computational structural engineering institute autumn conference 2002 oct. 18 - 19, 2002 vibration...

Computational Structural Engineering InstituteAutumn Conference 2002Oct. 18 - 19, 2002

VIBRATION CONTROL OF BRIDGE FOR SERVICEABILITY

Jun-Sik Ha1), Ji-Seong Jo2), Sun-Kyu Park3), In-Won Lee4)

1) Graduate Student, Department of Civil and Environmental Engineering, KAIST

2) Ph.D. Candidate, Department of Civil and Environmental Engineering, KAIST

3) Professor, Department of Civil Engineering, SungKyunKwan Univ.

4) Professor, Department of Civil and Environmental Engineering, KAIST

Jun-Sik Ha1), Ji-Seong Jo2), Sun-Kyu Park3), In-Won Lee4)

1) Graduate Student, Department of Civil and Environmental Engineering, KAIST

2) Ph.D. Candidate, Department of Civil and Environmental Engineering, KAIST

3) Professor, Department of Civil Engineering, SungKyunKwan Univ.

4) Professor, Department of Civil and Environmental Engineering, KAIST

Structural Dynamics & Vibration Control Lab., KAIST, KoreaStructural Dynamics & Vibration Control Lab., KAIST, Korea 22

CONTENTS

INTRODUCTION

FORMULATION OF MATHEMATICAL MODEL

NUMERICAL EXAMPLE

CONCLUSIONS


INTRODUCTION

Bridges, which have lightweight, are more

vulnerable to heavy weight vehicle.

The vibration induced by moving loads makes

passengers uncomfortable.


Objective of Study

Propose passive control device for the improvement

of serviceability.


FORMULATION OF MATHEMATICAL MODEL

Modeling

H

),(vb tx

dC

dv

dK ,T C

L

tv tv tv tv tv tv


Equation of Motion

Control Device

SD PP ,T C

)vv( db m


(1)

(2)

2

b

cos2

)]vv([

CC

dSD

CC

CC AE

HmPP

AE

TL

3

bb cos2

)]vv([

cos)(v(t)v

CC

dSDCd AE

HmPPt

(3)

0)](v(t)[vcos2

)(v)(v)](v),2/(v[

db

3

b

tH

AE

tKtCttLm

CC

ddddd

SD PP ,T C

)vv( db m


(4)

(5)

(6)

Bridge

),(vv

t

v4

b

4

b

2

b

2

txfx

EIt

CA

L

xxtqxtx i

iii

sin)( where )()(),(vb

),()()()( txfqEIqCqAi

iii

iii

ii


(7)

(8)

si

iisi

iisi

iis txfqEIqCqA ),()()()(

Multiplying eq.(3) by s

dxtxfdxqEI

dxqCdxqA

L

s

L

iiis

L

iiis

L

iiis

00

00

),()(

)()(


(9)

Applying orthogonal condition

dxtxfdxqmqdxCqdxAL

s

L

ssss

L

ss

L

s 00

22

0

2

0

2 ),(

L

L

nnnnnn

dxL

xnA

dxL

xntxf

tqtqtq

0

2

02

)(sin

]sin),([)()(2)(

Substituting mode shape function of beam

(10)


(11)

ddddw

L

SDw

L

KCL

vtnP

dxL

xnLxPPvtxP

dxL

xntxf

vvsin

]sin)}2()()([{

]sin),([

0

0

(12)

L

vtnPtKtC

tqtqtqAL

wdddd

nnnnnn

sin)(v)(v

)]()(2)([2

2

2)(sin

0

2 ALdx

L

xnA

L where


Optimization of Device Parameters

Using Pareto Optimization(“Engineering Optimization”, Singiresu S. Rao)

max

max

max

max )1(

uncon

con

uncon

con

a

a

d

dJ (13)

When J is minimized, the damping coefficient and spring constant in control device are optimum.


NUMERICAL EXAMPLES

Composite Steel Plate Girder Bridge “Generalized of Design for Short Span Steel Bridges Using Rolled Beam”,Magazine of the Korean Society of Steel Construction, vol.14, No.1, pp. 77~82.


Geometry and Material Properties

Geometry

4

2

00102.0

0708.0

)(18

mI

mA

mL

b

2003.0

m 1H

mAC

Bridge

Control device

Bridge

006.0

/14182

/1006.23

211

mkg

mNE

b

b

3

211

C

/6200

/101.2E

mkg

mN

C

Material Properties

Control device


Vehicle velocity

Number of modes : 3

km/h70m/s4.91v

Coefficient of Pareto optimization

4.0

Parameters


Optimization of Device Parameters The Normed Displacement of Mid-span

)/(101~101

)/(101~10161

61

msNC

mNK

d

d

As the damping coefficient and spring constant are increased, the normed displacement are decreased. Max : 46 % reduction


The Normed Acceleration of Mid-span

The optimal damping

constant exists. Max : 36 % reduction

)/(101~101

)/(101~10161

61

msNC

mNK

d

d


J of Mid-span

1

2

3

4

5

6

12

34

56

0.7

0.71

0.72

0.73

0.74

0.75

0.76

C(Ns/m)

K(N/m)

J

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

K(N/m)

C(Ns/m)

0.71031 0.71031 0.71031

0.71031 0.71031 0.71031

0.71341 0.71341 0.71341

0.71341 0.71341 0.71341

0.71652

0.71652 0.71652 0.716520.71962 0.71962 0.71962

0.72273 0.72273 0.722730.72584 0.72584 0.72584

0.72894 0.72894 0.728940.73205 0.73205 0.73205

0.73516 0.73516 0.735160.73826 0.73826 0.73826

0.74137 0.74137 0.741370.74448 0.74448 0.74448

0.74758 0.74758 0.747580.75069 0.75069 0.75069

0.75379 0.75379 0.75379

)/(101~101

)/(101~10161

61

msNC

mNK

d

d


Optimal Damping Coefficient and Spring Constant

)/(100.1

)/(105.85

5

msNC

mNK

d

d


Simulation Results Displacement of Mid-span

The maximum reduction

is 22%.

0 2 4 6 8

TIM E (s)

-0 .2

-0.1

0

DIS

PL

. a

t ce

nte

r (m

)

U ncontro lledC ontro lled


Acceleration of Mid-span

The maximum reduction

is 21.1%.

0 2 4 6 8

TIM E (s)

- 8

- 4

0

4

8

AC

C. a

t ce

nte

r (m

/s^2

)

U ncontro lledC ontro lled


mid-span responses

Uncontrolled Case

Controlled Case

Reduction (%)

Displacement

of mid-span(m)0.2241 0.1749 22.0

Acceleration

of mid-span(m/ )9.8963 7.8059 21.1

Table 1. Performances of proposed control device

2s


CONCLUSIONS

Proposed Passive Control Device Proposed Passive Control Device

can control both displacement and acceleration simultaneously.

can decay the steady-state responses much faster.

Therefore, proposed passive control device could be effectively used for vibration control of bridges.

Therefore, proposed passive control device could be effectively used for vibration control of bridges.


ACKNOWLEDGEMNT

This research is funded by the National Research Laboratory Grant (No.: 2000-N-NL-01-C-251) in Korea.

Thank you for your attention!

computational structural engineering institute autumn conference 2002 oct. 18 - 19, 2002 vibration...

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