Investigating Appropriate Conditions for Passive and Semi-Active 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 building’s response to seismic activity

5. Passive Control • Passive control is a widely used form of structural control • Passive control uses the building’s response to develop control forces • Requires no power source (WUSTL, 2003)

6. Semi-Active Control • Semi-active control uses the building’s 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 T≥1.5 s resulted in decreased displacement but increased acceleration with an increase in the damping ratio • Passive dampers are more efficient for structures with T<1.5 s • Variable dampers are more efficient for structures T≥1.5 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 building’s 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 ξmin = 0.05 to ξmax = 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. m m m m k k k k 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.