structural vibration control using semiactive tuned mass damper
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Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 1
Structural Vibration Control Using Semiactive Tuned Mass Damper
Han-Rok Ji, Graduate Student, KAIST, KoreaYeong-Jong Moon, Ph. D. Candidate, KAIST, KoreaChun-Ho Kim, Professor, Joongbu University, KoreaIn-Won Lee, Professor, KAIST, Korea
The Eighteenth KKCNN Symposium on Civil Engineering
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 2
Introduction
Semiactive Tuned Mass Damper
Numerical Analysis
Conclusions
CONTENTS
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 3
Introduction
Tuned Mass Damper ― widely used mechanical damping device― Simple and efficient vibration control system ― No external power, energy dissipation, inherent reliability― Restricted performance resulted from the fixed parameters
Semiactive Tuned Mass Damper ― Alternative device of conventional TMD ― Improved control performance with stability of TMD― High robustness and adaptability
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 4
Objective
Analytical study on semiactive TMD using MR damper for mitigating the vibration of structures
Application of various semiactive control algorithms to MR damper
Robustness analysis for the semiactive TMD system
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 5
Semiactive Tuned Mass Damper
m1
k1
c1
m2
c(t)
x1
x2
k2
m1
gxm
mxx
kkkkk
xx
ccccc
xx
mm
11
00
00
2
1
2
1
22
221
2
1
22
221
2
1
2
1
― Equation of Motion
(1)
SDOF system with semiactive TMD
– Controllable damping device is installed in the place of passive dashpot.– Produce the additional control effect to the primary structure.
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 6
)Vu(uucc)u(cc
ucc)u(ccu)u(
)yx(kxczcc
y
)yx(Az)yx(zzyxz
)xx(kycf
ba
ba
ba
nn
0000
1111
0010
1
011
1
c0 c1 k1
k0
c1 c0 k0
k1
Modified Bouc-Wen Model
Bouc-Wen
― modified Bouc-Wen model (Spencer et al., 1997)
(2)
• Dynamic model of MR damper
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 7
Semiactive Control Algorithms
― on-off velocity based groundhook control
― on-off displacement based groundhook control
― clipped optimal algorithm
― maximum energy dissipation algorithm
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 8
maxVVthen,vvvif 0211
• On-off velocity based groundhook control (Koo et al. 2003)
― Based on velocity of primary system (v1 ) and TMD (v2 )
minVVthen,vvvif 0211
(3)
• On-off displacement based groundhook control (Koo et al. 2003)
(4)
― Based on velocity of primary system (v1 ) and TMD (v2 )
displacement of primary system (x1 )
maxVVthen,vvxif 0211
minVVthen,vvxif 0211
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 9
― linear optimal controller and clipped algorithm
Fc : desired damper force by optimal controller
Fd : measured damper force
ddcmax FFFHVV
• Clipped optimal algorithm (Dyke et al, 1996)
(5)
)Fx(HVV dmax
• Maximum energy dissipation algorithm (Jansen and Dyke, 2000)
(6)
― Control voltage is determined so that the structure dissipates the maximum energy
Fd : measured damper force
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 10
kg,
,,
M
500100050010005001
mN
.....
..K 610
12120122412
01224
msecN
.........
C
910425841025871528434108431163
gx
• Three-story shear building MR damper
mTMD = 150 kg , kTMD = 36,401 N/m
• Input earthquake excitations
― amplitude scaled El Centro, Hachinohe earthquakes
Numerical Analysis
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 11
Value Value
coa 21.0 Nsec/cm a 140 N/cm
cob 3.50 Nsec/cmV b 695 N/cmV
ko 46.9 N/cm 363 cm-2
c1a 283 Nsec/cm 363 cm-2
c1b 2.95 Nsec/cmV A 301
k1 5.00 N/cm n 2
xo 14.3 cm 190 sec-1
• Parameters of MR damper (Spencer et al., 1997)
c0 c1 k1
k0
c1 c0 k0
k1
Modified Bouc-Wen model
Bouc-Wen
― maximum damper force : 1,500 N― minimum voltage : 0 V― maximum voltage : 2.25 V
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Response of building model
TMD passive off
passive on
on-offDBG
on-offVBG
clippedoptimal
MEDA
ScaledEl Centro
(PGA 0.10g)
J1 0.38 0.39 0.50 0.35 0.39 0.36 0.39
J2 0.37 0.37 0.52 0.33 0.34 0.32 0.34
J3 0.45 0.47 0.50 0.44 0.44 0.43 0.44
Scaled Hachinohe
(PGA 0.08g)
J1 0.35 0.36 0.51 0.35 0.40 0.36 0.40
J2 0.35 0.35 0.49 0.32 0.39 0.34 0.39
J3 0.38 0.41 0.47 0.36 0.37 0.35 0.37
J1 : normalized peak floor displacementJ2 : normalized peak interstory driftJ3 : normalized peak acceleration
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 13
0.2
0.3
0.4
0.5
0.6
TMD passiveoff
passiveon
on-offDBG
on-offVBG
clippedoptimal
MEDA
J₁J₂J₃
0.3
0.35
0.4
0.45
0.5
0.55
TMD passiveoff
passive on on-offDBG
on-offVBG
cl ippedoptimal
MEDA
J₁J₂J₃
― El Centro earthquake ― Hachinohe earthquake
― The efficiency of semiactive TMD is slightly better than that of TMD.
― Passive on mode has the worst performance.
Nor
mal
ized
val
ue
Nor
mal
ized
val
ue
― Evaluation criteria under two earthquakes
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 14
Robustness Analysis
• Response with stiffness matrix perturbation
1KK̂
: amount of perturbation
(-15%, -10%, -5%, +5%, +10% and +15%)
― Perturbed stiffness matrix
(7)
― Real structures can have structural uncertainties in many reasons.
― Control performance of TMD is restricted considerably due to off-tuning effect.— Stiffness perturbation is considered to verify the robustness of the semiactive TMD
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 15
-0.6
-0.3
0
0.3
0.6
0 5 10 15 20
TMDon-off DBG
-3
-1.5
0
1.5
3
0 5 10 15 20
TMDon-off DBG
Time (sec)
Inte
rsto
ry d
rift
(cm
)A
ccel
erat
ion
(m/s
ec2 )
Time history with +15% stiffness perturbation under Hachinohe earthquake
― The maximum and RMS values with semiactive TMD are reduced compared with that of conventional TMD.
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 16
0.2
0.4
0.6
0.8
1
1.2
-15% -10% -5% 0% 5% 10% 15%
TMDon-off DBGon-off VBGclipped optiamalMEDA
Nor
mal
ized
pea
k dr
ift (
J 2)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-15% -10% -5% 0% 5% 10% 15%
TMDon-off DBGon-off VBGclipped optiamalMEDA
Nor
mal
ized
pea
k ac
cele
ratio
n (J
3)― Overall performance of semiactive TMD is better than that of TMD.
― Efficient algorithm : on-off DBG control for interstory drift
clipped optimal control for acceleration
― Evaluation criteria under El Centro earthquake
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 17
Nor
mal
ized
pea
k dr
ift (
J 2)
Nor
mal
ized
pea
k ac
cele
ratio
n (J
3)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15% -10% -5% 0% 5% 10% 15%
TMDon-off DBGon-off VBGclipped optiamalMEDA
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-15% -10% -5% 0% 5% 10% 15%
TMDon-off DBGon-off VBGclipped optiamalMEDA
― Semiactive TMD is superior to conventional TMD.
― On-off DBG and clipped optimal algorithm have sufficient robustness.
― Evaluation criteria under Hachinohe earthquake
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 18
― Various semiactive control algorithms are adopted and the performance of each algorithm is evaluated.
― Semiactive TMD system shows slightly better performance than conventional TMD system.
― Analytical study on semiactive TMD with MR damper is performed.
Conclusions
Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 19
― Sufficient robustness is obtained under the structural perturbation with semiactive TMD.
― The on-off displacement based groundhook theory and clipped optimal algorithm is appropriate algorithm for semiactive TMD system.
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