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

  • Duan, Yuanfeng (Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University) ;
  • Ni, Yi-Qing (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University) ;
  • Zhang, Hongmei (Department of Civil Engineering, 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) ;
  • Dong, Shenghao (Department of Civil Engineering, College of Civil Engineering and Architecture, Zhejiang University)
  • 투고 : 2018.08.12
  • 심사 : 2018.12.30
  • 발행 : 2019.06.25

초록

In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Ministry of Science and Technology of China, Council of the Hong Kong Special Administrative Region, Hong Kong Polytechnic University

참고문헌

  1. Caracoglia, L. and Jones, N.P. (2007), "Damping of tautcable systems: Two dampers on a single stay", J. Eng. Mech. - ASCE, 133(10), 1050-1060. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:10(1050).
  2. Chen, Z.Q., Wang, X.Y., Ko, J.M., Ni, Y.Q., Spencer, B.F., 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.
  3. Cheng, S., Darivandi, N. and Ghrib, F. (2010), "The design of an optimal viscous damper for a bridge stay cable using energybased approach", J. Sound Vib., 329(22), 4689-4704. https://doi.org/10.1016/j.jsv.2010.05.027.
  4. Chen, Z.H., Lam, K. and Ni, Y.Q. (2016), "Enhanced damping for bridge cables using a self-sensing MR damper", Smart Mater. Struct., 25(8), 085019. https://doi.org/10.1088/0964-1726/25/8/085019
  5. Cremona, C. (2001), "A generalisation of the Pacheco's curve for linear damper design", Proceedings of the 4th International Symposium on Cable Dynamics, Liege.
  6. Cu, V.H., Han, B. and Pham, D.H. (2016), "Tuned masshigh damping rubber damper on a taut cable", J. Civil Eng.-KSCE, 21(3), 928-936.
  7. Cu, V.H., Han, B. and Wang, F. (2015),"Damping of a taut cable with two attached high damping rubber dampers", Struct. Eng. Mech., 55(6), 1261-1278. https://doi.org/10.12989/sem.2015.55.6.1261.
  8. 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.
  9. 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(6), 431-449. https://doi.org/10.1111/j.1467-8667.2005.00396.x.
  10. Duan, Y.F., Ni, Y.Q. and Ko, J.M. (2006), "Cable vibration control using magnetorheological dampers", J. Intel. Mat. Syst. Str., 17(4), 321-325. https://doi.org/10.1177/1045389X06054997
  11. Duan, Y.F., Ni, Y.Q., Zhang, H.M., Spencer, B.F., Jr., Ko, J.M. and Fang Y. (2019), "Design formulas for vibration control of taut cables using passive MR dampers", Smart Struct. Syst., Accepted.
  12. 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., e2277; https://doi.org/10.1002/stc.2277.
  13. 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.
  14. Huang, H., 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. http://dx.doi.org/10.12989/sss.2015.16.6.1003.
  15. Irvine, H.M. (1981), Cable Structures, MIT Press, Cambridge.
  16. Irvine, H.M. and Caughey, T.K. (1974), "The linear theory of free vibrations of a suspended cable", Proceedings of the Royal Society of London, 341(1626), 299-315. https://doi.org/10.1098/rspa.1974.0189.
  17. Irwin, P.A. (1997), "Wind vibrations of cables on cable-stayed bridges", Building to Last, 383-387.
  18. Johnson, E.A., Spencer, 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.
  19. Johnson, E.A., Christenson, R.E. and Spencer, 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.
  20. Johnson, E.A., Baker, G.A., Spencer, B.F. and Fujino, Y. (2007), "Semiactive damping of stay cables", J. Eng. Mech. -ASCE, 133(1), 1-11. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:1(1).
  21. Ko, J.M., Ni, Y.Q., Chen, Z.Q. and Spencer, B.F. (2002), "Implementation of MR dampers to Dongting Lake Bridge for cable vibration mitigation", Proceedings of the 3rd World Conference on Structural Control, Chichester.
  22. Kovacs I. (1982), "Zur frage der seilschwigungen und der seildampfung", Die Bautechnik, 59, 325-32 (in German).
  23. Krenk, S. (2000), "Vibrations of a taut cable with an external damper", J. Appl. Mech., 67(4), 772-776. https://doi.org/10.1115/1.1322037
  24. Krenk, S. and Nielsen, S.R. (2001), "Vibrations of a shallow cable with a viscous damper", Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458(2018), 339-357. https://doi.org/10.1098/rspa.2001.0879.
  25. 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.
  26. Krenk, S. and Hogsberg, J.R. (2005), "Damping of cables by a transverse force", J. Eng. Mech. -ASCE, 131(4), 340-348. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(340).
  27. Lu, L., Duan, Y.F., Spencer, B.F., Lu, X. and Zhou, Y. (2017), "Inertial mass damper for mitigating cable vibration", Struct. Control Health Monit., 24(10). https://doi.org/10.1002/stc.1986.
  28. 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).
  29. 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).
  30. Maslanka, M., Sapinski, B. and Snamina, J. (2007), "Experimental study of vibration control of a cable with an attached MR damper", J. Theor. Appl. Mech., 45(4), 893-917.
  31. Or, S.W., Duan, Y.F., Ni, Y.Q., Chen, Z.H. and Lam, K. (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.
  32. 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(6), 1961-1979. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(1961).
  33. Powell, J.A. (1994), "Modelling the oscillatory response of an electrorheological fluid", Smart Mater. Struct., 3(4), 416. https://doi.org/10.1088/0964-1726/3/4/005
  34. Sun, L.M. and Chen, L. (2015), "Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivative", J. Sound Vib., 335, 19-33. https://doi.org/10.1016/j.jsv.2014.09.016.
  35. Tabatabai, H. and Mehrabi, A.B. (2000), "Design of mechanical viscous dampers for stay cables", J. Bridge Eng., 5(2), 114-123. https://doi.org/10.1061/(ASCE)1084-0702(2000)5:2(114).
  36. Tanaka H. (2003), "Aerodynamics of cables", Proceedings of the 5th International Symposium on Cable Dynamics, Italy, Sep.
  37. 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.
  38. 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.s-Basel, 8(1), 118. https://doi.org/10.3390/app8010118.
  39. 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.
  40. Wu, W.J. and Cai, C.S. (2007), "Theoretical exploration of a taut cable and a TMD system", Eng. Struct., 29(6), 962-972. https://doi.org/10.1016/j.engstruct.2006.07.009.
  41. Xu, Y.L. and Yu, Z. (1998), "Vibration of inclined sag cables with oil dampers in cable-stayed bridges", J. Bridge Eng., 3(4), 194-203. https://doi.org/10.1061/(ASCE)1084-0702(1998)3:4(194).
  42. 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.
  43. Yamada, H. (1997), "Control of wind-induced cable vibrations from a viewpoint of wind resistant design of cable-stayed bridges", Proceedings of Int. Seminar on Cable Dynamics, Tokyo, Oct.
  44. Yoneda M. and Maeda K. (1989), "A study on practical estimation method for structural damping of stay cable with dampers", In Proceedings of Canada-Japan Workshop on Bridge Aerodynamics, Canada.
  45. 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.
  46. Zhou, H.J., Huang, X.G., 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), e2251. https://doi.org/10.1002/stc.2251.
  47. 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.
  48. Zhou, H.J., Sun, L.M. and Xing, F. (2014a), "Free vibration of taut cable with a damper and a spring", Struct. Control Health Monit., 21(6):996-1014. https://doi.org/10.1002/stc.1628.
  49. Zhou, H.J., Sun, L.M. and Xing, F. (2014b), "Damping of fullscale 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.
  50. 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.
  51. Zhou, Q., Nielsen, S.R.K. and Qu, W.L. (2006), "Semi-active control of three-dimensional vibrations of an inclined sag cable with magnetorheological dampers", J. Sound Vib., 296(1-2), 1-22. https://doi.org/10.1016/j.jsv.2005.10.028.
  52. Zhou, Q., Nielsen, S.R.K. and Qu, W.L. (2008), "Semi-active control of shallow cables with magnetorheological dampers under harmonic axial support motion", J. Sound Vib., 311(3-5), 683-706. https://doi.org/10.1016/j.jsv.2007.09.022.

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