mode 5AS23: Mode 3AS22: Mode 3AS16: Mode 2AS9: Mode 2AS5: Mode 3


Dry-Cable Vibration: Dependence on Wind (1)

0

30

60

90

120

150

180

0 5 10 15 20

Wind speed, U (m/s)

Yaw

ang

le, β

(°)

Mode 2Mode 3Mode 41D

0.0 0.5 1.0 1.5 2.0 2.5

R e (×105)

0

30

60

90

120

150

180

0 20 40 60 80

Reduced velocity, V rY

aw a

ngle

, β (°

)


Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz


Dry-Cable Vibration: Dependence on Wind (2)

Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz

ϕ*: Angle between vertical cable plane and the plane normal to the π plane

-60

-30

0

30

60

0 30 60 90 120 150 180

Yaw angle, β (°)

Maj

or a

xis a

ngle

, ϕ (

°)


ϕ*


Summary of Field Observations

The so-called rain-wind-induced vibration can occur without rainfallFrequent large-amplitude vibration, regardless of rainfall, occurs at a high reduced velocity range over a broad range of wind directionLarge-amplitude vibration at high reduced velocity is likely a vortex-induced type, but not Kármán vortex-induced


Wind Tunnel Tests: Example Setup

Length: 1.12 mDiameter: 0.091mMass:2.32 kgIncl. Angle: 16°Yaw Angle: 56.6°Damping Ratio: 0.35%


Wind Tunnel Tests: Configurations and Results

0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50 60

V r

ARM

S/D

α=16º, β=56.6ºα=16º, β=123.4ºα=0º, β=90º

(a)

(b)

(c)

(a): Vr=6.2

(b): Vr=27.3

(c): Vr=49.5

0.353.61-3.809003

0.353.52-3.91123.4162

0.353.52-3.7656.6161ζ (%)f (Hz)β (°)α (°)Config. #

(d)


Record (a): Locked-in Kármán Vortex Shedding

0 20 40 60 80 100 120 140 160 180-2-1012

Dis

p (c

m)

Time (s)

0 5 10 15 20 25 30 35 40 45 500

10

20

30

PSD

-Dis

p

Frequency(Hz)

o 3.54Hz

0 5 10 15 20 25 30 35 40 45 500

0.05

PSD

-Pre

ssur

e

Frequency(Hz)

o 3.54Hz

Configure # 1: α=16°; β=56.6°; U=2.1 m/s; Vr=6.2 Record Index


Record (b): Vortex shedding not locked-in

Configure # 1: α=16°; β=56.6°; U=9.1 m/s; Vr=27.3

0 20 40 60 80 100 120 140 160 180-2-1012

Dis

p. (c

m)

Time (s)

Record Index

0 5 10 15 20 25 30 35 40 45 500

0.05

0.1

PSD

-Pre

ssur

e

Frequency(Hz)

o 19.43 Hz

0 5 10 15 20 25 30 35 40 45 500

0.02

0.04

PSD

-Dis

p

Frequency(Hz)

o 3.64 Hz


Record (c): Large Amplitude at High Reduced Velocity

Configure # 1: α=16°; β=56.6°; U=16.9 m/s; Vr=49.5; Re=51.03 10×

0 20 40 60 80 100 120 140 160 180-2-1012

Dis

p (c

m)

Time (s)

0 5 10 15 20 25 30 35 40 45 500

2

4

PSD

-Dis

p

Frequency(Hz)

o 3.78 Hz

0 5 10 15 20 25 30 35 40 45 500

2

4

PSD

-Pre

ssur

e

Frequency(Hz)

o 3.78 Hz

Record Index


Record (d): Transition between Two Mechanisms

0 5 10 15 20 25 30 35 40 45 500

0.05

PSD

-Pre

ssur

e

Frequency(Hz)

o 24.15 Hzo 3.66 Hz

0 20 40 60 80 100 120 140 160 180-2-1012

Dis

p. (c

m)

Time (s)

0 5 10 15 20 25 30 35 40 45 500

0.05

PSD

-Dis

p.

Frequency(Hz)

o 3.69 Hz

Record IndexConfigure # 1: α=16°; β=56.6°; U=11.0 m/s; Vr=32.9


Summary of Wind Tunnel Test Results

Yawed and inclined circular cylinders are susceptible to wind excitation over a range of high reduced velocityThe wind excitation mechanism at high reduced velocity is likely related a type of three-dimensional vortex sheddingSpatial orientation of stay cables is important for aeroelastic stability


Acknowledgement

TXDOTFHWANSFJack Spangler, senior mechanical technician, JHUFormer students in Professor Nick Jones’s research group at JHU

Documents

Delong Zuo and Nicholas P. Jones Johns Hopkins … Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006 Understanding the Mechanism of Rain-Wind-Induced