Browse > Article
http://dx.doi.org/10.12989/sss.2019.23.6.521

Design formulas for vibration control of taut cables using passive MR dampers  

Duan, Yuanfeng (College of Civil Engineering and Architecture, Zhejiang University)
Ni, Yi-Qing (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University)
Zhang, Hongmei (College of Civil Engineering and Architecture, Zhejiang University)
Spencer, Billie.F. Jr. (Department of Civil and Environmental Engineering, The University of Illinois at Urbana-Champaign)
Ko, Jan-Ming (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University)
Fang, Yi (College of Civil Engineering and Architecture, Zhejiang University)
Publication Information
Smart Structures and Systems / v.23, no.6, 2019 , pp. 521-536 More about this Journal
Abstract
Using magnetorheological (MR) dampers in multiswitch open-loop control mode has been shown to be cost-effective for cable vibration mitigation. In this paper, a method for analyzing the damping performance of taut cables incorporating MR dampers in open-loop control mode is developed considering the effects of damping coefficient, damper stiffness, damper mass, and stiffness of the damper support. Making use of a three-element model of MR dampers and complex modal analysis, both numerical and asymptotic solutions are obtained. An analytical expression is obtained from the asymptotic solution to evaluate the equivalent damping ratio of the cable-damper system in the open-loop control mode. The individual and combined effects of the damping coefficient, damper stiffness, damper mass and stiffness of damper support on vibration control effectiveness are investigated in detail. The main thrust of the present study is to derive a general formula explicitly relating the normalized system damping ratio and the normalized damper parameters in consideration of all concerned effects, which can be easily used for the design of MR dampers to achieve optimal open-loop vibration control of taut cables.
Keywords
taut cable; vibration mitigation; MR damper; passive control; open-loop control;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Kim, I.H., Jung, H.J. and Koo J.H. (2010), "Experimental evaluation of a self-powered smart damping system in reducing vibrations of a full-scale stay cable", Smart Mater. Struct., 19(11), 11527.
2 Ko, J.M., Ni, Y.Q., Chen, Z.Q. and Spencer, Jr. B.F. (2003), "Implementation of MR dampers to Dongting Lake Bridge for cable vibration mitigation", In: Casciati F, editor. Proceedings of the 3rd World Conference on Structural Control, Chichester, England: John Wiley & Sons, 777-786.
3 Kovacs, I. (1982), "Zur Frage der seilschwingungen und der seildampfung", Die Bautechnik, 10, 325-332, (in German).
4 Krenk, S. (2004), "Complex modes and frequencies in damped structural vibrations", J. Sound Vib., 270(4-5), 981-996. https://doi.org/10.1016/S0022-460X(03)00768-5.   DOI
5 Krenk, S. (2000), "Vibrations of a taut cable with an external damper", J. Appl. Mech. - ASME, 67(4), 772-776. doi:10.1115/1.1322037.   DOI
6 Krenk, S. and Hogsberg, J.R. (2005), "Damping of cables by a transverse force", J. Eng. Mech. - ASCE, 131, 340-348. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(340).   DOI
7 Krenk, S. and Nielsen, S.R.K. (2002), "Vibrations of a shallow cable with a viscous damper", Proceedings of the Royal Society of London, Series A, 458, 339-357. https://doi.org/10.1098/rspa.2001.0879   DOI
8 Li, H., Liu, M., Li, J.H., Guan, X.C. and Ou, J.P. (2007), "Vibration control of stay cables of the Shandong Binzhou Yellow River Highway Bridge using Magnetorheological fluid dampers", J. Bridge Eng., 12(4), 401-409. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:4(401).   DOI
9 Lu, L. and Duan, Y.F., Spencer, B.F. Jr., Lu, X.L. and Zhou, Y. (2017), "Inertial mass damper for mitigating cable vibration", Structural Control Health Monit., 24, e1986, doi:10.1002/stc.1986.   DOI
10 Zhou, H.J. and Sun, L.M. (2013), "Damping of stay cable with passive-on magnetorheological dampers: a full-scale test", Int. J. Civil Eng., 11(3), 154-159.
11 Zhou, H.J., Sun, L.M. and Xing, F. (2014), "Damping of full-scale stay cable with viscous damper: experiment and analysis", Adv. Struct. Eng., 17(2), 265-274. https://doi.org/10.1260/1369-4332.17.2.265.   DOI
12 Matsumoto, M., Saitoh, T., Kitazawa, M., Shirato, H. and Nishizaki, T. (1995), "Response characteristics of rain-wind induced vibration of stay-cables of cable- stayed bridges", J. Wind Eng. Ind. Aerod., 57(2-3), 323-333. https://doi.org/10.1016/0167-6105(95)00010-O.   DOI
13 Main, J.A. and Jones, N.P. (2001), "Evaluation of viscous dampers for stay-cable vibration mitigation", J. Bridge Eng. - ASCE, 6(6), 385-397. https://doi.org/10.1061/(ASCE)1084-0702(2001)6:6(385).   DOI
14 Main, J.A. and Jones, N.P. (2002a), "Free vibrations of taut cable with attached damper. I: linear viscous damper", J. Eng. Mech. - ASCE, 128(10), 1062-1071. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1062).   DOI
15 Main, J.A. and Jones, N.P. (2002b), "Free vibrations of taut cable with attached damper. II: Nonlinear damper", J. Eng. Mech. - ASCE, 128(10), 1072-1081. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1072).   DOI
16 Ni, Y.Q., Wang, X.Y., Chen, Z.Q. and Ko, J.M. (2007), "Field observations of rain-wind-induced cable vibration in cablestayed Dongting Lake Bridge", J. Wind Eng. Ind. Aerod., 95(5), 303-328. https://doi.org/10.1016/j.jweia.2006.07.001.   DOI
17 Matsumoto, M., Shiraishi, N. and Shirato, H. (1992), "Rain-wind induced vibration of cables of cable-stayed bridges", J. Wind Eng. Ind. Aerod., 41-44, 2011-22. https://doi.org/10.1016/0167-6105(92)90628-N.   DOI
18 Miyata, T. (1991), "Design considerations for wind effects on long-span cable-stayed bridges", (Eds., Ito, M., Fujino, Y., Miyata, T., Narita, N.), Cable-Stayed Bridges: Recent Developments and their Future, Amsterdam: Elsevier, 235-256.
19 Ni, Y.Q., Chen, Y., Ko, J.M. and Cao, D.Q. (2002), "Neuro-control of cable vibration using semi-active magneto-rheological dampers", Eng. Struct., 24(3), 295-307. https://doi.org/10.1016/S0141-0296(01)00096-7.   DOI
20 Or, S.W., Duan, Y.F., Ni, Y.Q., Chen, Z.H. and Lam, K.H. (2008), "Development of Magnetorheological dampers with embedded piezoelectric force sensors for structural vibration control", J. Intel. Mat. Syst. Str., 19 (11), 1327-1338. https://doi.org/10.1177/1045389X07085673.   DOI
21 Ou, J.P. (2003), "Some recent advances of intelligent health monitoring systems for civil infrastructures in mainland China", (Eds., Wu, Z.S. and Abe, M.), Structural Health Monitoring and Intelligent Infrastructure, Netherlands: Balkema, 131-144.
22 Pacheco, B.M. and Fujino, Y. (1993), "Keeping cables calm", ASCE Civil Eng., 63(10), 56-58.
23 Pacheco, B.M., Fujino, Y. and Sulekh, A. (1993), "Estimation curve for modal damping in stay cables with viscous damper", J. Struct. Eng.- ASCE, 119, 1961-1979.   DOI
24 Spencer, Jr. B.F., Dyke, S.J., Sain, M.K. and Carlson, J.D. (1997), "Phenomenological model for magnetorheological dampers", J. Eng. Mech. - ASCE, 123(3), 230-238. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(230).   DOI
25 Persoon, A.J. and Noorlander, K. (1999), "Full-scale measurements on the Erasmus Bridge after rain/wind induced cable vibrations", (Eds., Larsen, A., Larose, G.L. and Livesey, F.M.), Wind Engineering into the 21st Century. Rotterdam: Balkema, 1019-1926.
26 Poston, R.W. (1998), "Cable-stay conundrum", ASCE Civil Eng., 68(8), 58-61.
27 Powell, J.A. (1994), "Modeling the oscillatory response of an electrorheological fluid", Smart Mater. Struct., 3(4), 416-438.   DOI
28 Sulekh, A. (1990), Non-Dimensionalized Curves for Modal Damping in Stay Cables with Viscous Dampers, Master thesis, Japan: Department of Civil Engineering, University of Tokyo.
29 Tanaka, H. (2003), "Aerodynamics of cables", Proceedings of the 5th International Symposium on Cable Dynamics. Belgium: AIM, 11-25.
30 Takano, H., Ogasawara, M., Ito, N., Shimosato, T., Takeda, K. and Murakami, T. (1997), "Vibrational damper for cables of the Tsurumi Tsubasa Bridge", J. Wind Eng. Ind. Aerod., 69-71, 807-818. https://doi.org/10.1016/S0167-6105(97)00207-9.   DOI
31 Verwiebe, C. (1998), "Rain-wind-induced vibrations of cables and bars", (Eds., Larsen, A. and Esdahl, S.), Bridge Aerodynamics: Proceedings of the International Symposium on Advances in Bridge Aerodynamics. Rotterdam: Balkema, 255-263.
32 Wang, X.Y., Ni, Y.Q., Ko, J.M. and Chen, Z.Q. (2005), "Optimal design of viscous dampers for multi-mode vibration control of bridge cables", Eng. Struct., 27(5), 792-800. https://doi.org/10.1016/j.engstruct.2004.12.013.   DOI
33 Butz, T. and von Stryk, O. (2002), "Modelling and simulation of electro- and magnetorheological fluid dampers", ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik, 82(1), 3-20. https://doi.org/10.1002/1521-4001(200201)82:1<3::AIDZAMM3>3.0.CO;2-O.   DOI
34 Virlogeux, M. (1998), "Cable vibrations in cable-stayed bridges", (Eds., Larsen, A. and Esdahl, S.), Bridge aerodynamics: Proceedings of the International Symposium on Advances in Bridge Aerodynamics. Rotterdam: Balkema, 213-233.
35 Wang, Z.H., Chen, Z.H., Gao, H. and Wang, H. (2018), "Development of a self-powered magnetorheological damper system for cable vibration control", Appl. Sci. -Basel, 8(1), 118. https://doi.org/10.3390/app8010118.   DOI
36 Wang, Z.H, Xu, Y.W., Gao, H., Chen, Z.Q., Xu, K. and Zhao S.B. (2019), "Vibration control of a stay cable with a rotary electromagnetic inertial mass damper", Smart Struct. Syst., Accepted.
37 Wang, W., Hua, X. and Wang X. (2019), "Mechanical behavior of magnetorheological dampers after long-term operation in a cable vibration control system", Struct. Control Health Monit., 26(1), e2280. https://doi.org/10.1002/stc.2280.   DOI
38 Watson, S.C. and Stafford, D. (1988), "Cables in trouble", ASCE Civil Eng., 58(4), 138-141.
39 Weber, F., Bhowmik, S. and Hogsberg, J. (2014), "Extended neural network-based scheme for real-time force tracking with magnetorheological dampers", Struct. Control Health Monit., 21(2), 225-247. https://doi.org/10.1002/stc.1569.   DOI
40 Huang, H.W., Liu, J.Y. and Sun, L.M. (2015), "Full-scale experimental verification on the vibration control of stay cable using optimally tuned MR damper", Smart Struct. Syst., 16(6), 1003-1021. https://doi.org/10.12989/sss.2015.16.6.1003.   DOI
41 Huang, H.W., Sun, L.M and Jiang X.L. (2012), "Vibration mitigation of stay cable using optimally tuned MR damper", Smart Struct. Syst., 9(1), 35-53. http://dx.doi.org/10.12989/sss.2012.9.1.035.   DOI
42 Huang, Z.H. and Jones N.P. (2011), "Damping of taut-cable systems: effects of linear elastic spring support", J. Eng. Mech., 137(7), 512-518. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000252.   DOI
43 Irwin, P.A. (1997), "Wind vibrations of cables on cable-stayed bridges", (Eds., Kempner, L. Jr., and Brown, C.B.), editors. Building to Last Structures Congress: Proceedings of the 15th Structures Congress, New York: American Society of Civil Engineers, 383-387.
44 Johnson, E.A., Baker, G.A., Spencer Jr. B.F. and Fujino, Y. (2007), "Semiactive damping of stay cables", J. Eng. Mech. - ASCE, 133, 1-11. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:1(1).   DOI
45 Duan, Y.F., Ni, Y.Q. and Ko, J.M. (2006), "Cable vibration control using Magneto-rheological (MR) dampers", J. Intel. Mat. Syst. Str., 17(4), 321-325. https://doi.org/10.1142/9789812702197_0121.   DOI
46 Chen, Z.H., Lam, K.H. and Ni, Y.Q. (2016), "Enhanced damping for bridge cables using a self-sensing MR damper", Smart Mater. Struct., 25(8), 085019.   DOI
47 Chen, Z.Q., Wang, X.Y., Ko, J.M., Ni, Y.Q., Spencer, B.F., Jr., Yang, G. and Hu, J.H. (2004), "MR damping system for mitigating wind-rain induced vibration on Dongting Lake Cable-Stayed Bridge", Wind Struct., 7(5), 293-304. http://dx.doi.org/10.12989/was.2004.7.5.293.   DOI
48 Duan, Y.F. (2004), Vibration Control of Stay Cables Using Semiactive Magneto-rheological (MR) Dampers, PhD thesis, Hong Kong: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong.
49 Duan, Y.F., Ni, Y.Q. and Ko, J.M. (2005), "State-derivative feedback control of cable vibration using semiactive magnetorheological dampers", Comput.-Aided Civil Infrastruct. Eng., 20, 431-449. https://doi.org/10.1111/j.1467-8667.2005.00396.x.   DOI
50 Johnson, E.A., Christenson, R.E. and Spencer, Jr. B.F. (2003), "Semiactive damping of cables with sag", Comput. - Aided Civil Infrastruct. Eng., 18(2), 132-146. https://doi.org/10.1111/1467-8667.00305.   DOI
51 Johnson, E.A., Spencer, Jr. B.F. and Fujino, Y. (1999), "Semiactive damping of stay cables: a preliminary study", Proceedings of the 17th International Modal Analysis Conference, Society for Experimental Mechanics, 417-423.
52 Jung, H.J., Spencer, Jr. B.F., Ni, Y.Q. and Lee, I.W. (2004), "Stateof-the-art of semiactive control systems using MR fluid dampers in civil engineering applications", Struct. Eng. Mech., 17, 493-526. http://dx.doi.org/10.12989/sem.2004.17.3_4.493.   DOI
53 Yamada, H. (1997), "Control of wind-induced cable vibrations from a viewpoint of the wind resistant design of cable-stayed bridges", Proceedings of International Seminar on Cable Dynamics. Tokyo: Japan Association for Wind Engineering, 129-138.
54 Weber, F., Distl, H. and Feltrin, G. (2009), "Cycle energy control of magnetorheological dampers on cables", Smart Mater. Struct., 18(1), 015005.   DOI
55 Duan, Y.F., Ni, Y.Q., Zhang, H.M., Spencer, B.F., Jr., Ko, J.M. and Dong S.H. (2019), "Design formulas for vibration control of sagged cables using passive MR dampers", Smart Struct. Syst., Accepted.
56 Duan, Y.F., Tao, J.J., Zhang, H.M., Wang, S.M. and Yun C.B. (2018), "Real-time hybrid simulation based on vector form intrinsic finite element and field programmable gate array", Struct. Control Health Monit., 26(1), e2277;https://doi.org/10.1002/stc.2277.
57 Guan, X.C., Huang Y., Li, H. and Ou, J.P. (2012), "Adaptive MR damper cable control system based on piezoelectric power harvesting", Smart Struct. Syst., 10(1), 33-46. https://doi.org/10.12989/sss.2012.10.1.033.   DOI
58 Hikami, Y. and Shiraishi, N. (1988), "Rain-wind induced vibrations of cables in cable stayed bridges", J. Wind Eng. Ind. Aerod., 29, 409-418.   DOI
59 Wu, W.J. and Cai, C.S. (2010), "Cable vibration control with a semiactive MR damper-numerical simulation and experimental verification", Struct. Eng. Mech., 34(5), 611-623. https://doi.org/10.12989/sem.2010.34.5.611.   DOI
60 Xu, Y.L. and Zhou, H.J. (2007), "Damping cable vibration for a cable-stayed bridge using adjustable fluid dampers", J. Sound Vib., 306(1-2), 349-360. https://doi.org/10.1016/j.jsv.2007.05.032   DOI
61 Yamaguchi, H. and Fujino, Y. (1998), "Stayed cable dynamics and its vibration control. In: Larsen A., Esdahl S, editors", Bridge aerodynamics: Proceedings of the International Symposium on Advances in Bridge Aerodynamics. Rotterdam: Balkema, 235-253.
62 Zhao, M. and Zhu, W.Q. (2011), "Stochastic optimal semi-active control of stay cables by using magneto-rheological damper", J. Vib. Control, 17(13), 1921-1929. https://doi.org/10.1177/1077546310371263.   DOI
63 Zhou, H.J., Huang X.J., Xiang N., He J.W., Sun, L.M. and Xing, F. (2018), "Free vibration of a taut cable with a damper and a concentrated mass", Struct. Control Health Monit., 25(11), 1-21. https://doi.org/10.1002/stc.2251.
64 Zhou, H.J., Xiang, N. and Huang, X. (2018), "Full-scale test of dampers for stay cable vibration mitigation and improvement measures", Struct. Monit. Maint., 5(4), 489-506. https://doi.org/10.12989/smm.2018.5.4.489.   DOI
65 Weber, F. and Boston, C. (2010), "Energy based optimization of viscous-friction dampers on cables", Smart Mater. Struct., 19(4), 045025.   DOI