delong zuo and nicholas p. jones johns hopkins … wind induced vibrations of cable stay bridges...
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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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Motivation
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Outline
Full-scale measurementFull-scale measurement systemCharacterization and categorization of observed stay cable vibrations
Wind tunnel testing of sectional models
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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.)
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Oops…Or…Ouch!
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
)
Lateral Displacement (cm)
Mode 2
-50 -25 0 25 50-50
-25
0
25
50
In-p
lane
Dis
plac
emen
t (cm
)
Lateral Displacement (cm)
Mode 3
-50 -25 0 25 50-50
-25
0
25
50
In-p
lane
Dis
plac
emen
t (cm
)
Lateral Displacement (cm)
Reconstructed
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Observed Types of Vibrations
(Kármán-) Vortex-induced vibration (VIV)Rain-wind induced vibration (RWIV)Large-amplitude dry cable vibrationDeck-induced vibrationVibrations not categorized
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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)
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Significant Modes and Wind Profile
Cable Modes
Wind Profile
UDeck
UTower≈ 1.35 UDeck
sSUND
=
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
(°)
Mode 5Mode 6Mode 7Mode 8Mode 9Mode 101 D
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 =
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Vortex-Induced Vibration: Dependence on Wind (2)
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
(°)
Mode 5Mode 6Mode 7Mode 8Mode 9Mode 101 D
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
(°)
Mode 5Mode 6Mode 7Mode 8Mode 9Mode 101 D
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Vortex-Induced Vibration: Dependence on Wind (3)
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
(°)
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
RWIV: Dependence on Wind (1)
0
30
60
90
120
150
180
0 20 40 60 80
Reduced velocity, V r
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 (°
)
Mode 2Mode 3Mode 4Mode 5Mode 61 D
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
RWIV: Dependence on Wind (2)
-60
-30
0
30
60
0 30 60 90 120 150 180
Yaw angle, β (°)
Maj
or a
xis a
ngle
, ϕ (°
)
Mode 2Mode 3Mode 4Mode 5Mode 61 D
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
(°)
Mode 2Mode 3Mode 4Mode 5Mode 61 D
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
RWIV: Dependence on Wind (3)
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
Reduced velocity, V r
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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 (°
)
Mode 2Mode 3Mode 41D
Stay AS24: L=197.8 m; α=21.11°; D=0.194 m; f1=0.57 Hz
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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 (
°)
Mode 2Mode 3Mode 41D
ϕ*
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
Wind Tunnel Tests: Example Setup
Length: 1.12 mDiameter: 0.091mMass:2.32 kgIncl. Angle: 16°Yaw Angle: 56.6°Damping Ratio: 0.35%
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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)
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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
2006 Wind Induced Vibrations of Cable Stay Bridges Workshop, St. Louis, MO, April 26, 2006
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