Effects of MR Damper Placement on Equivalent Damping ... - MCEER

<strong>Effects</strong> <strong>of</strong> <strong>MR</strong> <strong>Damper</strong> <strong>Placement</strong> on
Structure Vibration Parameters
By: Karla Villarreal
Advisors:
Claudia Wilson
Makola M. Abdullah, Ph.D.

Introduction
Control Systems
<strong>MR</strong> <strong>Damper</strong>
Background
Objective
Methodology
Results
Conclusion
Future Work
Overview

Introduction
Parking garage (FEMA 2004) (1)
Damage on 12 th street (Paso
Robles Earthquake 2003) (2)
Collapsed apartment buildings (Kandilli Observatory
and Earthquake Research Institute 1999) (3)

Control Systems
Systems that absorb vibration or movement
– Passive
– Active
No power required
Directly damps vibration
Requires power
Applies a force directly into the system to damp vibration
– Semi-Active
Requires minimal power
Applies a force that changes the system
Change helps dampen the vibration

Magneto-Rheological <strong>Damper</strong>
Semi-Active
Magneto
Rheology
Controllable fluid
Para-magnetic
particles
20-ton large-scale <strong>MR</strong> Fluid <strong>Damper</strong> (Yang 2001) (4)

Background
1940s
Serviceability
– Suspension systems
Shock absorbers
Seat suspensions
Prosthetics
– Other Uses
Exercise machines
Washing machines
– Semi-Active vibration control
Bridges
Buildings
LORD Corporation (2004) (5)

Research Objective
To find the effect <strong>of</strong> <strong>MR</strong> damper placement on
the equivalent damping ratio and on the natural
frequency <strong>of</strong> a building.

MATLAB:
– Uncontrolled
– Controlled
Simulink:
– <strong>MR</strong> damper
– Free vibration response
Graphical Analysis:
Methodology
– Free Vibration Building Response vs. Time
– Modal Building Response vs. Time
Data Analysis:
– Damping ratio (ζ)(
– Natural frequency shift
– Determine the sensitive current range
– Comparing <strong>MR</strong> damper placement results

Equations
Equation <strong>of</strong> Motion <strong>of</strong> building with earthquake
m ! x
+ cx!
+ kx = − f − mx !
g
<strong>Damper</strong> Equations (Spencer et al. 1997) (6)
A, γ , β , k , n,
x , k1 =
o
o
constants
f
y!
= c
=
c
0
o
y!
+ k ( x−x
1
+ c
1
1
o
)
[ αz
+ c x!
+ k ( x−
y)
]
o
o
Mechanical Model <strong>of</strong> the <strong>MR</strong> <strong>Damper</strong> (6)
z!
=−γ
x!
− y!
z z
n−1
−β(
x!
− y!
) z
n
+ A(
x!
− y!
)

<strong>MR</strong> <strong>Damper</strong>

Controlled and Uncontrolled Systems
• 3 DOF Building (8)
– Mass: 3.456*10 5 kg
– Stiffness: 1.2*10 8 kN/m
– 1 st natural frequency: 1.319 Hz
• 1 st simulation uncontrolled
• Subjected to FVR
– Constant input <strong>of</strong> zero force
– Given initial conditions
– 5 cm displacement on each
floor
• 2 nd simulation controlled by <strong>MR</strong>
<strong>Damper</strong>

Equiv. Damping and Freq. Shift
Frequency Shift
Equivalent Damping
Equation (7)
= 1
ζ
2π
*
ln
u
u
i
j
i +
j

Freq. Response
<strong>Placement</strong>:
1 st
st Floor
2 nd
nd Floor
3 rd
rd Floor
Current (A)
Resonant
Freq. (Hz)
Freq. Shift
(Hz)
Resonant
Freq. (Hz)
Freq. Shift
(Hz)
Resonant
Freq. (Hz)
Freq. Shift
(Hz)
No <strong>Damper</strong> 1.31977 0 1.31977 0 1.31977 0
0 1.32681 .00702 1.32443 .00467 1.32320 .00657
1 1.33374 .01396 1.325117 .00535 1.30979 .00997
2 1.33404 .01426 1.324994 .00523 1.30981 .00996
3 1.33576 .01597 1.320271 .01599 1.30933 .01044
4 1.33620 .01642 1.319383 .00038 1.30911 .01066
5 1.33590 .01611 1.319156 .00061 1.30904 .01073
6 1.35586 .01608 1.319104 .00066 1.30899 .01078

Equivalent Damping Ratios
<strong>Placement</strong>:
1 st
st Floor
2 nd
nd Floor
3 rd
rd Floor
Current (A)
Damping
Ratio (%)
Add.
Damping (%)
Damping
Ratio (%)
Add.
Damping (%)
Damping
Ratio (%)
Add.
Damping (%)
No <strong>Damper</strong> 2.19365 0 2.19365 0 2.19365 0
0 2.80357 .60992 3.91337 1.71972 1.59208 -.60157
1 5.99476 3.80111 3.60766 1.41401 1.27050 -.092315
2 6.28860 4.09495 4.86715 2.67350 2.30744 .011379
3 7.14884 4.95519 3.38542 1.19177 1.13409 -1.05956
4 7.42823 5.23458 2.19772 0.00408 1.08789 -1.10576
5 7.47207 5.27843 2.20284 0.00919 1.06836 -1.12529
6 7.47976 5.28612 2.20450 0.01086 1.05826 -1.13539

<strong>Damper</strong> <strong>Placement</strong> Results

Sensitive Current Range
Sensitive Current Range
Sensitive Current Range
6.00000
0.01800
Additional Damping (%)
5.00000
4.00000
3.00000
2.00000
1.00000
Frequency Shift (Hz)
0.01600
0.01400
0.01200
0.01000
0.00800
0.00600
0.00400
0.00000
0 1 2 3 4 5 6 7
Current (Amps)
0.00200
0.00000
0 1 2 3 4 5 6 7
Current (Amps)

Conclusion
1. Effect <strong>of</strong> <strong>MR</strong> <strong>Damper</strong> placement on natural
freq. shift:
Occurs at every floor
Larger shifts occur when <strong>MR</strong> <strong>Damper</strong> was
placed on the 1 st floor
2. Effect <strong>of</strong> <strong>MR</strong> <strong>Damper</strong> placement on ζ:
Values decreased as the <strong>MR</strong> <strong>Damper</strong> was moved
up in the building
Controlled best on 1 st Floor
3. Sensitive current range from 0-30
3 Amps

Future Work
Comparing the Sensitive
Current Range to the
Sensitive Voltage Range
Run simulations for
10 DOF
New project on “<strong>Effects</strong>
<strong>of</strong> <strong>MR</strong> <strong>Damper</strong>
placement on bridge
vibration response”

Acknowledgements
MCEER
REUJAT program
Makola M. Abdullah, Ph.D.
Claudia Wilson, M.S.C.E.
Tokyo University
– Dr. Yozo Fujino

References
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9. Reference the Stiffness stuff
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Using Optimal Considerations". ASCE Journal <strong>of</strong> Structural Engineering, 129 (10),
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