Optimal placement of MR dampers

for 20-story nonlinear

benchmark building

Optimal placement of MR dampers

for 20-story nonlinear

benchmark building

2003 년 대한토목학회 추계학술발표대회대구 EXCO2003 년 10 월 24, 25 일

장종우 , 한국과학기술원 건설 및 환경공학과 석사과정조상원 , 한국과학기술원 건설 및 환경공학과 박사과정윤우현 , 경원대학교 산업환경대학원 부교수이인원 , 한국과학기술원 건설 및 환경공학과 교수

Introduction

• Linear viscous dampers

- The larger structural responses of the dampers’ locations

are, the more effective the devices are.

- Many sequential procedures of optimal placement have

been proposed. : SSA, SSSA ( T. T. Soong 2002 )

• MR damper ( Magneto-rheological damper )

- More complicated control mechanism than linear viscous

dampers

- Very few verified and widely used methods for optimal placement

of MR dampers.

• Proposed optimal placement methods

- Similar to the sequential procedures for linear viscous dampers

- The next MR damper is implemented at the location with the

maximum responses.

• MR damper model

- Combination of Bouc-Wen model and linear

damper ( Yoshida and Dyke 2002 )

Proposed optimal placement method

u0bc0ac0c

αzx0cf

xAn

zxβ-1-n

zzx-γz

ubαaαα

v)--(uu

f : control force produced by damper

u : effective voltage

v : command voltage

V)sec/(cmN44.00bc

sec/cmN4.400ac

V)N/(cm5

104.9616bα

N/cm5

101.0872aα

1sec50η

1cm3β

1cm3γ

1.2A

1n

-

-

-

- Dynamic characteristics of MR damper

- Maximum capacity : 1000kN

Maximum command voltage : 10V

- Control algorithms

· Passive control : Passive-On and Passive-Off

· Semiactive control : Maximum energy dissipation algorithm

• Optimal placement of MR dampers

- Linear viscous damper

: Optimal location index ( T.T.Soong 2002 )

iδ2αiδ1αiγ

storeyiththeat

velocity&driftyinterstorepeakiδ,iδ

storeysofNo.,2,1,i

: The coefficients of each responses are not yet determined.

- MR damper

: Consider only one of the structural responses for the

optimal location index

· Peak interstory drift

· Peak interstory velocity

· Absolute acceleration

: Then, determine the coefficients and propose the optimal

location indices.

Numerical results

• Building models

- 20-story nonlinear

benchmark building

( Otori et al. 2000, 2002 )

- Plane : 30.48 36.58 (m)

- Height : 80.77 (m)

- Two basement levels

- 5 bays in the N-S

direction and 6 bays in

the E-W direction

- 3 DOFs at each node (horizontal, vertical, rotational)

: Total DOFs: 414 (138 nodes)

- MR dampers are implemented throughout the N-S

frames.

- Rayleigh damping matrix

- Inelastic behavior of the building

during strong earthquakes

: Bilinear hysteresis model

• Peak accelerations of applied earthquakes

El Centro Hachinohe Northridge Kobe

Peak acc. 0.349 g 0.230 g 0.844 g 0.834 g

g : acceleration of gravity

• Optimal locations of MR dampers (Passive-On algorithm) - Optimal location index ( Interstory drift )

: Before normalization of earthquakes’ scales

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

: After normalization of earthquakes’ scales

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

- Optimal location index ( Interstory velocity )

: Before normalization of earthquakes’ scales

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

: After normalization of earthquakes’ scales

. Int. drift Int. velocity Benchmark

El Centr

o

J1 0.569 0.739 0.612

J2 0.550 0.735 0.599

J3 0.824 0.903 0.976

Hach.

J1 0.635 0.870 0.683

J2 0.844 0.871 0.845

J3 1.012 1.223 0.995

North.

J1 0.677 0.899 0.766

J2 1.275 1.500 1.132

J3 1.134 0.985 1.133

Kobe

J1 0.519 0.563 0.700

J2 0.937 0.843 1.062

J3 1.230 1.063 1.213

· J1 : max. int. drift

· J2 : max. abs. acc.

· J3 : max. base shear

- Comparison of evaluation criteria

· Damper locations in the Benchmark problem

Floor No. 1 2~3 4~20

No. of dampers

4 2 1

• Optimal location index : Absolute acceleration

: Graph of evaluation criteria

20 20 20 14 14 14 14 14 14 14

13 13 13 ……

0.4

0.8

1.2

1.6

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Eval. criteria

No. of dampers

- El Centro earthquake

: Optimal placements

0.40.60.8

11.21.41.61.8

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Eval. criteria

No. of dampers

: Graph of evaluation criteria

12 12 12 11 11 11 11 11 11

11 11 11 ……

- Kobe earthquake

: Optimal placements

J1 J2 J3

-- El Centro earthquake

· Interstory drift index : 25 dampers only on the first floor

· Interstory velocity index : 25 dampers only on the 20th floor

• Optimal locations of MR dampers (Passive-Off algorithm)

. Int. drift Int. velocity Benchmark

J1 0.978 0.861 0.965

J2 0.993 0.953 0.975

J3 0.981 0.906 0.962

- Kobe earthquake

· Interstory drift index : 25 dampers only on the 19th floor

· Interstory velocity index : 25 dampers only on the 20th floor

. Int. drift Int. velocity Benchmark

J1 0.943 0.945 0.999

J2 1.005 0.990 1.026

J3 1.010 0.993 1.004

• Optimal locations of MR dampers (MEDA algorithm) - Optimal location index ( Interstory drift )

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

El Centro

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Northridge

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Kobe

No. of dampers

Floor No.

0 2 4 6 8

13579

1113151719

Hachinohe

No. of dampers

Floor No.

- Optimal location index ( Interstory velocity )

. Int. drift Int. velocity Benchmark

El Centr

o

J1 0.639 0.759 0.640

J2 0.963 1.255 1.041

J3 0.832 0.938 0.975

Hach.

J1 0.638 0.781 0.683

J2 0.814 1.479 0.845

J3 1.025 1.182 0.995

North.

J1 0.715 0.959 0.815

J2 1.180 1.120 0.948

J3 1.087 0.954 1.059

Kobe

J1 0.557 0.534 0.645

J2 0.857 0.870 0.877

J3 0.974 0.976 1.036

· J1 : max. int. drift

· J2 : max. abs. acc.

· J3 : max. base shear

- Comparison of evaluation criteria

· Damper locations in the Benchmark problem

Floor No. 1 2~3 4~20

No. of dampers

4 2 1

• Passive-On algorithm - Peak interstory drift index is the most efficient in most

cases.

- Peak interstory velocity index is not very efficient.

- Peak absolute acceleration is inadequate for the optimal

location index.

• Passive-Off algorithm - MR dampers are implemented only on one floor.

- The proposed sequential method is not adequate

for Passive-Off algorithm.

• Maximum energy dissipation algorithm - The optimal locations of MR dampers are similar to those

under passive-on algorithm.

Conclusion