The flexibility and low damping of the long span suspended cables in suspension bridges make them prone to non-linear vibrations due to wind and moving loads. In this paper we consider the dynamic response of a suspension bridge due to a vertical load moving with a constant speed on the bridge deck. Control mechanisms are suggested to generate control forces to control the non-linear vibrations in the bridge deck and the suspended cables. A simple design is presented for the controller based on the feedback of the velocity measurements taken at the control force location. The design is made first on a linear model before applying it to the actual non-linear system. The method is applied on three different types of control mechanisms. Comparison between the controlled responses using the three controllers indicates that, in addition to the method of designing the control actions, the feasibility of the active control depends mainly on the type of the control mechanism.
Abdel-Rohman, M. , 1986, “Active control of distributed parameters structures by point-wise control actions,” in Proceedings of the 3rd ASCE Dynamic Response of Structures, Engineering Mechanics Specialty Conference, Los Angeles, CA, pp. 756-763 .
2.
Abdel-Rohman, M. , 1987, “Time delay effect in actively damped structures,”ASCE Journal of Engineering Mechanics, 113, 1709-1719 .
3.
Abdel-Rohman, M. and Askar, H. , 1994, “Active control of non-linear vibrations in cable-stayed bridges by tendons,”Journal of Kuwait University, Science21, 153-166 .
4.
Abdel-Rohman, M. and Askar, H. , 1996, “Control by passive TMD of wind-induced vibrations in cable-stayed bridges by tendons,”Journal of Vibration and Control2, 251-267 .
5.
Abdel-Rohman, M. and Leipholz, H. H. , 1978, “Structural control by the pole assignment method,”ASCE Journal of Engineering Mechanics, 104, 1159-1175 .
6.
Abdel-Rohman, M. and Leipholz, H. H. , 1984, “Optimal feedback control of elastic distributed parameter structures,”Computers & Structures19(5/6), 801-805 .
7.
Abdel-Rohman, M. and Nayfeh, A. H. , 1987, “Active control of non-linear oscillations in bridges,”ASCE Journal of Engineering Mechanics, 113(EM2), 335-348 .
8.
Abdel-Rohman, M. and Spencer, B. F. , 2004, “Control of wind-induced non-linear oscillations in suspended cables,”Nonlinear Dynamics37(4), 341-355 .
9.
Agrawal, A. K. , Yang, J. N. , and He, W. L. , 2003, “Applications of some semi-active control systems to benchmark cable-stayed bridges,”Journal of Structural Engineering129(7), 884-894 .
10.
Anderson, B. O. D. and Moore, J. B. , 1990, Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, NJ .
11.
Balas, M. J. , 1979, “Direct velocity feedback control of large space structures,”Journal of Guidance, Control and Dynamics2(3), 252-253 .
12.
Chang, C. C. , Gu, M. , and Tang, K. H. , 2003, “Tuned mass dampers for dual-mode buffeting control of bridges,”Journal of Bridge Engineering8(4), 237-240 .
13.
del Arco, D. C. and Aparicio, A. C. , 1999, “Improving suspension bridge wind stability with aerodynamic appendages,”Journal of Structural Engineering125(12), 1367-1375 .
14.
Dyke, S.J. , Caicedo, J.M. , Tauran, G. , Bergman, L.A. , and Hague, S. , 2003, “Phase I benchmark control problem for seismic response of cable-stayed bridges,”Journal of Structural Engineering: Special Issue on Semi-Active Control129(7).
15.
Huynh, T. and Thoft-Christensen, P. , 2001, “Suspension bridge flutter for girders with separate control flaps,”ASCE Journal of Bridge Engineering, 6(3), 168-175 .
16.
Irvine, M. , 1992, Cable Structures, Dover, New York .
17.
Johnson, E. A. , Christenson, R. E. , and Spencer, B. F. , 2003, “Semi-active damping of cables with sag,”Computer-Aided Civil and Infrastructure Engineering18(2), 132-146 .
18.
Lee, C. L. and Perkins, N. C. , 1992, “Non-linear oscillations of suspended cables containing a two-to-one internal resonance,”Nonlinear Dynamics3, 465-490 .
19.
Leipholz, H. H. and Abdel-Rohman, M. , 1986, Control of Structures, Martinus Nijhoff, Boston, MA .
20.
Lin, F. , 1997, Robust Control Design: An Optimal Control Approach, AFI Press .
21.
Luongo, A. and Piccardo, G. , 1998, “Non-linear galloping of sagged cables in 1:2 internal resonance,”Journal of Sound and Vibration214(5), 915-940 .
22.
Mahmoud, M. S. , Hassan, M. F. , and Darwish, M. G. , 1985, Large-Scale Control Systems: Theories and Techniques, Dekker, New York .
23.
Murphy, T. P. and Collins, K. R. , 2004, “Retrofitting suspension bridges using distributed dampers,”Journal of Structural Engineering130(10), 1466-1474 .
24.
Nayfeh, A. H. and Mook, D. T. , 1979, Non-linear Oscillations, Wiley, NewYork .
25.
Park, K. S. , Jung, H. J , Spencer B. F. , and Lee, I. W. , 2003, “Hybrid control systems for seismic protection of a phase II benchmark cable-stayed bridge,”Journal of Structural Control: Special Issue on the Cable Stayed Bridge Seismic Benchmark Control Problem10(3-4), 231-247 .
26.
Phongkumising, S. , Wilde, K. , and Fujino, Y. , 2001, “Analytical study on flutter suppression by eccentric mass method on FEM model of large-span suspension bridge,”Journal of Wind Engineering and Industrial Aerodynamics89, 515-534 .
27.
Preumont, A. and Frederic B. , 2002, “Active tendon control of cable-stayed bridges: theory and implementation,” in Proceedings of IMAC-XX Conference on Structural Dynamics, the International Society for Optical Engineering, Los Angeles, CA, Vol. 4753, pp. 663-669 .
28.
Rao, G. V. and Iyengar, R. N. , 1991, “Internal resonance and non-linear response of a cable under periodic excitation,”Journal of Sound and Vibration149(1), 25-41 .
29.
Spencer, B. F. and Nagarajaiah, S. , 2003, “State of the art of structural control,”Journal of Structural Engineering129(7), 845-856 .
30.
Thoft-Christensen, P. , 2001, “Improving the dynamics of suspension bridges using active control systems,” in Proceedings of the 2nd International Workshop on Life-Cycle Cost Analysis and Design of Civil Infrastructure Systems, Ube, Yamaguchi, Japan, pp. 293-304 .
31.
Wilde, K. , Omenzetter, P. , and Fujino, Y. , 2001, “Suppression of bridge flutter by active deck-flaps control system,”Journal of Engineering Mechanics127(1), 80-89 .
32.
Zeribi, M. , Almutairy, N. , Abdel-Rohman, M. , and Terro, M. , 2004, “Non-linear and robust control schemes for offshore steel jacket platforms,”Nonlinear Dynamics35, 61-80 .
