Aerodynami stability (Tài liệu nghiên cứu sự ổn định động lực học của các cây cầu )

Davenport Wind Engineering Group• Wind tunnel tests of bridge models The Section Models The Full Bridge Aeroelastic Models The Taut Strip Models EXPERIMENTS : BRIDGES The University of W

Aerodynamic Stability

of a Longspan Bridge

Jongdae Kim, Ph.D.

Alan G Davenport Wind Engineering Group

• BLWTL 2

The second generation wind tunnel at The University of Western Ontario was constructed

in 1984 It includes three test sections.

Length (m) Width (m) Height (m) Max Speed(km/hr)

High Speed Test Section 39 3.4 2.5 100

Low Speed Test Section 52 5 4 36

WIND ENGINEERING : Generals

The University of Western Ontario

Low Speed Test Section 52 5 4 36

WTC Testing at Colorado State University (1964)

1:500 Model of New York City with World Trade Center Towers

The Meteorological Wind Tunnel at CSU (1964)

• BLWTL (London, Ontario, Canada)

- The Boundary Layer Wind Tunnel Lab

• RWDI (Guelph, Ontario, Canada)

- Rowan Williams Davies and Irwin Inc.

• CPP (Fort Collins, Colorado, USA)

- Cermak, Peterka, Peterson

• BMTFM (Teddington, Middlesex, UK)

- British Maritime Technology, Fluid Mechanics

Big Wind Tunnels

The University of Western Ontario

• BLWTL (London, Ontario, Canada)

- The Boundary Layer Wind Tunnel Lab

• RWDI (Guelph, Ontario, Canada)

- Rowan Williams Davies and Irwin Inc.

• CPP (Fort Collins, Colorado, USA)

- Cermak, Peterka, Peterson

• BMTFM (Teddington, Middlesex, UK)

- British Maritime Technology, Fluid Mechanics

Alan G Davenport Wind Engineering Group

Alan G Davenport Wind Engineering Group

• Wind tunnel tests of bridge models

The Section Models

The Full Bridge Aeroelastic Models The Taut Strip Models

EXPERIMENTS : BRIDGES

The University of Western Ontario

• Wind tunnel tests of bridge models

The Section Models

The Full Bridge Aeroelastic Models The Taut Strip Models

Alan G Davenport Wind Engineering Group

Section Model Tests

The University of Western Ontario

Alan G Davenport Wind Engineering Group

The Full Bridge Aeroelastic Model Tests

The University of Western Ontario

Alan G Davenport Wind Engineering Group

The Taut Strip Model Tests

The University of Western Ontario

• Aerodynamic Stability

• Flutter Derivatives from Free Oscillation Test

• Flutter Derivatives from Forced Oscillation Test

• Flutter Derivatives from CFD Analysi

• Aerodynamic Stability

• Flutter Derivatives from Free Oscillation Test

• Flutter Derivatives from Forced Oscillation Test

• Flutter Derivatives from CFD Analysi

Aerodynamic Stability

The primary concerns for long-span bridges for wind effects

To design an optimized bridge deck configuration

satisfying the stability criteria for the design

wind speed, wind tunnel tests have

traditionally been carried out by changing deck configurations in an ad-hoc manner until the stability is assured After a decision has been reached regarding the optimized bridge deck configuration, detailed wind tunnel tests are

performed, which in some circumstances,

include estimates of the aerodynamic

derivatives for the aerodynamic stability

analysis and aerodynamic admittance functions for the serviceability analysis of the structure.

Aerodynamically Stable Bridge

To design an optimized bridge deck configuration

satisfying the stability criteria for the design

wind speed, wind tunnel tests have

traditionally been carried out by changing deck configurations in an ad-hoc manner until the stability is assured After a decision has been reached regarding the optimized bridge deck configuration, detailed wind tunnel tests are

performed, which in some circumstances,

include estimates of the aerodynamic

derivatives for the aerodynamic stability

analysis and aerodynamic admittance functions for the serviceability analysis of the structure.

Static Model Test (Fixed deck)

 Force coefficients (drag, lift, moment coeff)

Dynamic Model Test (Free moving deck)

vibration, flutter, etc)

Static & Dynamic Model Tests

Static Model Test (Fixed deck)

 Force coefficients (drag, lift, moment coeff)

Dynamic Model Test (Free moving deck)

vibration, flutter, etc)

Bridge Model (Plate Girder Bridge)

SIMILITUDE REQUIREMENT

VALUE

0.016666667

1

2.78E-04 4.63E-06 7.72E-08 1.29E-09

Mass Moment of Inertia per Unit Length

Mass Moment of Inertia

 = 

3 L

VALUE

0.016666667

1

2.78E-04 4.63E-06 7.72E-08 1.29E-09

Mass Moment of Inertia per Unit Length

Mass Moment of Inertia

 = 

2 L m

 =

2 L M

 =

V L

Bridge Model (Plate Girder Bridge)

MODEL

TYPICAL PROTOTYPE (at 1:60 Scale)

Static Model Test

-2-1012

-2-1012

Dynamic Model Test

DYNAMIC SECTION MODEL RIG

Details of Dynamic Section Model Rig

Dynamic Section Model – Smooth Flow Condition

Dynamic Section Model – Turbulent Flow Condition (Large Grid)

Dynamic Section Model – Turbulent Flow Condition (Small Grid)

00.020.040.060.080.1

a36202.mst

00.020.040.060.080.1

Dynamic Section Model Test Results – Vertical Response

a36302.mst

00.020.040.060.080.1

a36202.mst

00.020.040.060.080.1

Smooth Flow Small Grid Large Grid

-0.1-0.08-0.06-0.04-0.020

Dynamic Section Model Test Results – Torsional Response

Smooth Flow Small Grid Large Grid

a36202.mst

-0.1-0.08-0.06-0.04-0.020

Flutter Instability Criteria (How to know the onset of flutter)

1 Random (Peak factor=3~4)

 Sinusoidal (Peak factor=1.41)

2 Response greater than an acceptable magnitude

3 Steepness change of response curve5.

Flutter Derivatives from

Free Oscillation Test

Sign Convention

WIND

DISPLACED MODEL

MODEL AT REST WIND

DISPLACED MODEL

MODEL AT REST

SKETCH SHOWING THE SIGN CONVENTION OF DISPLACEMENTS IN THE AERODYNAMIC DERIVATIVE TEST

Governing Equations of the Deck Motion

* 5

* 4 2

* 3 2

* 2

* 1

B U

2

6 2

* 5

* 4 2

* 3 2

* 2

* 1 2

B U

2

6 2

* 5

* 4 2

* 3 2

* 2

* 1

Flutter Derivatives from Free Oscillation Test

AX

X =

dt d

/ /

/

/ 2

/ /

/

1 0

0 0

0 1

0 0

* 2 2

* 1 2 2

* 3

2 2

* 4

2 2

* 2 1

* 1 1

* 3

2 1 2

* 4

2 1

Um B

KA C Um

KA C m

A K C Bm

A K C

Um B

KH C Um

KH C m

H K C Bm

H K

/ /

/

/ 2

/ /

/

1 0

0 0

0 1

0 0

* 2 2

* 1 2 2

* 3

2 2

* 4

2 2

* 2 1

* 1 1

* 3

2 1 2

* 4

2 1

Um B

KA C Um

KA C m

A K C Bm

A K C

Um B

KH C Um

KH C m

H K C Bm

H K

A

B U

Flutter Derivatives from Free Oscillation Test

PEM (Predictor-Error Minimization Method)

1 Section model mounted on soft springs

- permitting the vertical and torsional motions

2 Ballast the sprung model with additional mass

- to represent the dynamically scaled mass and mass moment

of inertia, as well as the corresponding frequency ratio.

3 25~30 two-degree-of-freedom initial displacements

to the model at each wind speed.

- A pneumatic “displace and release” system is used

to provide consistent initial lift and torsional displacements.

4 Record the response after release from the initial

5 Aerodynamic Derivatives

- Parameter Estimation Method

Procedure

1 Section model mounted on soft springs

- permitting the vertical and torsional motions

2 Ballast the sprung model with additional mass

- to represent the dynamically scaled mass and mass moment

of inertia, as well as the corresponding frequency ratio.

3 25~30 two-degree-of-freedom initial displacements

to the model at each wind speed.

- A pneumatic “displace and release” system is used

to provide consistent initial lift and torsional displacements.

4 Record the response after release from the initial

5 Aerodynamic Derivatives

- Parameter Estimation Method

Free Oscillation Test

Setup

Pneumatic Cylinder Retracted

Pneumatic Cylinder Extended

0 100 200 300 400 500 600 700 -0.02

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Vibration Tests: Time history

Free Oscillation Tests: Aerodynamic Derivatives

Aerodynamic Derivatives from Free Oscillation Tests

-202

Vrh=U/(B*fv)

A1*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A2*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A3*

NPT100NPT150NPT200

-101

Vrh=U/(B*fv)

A4*

NPT100NPT150NPT200

Aerodynamic Derivatives from Free Oscillation Tests

-202

Vrh=U/(B*fv)

A1*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A2*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A3*

NPT100NPT150NPT200

-101

Vrh=U/(B*fv)

A4*

NPT100NPT150NPT200

Free Oscillation Tests: Aerodynamic Derivatives

Aerodynamic Derivatives from Free Oscillation Tests

-202

Vrh=U/(B*fv)

A1*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A2*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A3*

NPT100NPT150NPT200

-101

Vrh=U/(B*fv)

A4*

NPT100NPT150NPT200

Aerodynamic Derivatives from Free Oscillation Tests

-202

Vrh=U/(B*fv)

A1*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A2*

NPT100NPT150NPT200

-101

Vra=U/(B*fa)

A3*

NPT100NPT150NPT200

-101

Vrh=U/(B*fv)

A4*

NPT100NPT150NPT200

Flutter Derivatives from Forced Oscillation Test

1 Measure time histories of the input motion and individual surface

pressures on the model at each frequency of excitation and wind

speed

2 Edge displacement = +/- 0.01 m (model scale).

3 The length of the time history = at least 1000 cycles of input

motion in order to provide stable estimates of the derivatives.

4 Calculated vertical force and torsional moment from surface

pressure integration

5 Measure vertical and rotational displacement/acceleration

6 Low-pass filter (with 20Hz) the data to remove high frequency noise

7 Calculate the Aerodynamic Derivatives from the input and output

data correlations

Procedure

1 Measure time histories of the input motion and individual surface

pressures on the model at each frequency of excitation and wind

speed

2 Edge displacement = +/- 0.01 m (model scale).

3 The length of the time history = at least 1000 cycles of input

motion in order to provide stable estimates of the derivatives.

4 Calculated vertical force and torsional moment from surface

pressure integration

5 Measure vertical and rotational displacement/acceleration

6 Low-pass filter (with 20Hz) the data to remove high frequency noise

7 Calculate the Aerodynamic Derivatives from the input and output

data correlations

Flutter Derivatives from Forced Oscillation Test

For 2D bridge motion (Heaving & Rotating)

Lift Motion - Lift Pressures

Lift Motion -Torsional Pressures

Torsional Motion - Torsional Pressures

Torsional Motion -Lift Pressures

For 2D bridge motion (Heaving & Rotating)

Lift Motion - Lift Pressures

Lift Motion -Torsional Pressures

Torsional Motion - Torsional Pressures

Torsional Motion -Lift Pressures

Flutter Derivatives from Forced Oscillation Test

Lift Motion - Lift Pressures (Fix Rotation)

[ KH h U K H h B ]

B U

[ KH h ] U KH B U K H K H h B KH p U K H p B B

* 5

* 4 2

* 3 2

* 2

* 1

[ KH h U K H h B ]

B U

C B

U

L

2 1

* 4

2

* 1 2

+

=



Flutter Derivatives from Forced Oscillation Test

The relationship between the measured input vertical acceleration and velocity can be written using complex functions:

h dt

h h

Similarly, the relationship between the input acceleration and

the displacement can be written:

i

i h

i dt

h

i dt

h h

Flutter Derivatives from Forced Oscillation Test

The aerodynamic derivatives then can be expressed in terms of the imaginary and real components of the complex transfer function

between the input vertical acceleration and the output lift coefficient:

4

* 1

C K

C K

2

) (

2

*

Flutter Derivatives from Forced Oscillation Test

Lift Motion -Torsional Pressures

(Fix Rotation)

B U

2

6 2

* 5

* 4 2

* 3 2

* 2

* 1 2

M

2 1

* 4

2

* 1 2

Flutter Derivatives from Forced Oscillation Test

The aerodynamic derivatives then can be expressed in terms of the imaginary and real components of the complex transfer function

between the input vertical acceleration and the output moment

coefficient:

* 4

* 1 2

2

A

iA B

U h

* 1 2

2

A

iA B

U h

C K

C K

2

*

4 ( ) 

Flutter Derivatives from Forced Oscillation Test

Torsional Motion - Torsional Pressures

(Fix Heaving)

B U

2

6 2

* 5

* 4 2

* 3 2

* 2

* 1 2

2 2

/ 2

1

A K U

B KA B

2

* 2 2

2

/ 2

B U

2 2

/ 2

1

A K U

B KA B

U

Flutter Derivatives from Forced Oscillation Test

The aerodynamic derivatives then can be expressed in terms of the imaginary and real components of the complex transfer function

between the input rotational acceleration and the output moment coefficient:

* 3

* 2 2

2

A

iA B

* 2 2

2

A

iA B

 

Flutter Derivatives from Forced Oscillation Test

Torsional Motion -Lift Pressures (Fix Heaving)

B U

2

6 2

* 5

* 4 2

* 3 2

* 2

* 1 2

2

/ 2

1

H K U

B KH B

2

/ 2

1

H K U

B KH B

2

* 2 2

/ 2

B U

L

Flutter Derivatives from Forced Oscillation Test

The aerodynamic derivatives then can be expressed in terms of the

imaginary and real components of the complex transfer function

between the input rotational acceleration and the output lift coefficient:

* 3

* 2 2

2

H

iH B

* 2 2

2

H

iH B

 

POWER SPECTRAL ANALYSIS OF INPUT MOTION AND OUTPUT FORCES – VERTICAL

EXCITATION TIME SERIES OF INPUT MOTION AND OUTPUT

FORCE COEFFICIENT – VERTICAL EXCITATION

TRANSFER FUNCTION ANALYSIS OF INPUT MOTION AND OUTPUT FORCES – VERTICAL

EXCITATION

COHERENCE FUNCTION ANALYSIS OF INPUT

MOTION AND OUTPUT FORCES – VERTICAL

EXCITATION

POWER SPECTRAL ANALYSIS OF INPUT MOTION AND OUTPUT FORCES – TORSIONAL

EXCITATION TIME SERIES OF INPUT MOTION AND OUTPUT

FORCE COEFFICIENT – TORSIONAL EXCITATION

TRANSFER FUNCTION ANALYSIS OF INPUT MOTION AND OUTPUT FORCES – TORSIONAL

EXCITATION

COHERENCE FUNCTION ANALYSIS OF INPUT

MOTION AND OUTPUT FORCES – TORSIONAL

EXCITATION

Forced Oscillation Tests: Aerodynamic Derivatives

Aerodynamic Derivatives from Displacement-Force Transfer Function: ring1, 2, 3

-101

V/(fh*B)A1*

-101

V/(fa*B)A2*

-101

V/(fa*B)A3*

-101

V/(fh*B)A4*

Aerodynamic Derivatives from Displacement-Force Transfer Function: ring1, 2, 3

-101

V/(fh*B)A1*

-101

V/(fa*B)A2*

-101

V/(fa*B)A3*

-101

V/(fh*B)A4*

Forced Oscillation Tests: Aerodynamic Derivatives

Aerodynamic Derivatives from Displacement-Force Transfer Function: ring1, 2, 3

-101

V/(fh*B)A1*

-101

V/(fa*B)A2*

-101

V/(fa*B)A3*

-101

V/(fh*B)A4*

Aerodynamic Derivatives from Displacement-Force Transfer Function: ring1, 2, 3

-101

V/(fh*B)A1*

-101

V/(fa*B)A2*

-101

V/(fa*B)A3*

-101

V/(fh*B)A4*

Flutter Derivatives

Vrh=U/(B*fv)

A1*

FreeForced

-101

Vra=U/(B*fa)

A2*

FreeForced

-101

Vra=U/(B*fa)

A3*

FreeForced

-101

Vrh=U/(B*fv)

A4*

FreeForced

-202

Vrh=U/(B*fv)

A1*

FreeForced

-101

Vra=U/(B*fa)

A2*

FreeForced

-101

Vra=U/(B*fa)

A3*

FreeForced

-101

Vrh=U/(B*fv)

A4*

FreeForced

-202

Flutter Derivatives from

CFD Simulations

- Forced Oscillation Test

- Fluid Structure Interaction (FSI)

- Forced Oscillation Test

- Fluid Structure Interaction (FSI)

Q&A

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