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Effects of MR Damper Placement onEffects of MR Damper Placement on
Structure Vibration ParametersStructure Vibration Parameters
By: Karla VillarrealBy: Karla Villarreal
Advisors:Advisors:
Claudia WilsonClaudia Wilson
Makola M. Abdullah, Ph.D.Makola M. Abdullah, Ph.D.
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OverviewOverviewIntroductionIntroductionControl SystemsControl Systems
MR DamperMR Damper
BackgroundBackground
ObjectiveObjective
MethodologyMethodology
ResultsResultsConclusionConclusion
Future WorkFuture Work
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Collapsed apartment buildings (Kandilli Observatory
and Earthquake Research Institute 1999) (3)
IntroductionIntroduction
Parking garage (FEMA 2004) (1)
Damage on 12th street (Paso
Robles Earthquake 2003) (2)
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MagnetoMagneto
--Rheological DamperRheological Damper
SemiSemi--ActiveActiveMagnetoMagneto
RheologyRheologyControllable fluidControllable fluid
ParaPara--magneticmagneticparticles
20-ton large-scale MR Fluid Damper (Yang 2001) (4)
particles
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BackgroundBackground
1940s1940s
ServiceabilityServiceability
Suspension systemsSuspension systems
Shock absorbersShock absorbers
Seat suspensionsSeat suspensions
ProstheticsProsthetics Other UsesOther Uses
Exercise machinesExercise machines
Washing machinesWashing machines
SemiSemi--Active vibration controlActive vibration control
BridgesBridges
BuildingsBuildings
LORD Corporation (2004) (5)
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Research ObjectiveResearch Objective
To find the effect of MR damper placement onTo find the effect of MR damper placement onthe equivalent damping ratio and on the naturalthe equivalent damping ratio and on the natural
frequency of a building.frequency of a building.
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MethodologyMethodology
MATLAB:MATLAB: UncontrolledUncontrolled
ControlledControlled
Simulink:Simulink: MR damperMR damper
Free vibration responseFree vibration response
Graphical Analysis:Graphical Analysis: Free Vibration Building Response vs. TimeFree Vibration Building Response vs. Time Modal Building Response vs. TimeModal Building Response vs. Time
Data Analysis:Data Analysis: Damping ratio (Damping ratio ())Natural frequency shiftNatural frequency shift
Determine the sensitive current rangeDetermine the sensitive current range
Comparing MR damper placement resultsComparing MR damper placement results
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EquationsEquations
Equation of Motion of building with earthquakeEquation of Motion of building with earthquake
[ ]
)()(
)(1
)(
1
1
10
yxAzyxzzyxz
yxkxczcc
y
xxkycf
nn
oo
o
o
!!!!!!!
!!
!
+=
++
+
=
+=
Mechanical Model of the MR Damper (6)
gxmfkxxcxm !!!!! =++
Damper EquationsDamper Equations (Spencer et al. 1997) (6)(Spencer et al. 1997) (6)
constants,,,,,, 1 =kxnkA oo
MR D
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MR Damper
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Controlled and Uncontrolled Systems
3 DOF Building (8)
Mass: 3.456*105 kg
Stiffness: 1.2*108 kN/m
1st natural frequency: 1.319 Hz
Subjected to FVR
Constant input of zero force Given initial conditions
5 cm displacement on eachfloor
2nd simulation controlled by MRDamper
1st simulation uncontrolled
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Equiv. Damping and Freq. ShiftEquiv. Damping and Freq. Shift
Frequency ShiftFrequency Shift
ji
i
u
u
j += ln
*2
1
Equivalent DampingEquivalent Damping
EquationEquation (7)(7)
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Freq. ResponseFreq. ResponsePlacement:Placement: 11stst FloorFloor 22ndnd FloorFloor 33rdrd FloorFloor
Current (A)Current (A) ResonantResonant
Freq. (Hz)Freq. (Hz)
Freq. ShiftFreq. Shift
(Hz)(Hz)
ResonantResonant
Freq. (Hz)Freq. (Hz)
Freq. ShiftFreq. Shift
(Hz)(Hz)
ResonantResonant
Freq. (Hz)Freq. (Hz)
Freq. ShiftFreq. Shift
(Hz)(Hz)
No DamperNo Damper 1.319771.31977 00 1.319771.31977 00 1.319771.31977 00
00 1.326811.32681 .00702.00702 1.324431.32443 .00467.00467 1.323201.32320 .00657.00657
11 1.333741.33374 .01396.01396 1.3251171.325117 .00535.00535 1.309791.30979 .00997.00997
22 1.334041.33404 .01426.01426 1.3249941.324994 .00523.00523 1.309811.30981 .00996.00996
33 1.335761.33576 .01597.01597 1.3202711.320271 .01599.01599 1.309331.30933 .01044.01044
44 1.336201.33620 .01642.01642 1.3193831.319383 .00038.00038 1.309111.30911 .01066.01066
55 1.335901.33590 .01611.01611 1.3191561.319156 .00061.00061 1.309041.30904 .01073.01073
66 1.355861.35586 .01608.01608 1.3191041.319104 .00066.00066 1.308991.30899 .01078.01078
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Equivalent Damping RatiosEquivalent Damping Ratios
Placement:Placement: 11stst FloorFloor 22ndnd FloorFloor 33rdrd FloorFloor
Current (A)Current (A) DampingDamping
Ratio (%)Ratio (%)
Add.Add.
Damping (%)Damping (%)
DampingDamping
Ratio (%)Ratio (%)
Add.Add.
Damping (%)Damping (%)
DampingDamping
Ratio (%)Ratio (%)
Add.Add.
Damping (%)Damping (%)
No DamperNo Damper 2.193652.19365 00 2.193652.19365 00 2.193652.19365 00
00 2.803572.80357 .60992.60992 3.913373.91337 1.719721.71972 1.592081.59208 --.60157.60157
11 5.994765.99476 3.801113.80111 3.607663.60766 1.414011.41401 1.270501.27050 --.092315.092315
22 6.288606.28860 4.094954.09495 4.867154.86715 2.673502.67350 2.307442.30744 .011379.011379
33 7.148847.14884 4.955194.95519 3.385423.38542 1.191771.19177 1.134091.13409 --1.059561.05956
44 7.428237.42823 5.234585.23458 2.197722.19772 0.004080.00408 1.087891.08789 --1.105761.10576
55 7.472077.47207 5.278435.27843 2.202842.20284 0.009190.00919 1.068361.06836 --1.125291.12529
66 7.479767.47976 5.286125.28612 2.204502.20450 0.010860.01086 1.058261.05826 --1.135391.13539
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Damper Placement ResultsDamper Placement Results
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Sensitive Current RangeSensitive Current Range
Sensitive Current Range
0.00000
1.00000
2.00000
3.00000
4.00000
5.00000
6.00000
0 1 2 3 4 5 6 7
Current (Amps)
AdditionalDam
ping(%)
Sensitive Current Range
0.00000
0.00200
0.00400
0.00600
0.00800
0.01000
0.01200
0.01400
0.01600
0.01800
0 1 2 3 4 5 6 7
Current (Amps)
FrequencyShift(Hz)
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ConclusionConclusion
1.1. Effect of MR Damper placement on naturalEffect of MR Damper placement on natural
freq. shift:freq. shift:
Occurs at every floorOccurs at every floor
Larger shifts occur when MR Damper wasLarger shifts occur when MR Damper was
placed on the 1placed on the 1stst floorfloor
2.2. Effect of MR Damper placement onEffect of MR Damper placement on ::
Values decreased as the MR Damper was movedValues decreased as the MR Damper was moved
up in the buildingup in the building
Controlled best on 1Controlled best on 1stst FloorFloor
3.3. Sensitive current range from 0Sensitive current range from 0--3 Amps3 Amps
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Future WorkFuture Work
Comparing the SensitiveComparing the Sensitive
Current Range to theCurrent Range to theSensitive Voltage RangeSensitive Voltage Range
Run simulations forRun simulations for10 DOF10 DOF
New project onNew project on EffectsEffects
of MR Damperof MR Damperplacement on bridgeplacement on bridge
vibration responsevibration response
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AcknowledgementsAcknowledgements
MCEERMCEER
REUJAT programREUJAT program
Makola M. Abdullah, Ph.D.Makola M. Abdullah, Ph.D.
Claudia Wilson, M.S.C.E.Claudia Wilson, M.S.C.E.Tokyo UniversityTokyo University
Dr.Dr. YozoYozo FujinoFujino
R fR f
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