1. Computational Structural Engineering Institute Autumn Conference 2002 Oct. 18 - 19, 2002 VIBRATION CONTROL OF BRIDGE FOR SERVICEABILITY Jun-Sik Ha 1), Ji-Seong Jo 2), Sun-Kyu Park 3), In-Won Lee 4) 1) Graduate Student, Department of Civil and Environmental Engineering, KAIST 2) Ph.D. Candidate, Department of Civil and Environmental Engineering, KAIST 3) Professor, Department of Civil Engineering, SungKyunKwan Univ. 4) Professor, Department of Civil and Environmental Engineering, KAIST

2. Structural Dynamics & Vibration Control Lab., KAIST, Korea 2 CONTENTS  I NTRODUCTION  F ORMULATION OF MATHEMATICAL MODEL  N UMERICAL EXAMPLE  C ONCLUSIONS

3. Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 INTRODUCTION Bridges, which have lightweight, are more vulnerable to heavy weight vehicle. The vibration induced by moving loads makes passengers uncomfortable.

4. Structural Dynamics & Vibration Control Lab., KAIST, Korea 4  Objective of Study Propose passive control device for the improvement of serviceability.

5. Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 FORMULATION OF MATHEMATICAL MODEL  Modeling

6. Structural Dynamics & Vibration Control Lab., KAIST, Korea 6  Equation of Motion  Control Device

7. Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 (1) (2) (3)

8. Structural Dynamics & Vibration Control Lab., KAIST, Korea 8 (4) (5) (6)  Bridge

9. Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 (7) (8)  Multiplying eq.(3) by

10. Structural Dynamics & Vibration Control Lab., KAIST, Korea 10 (9)  Applying orthogonal condition  Substituting mode shape function of beam (10)

11. Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 (11) (12) where

12. Structural Dynamics & Vibration Control Lab., KAIST, Korea 12  Optimization of Device Parameters  Using Pareto Optimization (“Engineering Optimization”, Singiresu S. Rao) (13) When J is minimized, the damping coefficient and spring constant in control device are optimum.

13. Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 NUMERICAL EXAMPLES  Composite Steel Plate Girder Bridge “Generalized of Design for Short Span Steel Bridges Using Rolled Beam”, Magazine of the Korean Society of Steel Construction, vol.14, No.1, pp. 77~82.

14. Structural Dynamics & Vibration Control Lab., KAIST, Korea 14  Geometry and Material Properties  Geometry Bridge Control device Bridge  Material Properties Control device

15. Structural Dynamics & Vibration Control Lab., KAIST, Korea 15 Vehicle velocity Number of modes : 3 Coefficient of Pareto optimization  Parameters

16. Structural Dynamics & Vibration Control Lab., KAIST, Korea 16  Optimization of Device Parameters  The Normed Displacement of Mid-span  As the damping coefficient and spring constant are increased, the normed displacement are decreased.  Max : 46 % reduction

17. Structural Dynamics & Vibration Control Lab., KAIST, Korea 17  The Normed Acceleration of Mid-span  The optimal damping constant exists.  Max : 36 % reduction

18. Structural Dynamics & Vibration Control Lab., KAIST, Korea 18  J of Mid-span

19. Structural Dynamics & Vibration Control Lab., KAIST, Korea 19  Optimal Damping Coefficient and Spring Constant

20. Structural Dynamics & Vibration Control Lab., KAIST, Korea 20  Simulation Results  Displacement of Mid-span  The maximum reduction is 22%.

21. Structural Dynamics & Vibration Control Lab., KAIST, Korea 21  Acceleration of Mid-span  The maximum reduction is 21.1%.

22. Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 mid-span responses Uncontrolled Case Controlled Case Reduction (%) Displacement of mid-span(m) 0.22410.174922.0 Acceleration of mid-span(m/ ) 9.89637.805921.1 Table 1. Performances of proposed control device

23. Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 CONCLUSIONS  Proposed Passive Control Device can control both displacement and acceleration simultaneously. can decay the steady-state responses much faster.  Therefore, proposed passive control device could be effectively used for vibration control of bridges.

24. Structural Dynamics & Vibration Control Lab., KAIST, Korea 24 ACKNOWLEDGEMNT This research is funded by the National Research Laboratory Grant (No.: 2000-N-NL-01-C-251) in Korea. Thank you for your attention!