Investigating Appropriate Conditions for Passive and SemiActive Control Devices

1
Investigating Appropriate Conditions for Passive
and Semi-Active Control Devices

• Waleed T. Barnawi
• Advisors
• Kenneth K. Walsh, Ph.D.
• Tzu-Ying Lee, Ph. D. Candidate
• Makola M. Abdullah, Ph.D.

2
Outline

• Background
• Objectives
• Procedure
• Results
• Conclusion
• Future Work
• Acknowledgements

3
Background

• Earthquakes may cause billions of dollars of
  damage, severe loss of life, and major outages
• 1994 Northridge Earthquake
• Magnitude 6.7
• Over 20 billion dollars of damage (IRIS, 2005)
• Earthquakes of this size occur 20 times a year
  worldwide (IRIS, 2005)
• Structures excited by earthquakes could result in
  large accelerations
• Hospital
• Communication towers

4
Control Devices

• Buildings have little inherent damping
• Over the last three decades, there has been much
  development and diversity of control devices to
  protect structures from dynamic loads
• Base Isolation
• Tuned Mass Dampers
• Supplemental Dampers
• Control devices provide a reduction in buildings
  response to seismic activity

5
Passive Control

• Passive control is a widely used form of
  structural control
• Passive control uses the buildings response to
  develop control forces
• Requires no power source

(WUSTL, 2003)
6
Semi-Active Control

• Semi-active control uses the buildings response
  and a feedback feature to develop control forces
• Requires a small power source
• Variable stiffness
• Variable damper
• Friction
• Fluid

(WUSTL, 2003)
7
Passive vs. Semi-Active

• Use of variable dampers to control the response
  of bridges (Feng and Shinozuka 1990, 1993)
• Isolated bridge modeled as a SDOF structure
• Increase in the damping ratio will reduce
  displacement, but may increase acceleration
• Variable dampers will reduce displacement and
  acceleration more effectively than passive
  control
• Using semi-active control to reduce the response
  in buildings (Symans and Constantinou 1996)
• Conducted an experiment a with a three-story
  model
• Passive control performed as well as the
  semi-control
• Inefficient to use a semi-active damper over a
  passive damper

8
Effectiveness of Semi-Active Control (Sadek and
Mohraz, 1998)

• Six SDOF structures with different fundamental
  vibration periods (T) subject to 20 earthquake
  excitations
• Each structure was subject to an increase in
  passive damping from Cmin to Cmax
• Response of structures was averaged over the 20
  earthquakes
• Structures with T1.5 s resulted in decreased
  displacement but increased acceleration with an
  increase in the damping ratio
• Passive dampers are more efficient for structures
  with Tlt1.5 s
• Variable dampers are more efficient for
  structures T1.5 s

9
Objectives

• Develop criteria to determine when flexibility
  occurs in MDOF structures
• Use criteria to establish conditions for using
  passive or semi-active devices to effectively
  reduce a buildings response

10
Procedure

• Analyze various MDOF structures to develop the
  criteria for determining when flexibility occurs
• A flexible structure has a decrease in
  displacement and an increase in acceleration with
  an increase in the damping ratio
• Model a 3DOF structure
• Vary the fundamental vibration period
• Use a range of 20 earthquakes
• Perform test for rigid and flexible structures to
  determine the efficiency of passive and
  semi-active control devices
• Structures will be subjected to an increase in
  damping ratio from ?min 0.05 to ?max 0.40
• Response ratios are the peak response with a
  damper over the peak response without a damper
• Compute and average the response ratios for the
  first floor of each structure for the earthquake
  data
• Compare the response ratios for passive and
  semi-active control of rigid and flexible
  structures

11
Governing Equation
Mass Matrix
Damping Matrix
Stiffness Matrix
Displacement vector of building at time t
Location of the control forces generated by the
dampers
Control force vector at time t
Vector of ones
Acceleration of earthquake at time t
State Space
12
LQR Algorithm
Performance Equation
duration of the earthquake
weighting matrix that place emphasis on the
states
weighting matrix that place emphasis on the
control forces
Algebraic Riccati Equation
solution to the Algebraic Riccati Equation
Vector of optimum control forces
number of floors
number of dampers
13
LQR Algorithm
Vector of optimum control forces
Gain Matrix
Damping coefficient of Semi-Active damper
Selection of Damping coefficient
14
Semi-Active Control Cases
Semi-Active damper on each floor (SA all f)
Semi-active damper on first floor (SA 1st f)
x3
m
x3
k
x2
m
x2
k
x1
x1
15
Building Properties
16
Point of flexibility
17
Passive Time History (Rigid)
18
Passive Time History (Rigid)
19
Passive Time History (Flexible)
20
Passive Time History (Flexible)
21
Selection of q
22
S.A. Time History (Rigid)
23
S.A. Time History (Rigid)
24
S.A. Time History (Flexible)
25
S.A. Time History (Flexible)
26
Best semi-active responses
27
Conclusion

• Structures with a T 2 s. exhibit flexibility
  with increased passive damping
• Rigid structures
• A variable damper on each floor provides the
  optimum performance
• The passive cmax case gives the next best
  reduction in response
• Flexible structures
• A variable damper on each floor provides the
  optimum performance
• Semi-active control is more efficient in reducing
  the response than passive control

28
Future Work

• Increase the number of floors of the structure to
  test if the criteria for flexibility is
  consistent
• Use different combination of passive and
  semi-active control to test the changes in the
  response

29
Acknowledgements

• Florida A M University
• Kenneth K. Walsh, Ph. D.
• Makola M. Abdullah, Ph. D.
• REUJAT
• Shirley Dyke, Ph. D.
• Juan Caicedo, Ph. D.
• TITech
• Kazuhiko Kawashima, Ph. D.
• Tzu-Ying Lee, Ph. D. Candidate
• REU Program
• Sabanayagam Thevanayagam, Ph. D.

30
References

• Feng, Q. and Shinozuka, M. (1990). Use of a
  variable damper for hybrid control of bridge
  response under earthquake. Proc., U.S. Nat.
  Workshop on Struct. Control, Univ. of Southern
  California, Los Angeles, Calif., 107-112.
• Feng, Q. and Shinozuka, M. (1993). Control of
  seismic response of bridge structures using
  variable dampers. J. Intelligent Mat. Sys. And
  Struct., 4, 117-122.
• Sadek, F. and Mohraz, B. (1998). Semiactive
  Control Algorithms for Structures with Variable
  Dampers. J. Engrg. Mech., Sept., pp. 981-990.
• Sadek, F. and Mohraz, B. (1998). Variable
  Dampers for Semi-Active Control of Flexible
  Structures. Proc., U.S. 6th Nat. Conf.
  Earthquake Engrg., Earthquake Engrg. Research
  Inst., Oakland, CA., 1-12.
• Symans, M. D. and Constantinou, M.C. (1996).
  Semi-Active Control of Earthquake Induced
  Vibration Eleventh World Conference on
  Earthquake Engineering, Acapulco, Mexico, June,
  Paper No. 95.
• The IRIS Consortium Education and Outreach
  Series No. 3 16 July 2005. The IRIS Consortium 2
  Aug. 2005. lthttp//www.iris.edu/edu/onepagers.htmgt