WIND-INDUCED VIBRATION AND CONTROL OF CABLE-STAYED BRIDGES

KAMAL KRISHNA BERA

Under the guidance of

Prof. Naresh K. Chandiramani

DEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY BOMBAY

Main Components:

Bridge Deck

Stay cables

Towers or pylons

CABLE-STAYED BRIDGE

Advantages: stiffness > suspension bridge cables temporary and permanent supports to bridge deck symmetrical bridge large ground anchorages not required.

MODELLING

Deck

•Spine (Central) Beam Model

• Multi-scale modeling components of interest: shell elements or solid elements

other components: line elements

Cable•Truss Element

][][][ get KKK

000000

000000

001001

000000

000000

001001

][c

eqe L

AEK

3

2

12

)(1

T

AEwL

EEeq

Equivalent Modulus of Elasticity

Elastic linear stiffness matrix Geometric stiffness matrix

100100

010010

000000

100100

010010

000000

][c

g L

TK

AEROSTATIC INSTABILITY

• Wind speed components

),,,()( tzyxuzU

),,,( tzyxv

),,,( tzyxw

Longitudinal direction:

Lateral direction:

Vertical direction:

• Mean wind load

)(2

1)( 2 DD BCUF

)(2

1)( 2 LL BCUF

)(2

1)( 2 MBCUM

• Torsional Divergence

)(2

1 22 MCBUK

)0()0()( MMM CCC

)0(2

1)0(

2

1 2222MM CBUCBUK

)0(

22

Mcr CB

KU

AERODYNAMIC INSTABILITY

I. Vortex Induced Vibration

Lock in Phenomenon

)2sin(2

1 2 tfDCU sL D

USf tst

Vortex shedding frequency

tS Strouhal number

)sin(2

1)2( 22 tDCUyyym sLnn

222

2

max 164 tc

L

n

L

SS

DC

m

UDCy

2D

mSc

Scruton number

U

II. Galloping Instability

Instability by Negative Aerodynamic Damping in cross wind direction

At very low reduced frequency

o across-wind oscillation of structure

o modifies effective angle of attack

o change in aerodynamic forces

U

yC

d

dCBUF D

L

excitedselfy

0

2

2

1)(

U

yC

d

dCBUkyycym D

L

0

2

2

1

02

1

0

kyyCd

dCUBcym D

L

UB

cC

d

dCD

L

2

0

Instability Criterion

III. FLUTTER

Coupled Vertical and Torsional vibration

Both under Laminar and Turbulent Wind flow

o Wind-structure interaction

o Self-excited Aerodynamic Forces

o Instability at Critical Wind Speed

Failure of Original Tacoma Narrows Bridge (1940)

B

hHKHK

U

BKH

U

hKHBULse 4

23

221

2

2

1

B

hAKAK

U

BKA

U

hKABUM se 4

23

221

22

2

1

Scanlan and Tomko (1971)

)(2)](1[)(2 2 kCUUbkChkUChbbLse

)()](2

1[

8)( 2

22 kCUUbkC

bhkUCbM se

Theodorsen (1934)

FrequencyReduced2 U

BkK

)()()( kiGkFkC

2-D Flutter Analysis

Eigen value of matrix A 21 iiiii j ,hi

0iCritical State Corresponding wind speed

Flutter Speed

IV. BUFFETING

Vertical, Lateral and Torsional motion

under wide ranges of wind speed

increases monotonically with increasing wind speed

Mean Wind Speed Fluctuating Wind Speed (turbulence)

Static Wind Force Dynamic Wind Force

Random Vibration of bridge

Buffeting Forces

BCtUtL L )()(2

1)( 0

2

U

tuUtwtuUtU

)(21)()()( 2222

U

tw

U

tu

U

tw

tuU

tw )()(1

)(

)(

)(1

Lift force in transient wind axis

)sin()()cos()()( tDtLtL

)()(

)(2

1)()()(

)(2)(

2

1)(

0

02

0002

staticb

LDLL

LtL

BCUU

twCC

U

tuCBUtL

Lift force in mean wind axis

)()()( 000 DDD CCC

WIND INDUCED VIBRATION CONTROL

I. Modification of structural parameters

mass, damping and stiffness

II. Aerodynamic measures

Wedge-shaped fairings , Actively controlled surfaces , “deck-flap”

system

III. Mechanical measures

Passive, Active, Semi-active and Hybrid Control systems

Active Control System

Korlin and Starossek (2004)

o Rotational Mass Damper (RMD)

o Movable Eccentric Mass Damper (MEMD)

Effectively Control Flutter

• Requires High Energy Input • lower energy consumption,• movement cause undesirable

horizontal movement of bridge

Semi-active Control System

Pourzeynali and Datta (2005)

o Semi-active Tuned Mass Damper (STMD)

CaseWind Speed

(m/s)Max. Torsional

amp. (rad.)

Uncontrolled 55.52 (flutter, sustained

oscillation)0.02

Controlled with tuned mass damper (20% damping) 98 (flutter, sustained oscillation) 0.02

Controlled with semi-active tuned mass damper (max. damping 21.6%)

110 (decaying oscillation) 0.0063

More Literature Study

Finite Element Modelling

Flutter Analysis

……………………. …………………………..

Cable-bridge deck vibration interaction

Control with Active Tuned Mass Damper (ATMD), Active

Tendon Systems

Non-linear Flutter / Buffeting

FUTURE WORKS

THANK YOU

Vortex-Induced Vibration Galloping Instability Flutter Buffeting

Occurs at low wind speed and low turbulence condition.

Occur at much lower frequency than vortex shedding.

Usually occur at very high wind speed.

Occur over a wide range of wind speed.

Due to Lock-in, vortex shedding frequency natural frequency of bridge components.

Motion of structure in vertical direction causes change in angle of attack of original flow velocity.

Due to self-excited aerodynamic forces resulting from wind –structure interaction.

Due to velocity fluctuation in the incoming flow i.e. turbulence.

Resulting motion normal to flow, for bridge deck it is in the vertical direction.

Large amplitude vibration in normal to mean wind direction.

Flutter can be 1D (vertical or torsional), 2D (coupled vertical and torsional motion) or 3D (coupled vertical, torsional and lateral motion).

Random vibration.Motion can be any combination of lateral, torsional and vertical.

Simple harmonic force due to alternate vortex shedding as well as motion induced force.

Self-excited forces. Self-excited forces. Not self-excited.

Increase in damping reduces instability.

Increase in damping reduces instability.

Effect of increase in damping is very low.

Increase in damping reduces response.

KAMAL KRISHNA BERA

Under the guidance of

Prof. Naresh K. Chandiramani

DEPARTMENT OF CIVIL ENGINEERINGINDIAN INSTITUTE OF TECHNOLOGY BOMBAY

WIND-INDUCED VIBRATION AND CONTROL OF CABLE-STAYED BRIDGES