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Cable vibration control with internal and external dampers: Theoretical analysis and field test validation

  • Di, Fangdian (Department of Bridge Engineering, Tongji University) ;
  • Sun, Limin (Department of Bridge Engineering, Tongji University) ;
  • Chen, Lin (Department of Bridge Engineering, Tongji University)
  • Received : 2019.10.19
  • Accepted : 2020.08.22
  • Published : 2020.11.25
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Abstract

For vibration control of stay cables in cable-stayed bridges, viscous dampers are frequently used, and they are regularly installed between the cable and the bridge deck. In practice, neoprene rubber bushings (or of other types) are also widely installed inside the cable guide pipe, mainly for reducing the bending stresses of the cable near its anchorages. Therefore, it is important to understand the effect of the bushings on the performance of the external damper. Besides, for long cables, external dampers installed at a single position near a cable end can no longer provide enough damping due to the sag effect and the limited installation distance. It is thus of interest to improve cable damping by additionally installing dampers inside the guide pipe. This paper hence studies the combined effects of an external damper and an internal damper (which can also model the bushings) on a stay cable. The internal damper is assumed to be a High Damping Rubber (HDR) damper, and the external damper is considered to be a viscous damper with intrinsic stiffness, and the cable sag is also considered. Both the cases when the two dampers are installed close to one cable end and respectively close to the two cable ends are studied. Asymptotic design formulas are derived for both cases considering that the dampers are close to the cable ends. It is shown that when the two dampers are placed close to different cable ends, their combined damping effects are approximately the sum of their separate contributions, regardless of small cable sag and damper intrinsic stiffness. When the two dampers are installed close to the same end, maximum damping that can be achieved by the external damper is generally degraded, regardless of properties of the HDR damper. Field tests on an existing cable-stayed bridge have further validated the influence of the internal damper on the performance of the external damper. The results suggest that the HDR is optimally placed in the guide pipe of the cable-pylon anchorage when installing viscous dampers at one position is insufficient. When an HDR damper or the bushing has to be installed near the external damper, their combined damping effects need to be evaluated using the presented methods.

Keywords

Acknowledgement

This study was partly supported by the National Natural Science Foundation of China (Grant nos. 51978506, 51608390), which is gratefully acknowledged.

References

  1. Caracoglia, L. and Jones, N.P. (2007), "Damping of taut-cable systems: Two dampers on a single stay", J. Eng. Mech., 133(10), 1050-1060. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:10(1050).
  2. Carne, T.G. (1981), "Guy cable design and damping for vertical axis wind turbines", Technical Report No. SAND80-2669, Sandia National Laboratories, Albuquerque, Mexico.
  3. Chen, L. and Sun, L. (2016), "Steady-state analysis of cable with nonlinear damper via harmonic balance method for maximizing damping", J. Struct. Eng., 143(2), 04016172. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001645.
  4. Chen, Z.Q., Wang, X.Y., Ko, J.M., Ni, Y.Q., Spencer Jr, B.F. and Yang, G. (2003), "MR damping system on Dongting lake cablestayed bridge", Proceedings of the Smart Structures and Materials 2003: Smart Systems and Nondestructive Evaluation for Civil Infrastructures: International Society for Optics and Photonics, San Diego, USA, June. https://doi.org/10.1117/12.498072.
  5. Chen, L., Sun, L. and Nagarajaiah, S. (2015), "Cable with discrete negative stiffness device and viscous damper: Passive realization and general characteristics", Smart Struct. Syst., Int. J., 15(3), 627-643. http://dx.doi.org/10.12989/sss.2015.15.3.627.
  6. Chen, L., Sun, L. and Nagarajaiah, S. (2016), "Cable vibration control with both lateral and rotational dampers attached at an intermediate location", J. Sound Vib., 377, 38-57. https://doi.org/10.1016/j.jsv.2016.04.028.
  7. Chen, L., Di, F., Xu, Y., Sun, L., Xu, Y. and Wang, L. (2020), "Multimode cable vibration control using a viscous-shear damper: Case studies on the Sutong bridge", Struct. Control Health Monit., 27(6), e2536. https://doi.org/10.1002/stc.2536.
  8. Cu, V.H., Han, B. and Wang, F. (2015), "Damping of a taut cable with two attached high damping rubber dampers", Struct. Eng. Mech., Int. J., 55(6), 1261-1278. https://doi.org/10.12989/sem.2015.55.6.1261.
  9. De Sa Caetano, E. (2007), Cable Vibrations in Cable-stayed Bridges, Zurich, Switzerland.
  10. Duan, Y., Ni, Y.Q., Zhang, H., Spencer Jr, B.F., Ko, J.M. and Dong, S. (2019a), "Design formulas for vibration control of sagged cables using passive MR dampers", Smart Struct. Syst., Int. J., 23(6), 537-551. https://doi.org/10.12989/sss.2019.23.6.537.
  11. Duan, Y., Ni, Y.Q., Zhang, H., Spencer Jr, B.F., Ko, J.M. and Fang, Y. (2019b), "Design formulas for vibration control of taut cables using passive MR dampers", Smart Struct. Syst., Int. J., 23(6), 521-536. https://doi.org/10.12989/sss.2019.23.6.521.
  12. Fujino, Y. and Hoang, N. (2008), "Design formulas for damping of a stay cable with a damper", J. Struct. Eng., 134(2), 269-278. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:2(269).
  13. Fujino, Y., Kichiro, K. and Tanaka, H. (2012), Wind Resistant Design of Bridges in Japan, Springer, Tokyo, Japan.
  14. Hikami, Y. and Shiraishi, N. (1988), "Rain-wind induced vibrations of cables stayed bridges", J. Wind Eng. Ind. Aerodyn., 29(1-3), 409-418. https://doi.org/10.1016/0167-6105(88)90179-1.
  15. Hoang, N. and Fujino, Y. (2007), "Analytical study on bending effects in a stay cable with a damper", J. Eng. Mech., 133(11), 1241-1246. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:11(1241).
  16. Hoang, N. and Fujino, Y. (2008), "Combined damping effect of two dampers on a stay cable", J. Bridge. Eng., 13(3), 299-303. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:3(299).
  17. Huang, Z., Hua, X., Chen, Z. and Niu, H. (2019), "Performance evaluation of inerter-based damping devices for structural vibration control of stay cables", Smart Struct. Syst., Int. J., 23(6), 615-626. https://doi.org/10.12989/sss.2019.23.6.615.
  18. Irvine, H.M. (1981), Cable Structures, MIT Press, Cambridge, MA, USA.
  19. Irvine, H.M. and Caughey, T.K. (1974), "The linear theory of free vibrations of a suspended cable", Proc. R. Soc. A, 341(1626), 299-315. https://doi.org/10.1098/rspa.1974.0189.
  20. Kovacs, I. (1982), "Zur frage der seilschwingungen und der seildämpfung", Bautechnik, 59(10), 325-332. https://doi.org/view/1035863.
  21. 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.
  22. Krenk, S. and Nielsen, S.R. (2002), "Vibrations of a shallow cable with a viscous damper", Proc. R. Soc. A, 458(2018), 339-357. https://doi.org/10.1098/rspa.2001.0879.
  23. Lu, L., Duan, Y.F., Spencer Jr, B.F., Lu, X. and Zhou, Y. (2017), "Inertial mass damper for mitigating cable vibration", Struct. Control Health Monit., 24(10), e1986. https://doi.org/10.1002/stc.1986.
  24. Lu, L., Fermandois, G.A., Lu, X., Spencer Jr, B.F., Duan, Y.F. and Zhou, Y. (2019), "Experimental evaluation of an inertial mass damper and its analytical model for cable vibration mitigation", Smart Struct. Syst., Int. J., 23(6), 589-613. https://doi.org/10.12989/sss.2019.23.6.589.
  25. Main, J.A. (2002), "Modeling the vibrations of a stay cable with attached damper", Ph.D. Dissertation, Johns Hopkins University, Baltimore, USA.
  26. Main, J.A. and Jones, N.P. (2002a), "Free vibrations of taut cable with attached damper. I: Linear viscous damper", J. Eng. Mech., 128(10), 1062-1071. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1062).
  27. Main, J.A. and Jones, N.P. (2002b), "Free vibrations of taut cable with attached damper. II: Nonlinear damper", J. Eng. Mech., 128(10), 1072-1081. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1072).
  28. Main, J.A. and Jones, N.P. (2003), "Influence of rubber bushings on stay-cable damper effectiveness", Proceedings of Fifth International Symposium on Cable Dynamics, Santa Margherita Ligure, Italy, September.
  29. Main, J.A. and Jones, N.P. (2007), "Vibration of tensioned beams with intermediate damper. I: Formulation, influence of damper location", J. Eng. Mech., 133(4), 379-388. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:4(369).
  30. Matsumoto, M., Yagi, T., Shigemura, Y. and Tsushima, D. (2001), "Vortex-induced cable vibration of cable-stayed bridges at high reduced wind velocity", J. Wind Eng. Ind. Aerodyn., 89(7-8), 633-647. https://doi.org/10.1016/S0167-6105(01)00063-0.
  31. Nakamura, A., Kasuga, A. and Arai, H. (1998), "The effects of mechanical dampers on stay cables with high-damping rubber", Constr. Build. Mater., 12(2-3), 115-123. https://doi.org/10.1016/S0950-0618(97)00013-5.
  32. Nielsen, S.R. and Krenk, S. (2003), "Whirling motion of a shallow cable with viscous dampers", J. Sound Vib., 265(2), 417-435. https://doi.org/10.1016/S0022-460X(02)01455-4.
  33. Pacheco, B.M., Fujino, Y. and Sulekh, A. (1993), "Estimation curve for modal damping in stay cables with viscous damper", J. Struct. Eng., 119(6), 1961-1979. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(1961).
  34. Sun, L. and Chen, L. (2015), "Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives", J. Sound Vib., 335, 19-33. https://doi.org/10.1016/j.jsv.2014.09.016.
  35. Sun, L. and Huang, H. (2008), "Design, implementation and measurement of cable dampers for large cable-stayed bridges", IABSE Congress Rep., 17(16), 242-243.
  36. Sun, L., Hong, D. and Chen, L. (2017), "Cables interconnected with tuned inerter damper for vibration mitigation", Eng. Struct., 151, 57-67. https://doi.org/10.1016/j.engstruct.2017.08.009.
  37. Sun, L., Hong, D. and Chen, L. (2019a), "In‐plane free vibrations of shallow cables with cross‐ties", Struct. Control Health Monit., 26(10), e2421. https://doi.org/10.1002/stc.2421.
  38. Sun, L., Xu, Y. and Chen, L. (2019b), "Damping effects of nonlinear dampers on a shallow cable", Eng. Struct., 196, 109305. https://doi.org/10.1016/j.engstruct.2019.109305.
  39. 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).
  40. 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. Aerodyn., 69, 807-818. https://doi.org/10.1016/S0167-6105(97)00207-9.
  41. Uno, K., Kitagawa, S., Tsutsumi, H., Inoue, A. and Nakaya, S. (1991), "A simple method of designing cable vibration dampers of cable-stayed bridges", J. Struct. Eng., 37(1991), 789-798.
  42. Wang, X.Y., Ni, Y.Q., Ko, J.M. and Chen, Z.Q. (2005), "Optimal design of viscous dampers for multimode vibration control of bridge cables", Eng. Struct., 27(5), 792-800. https://doi.org/10.1016/j.engstruct.2004.12.013.
  43. 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., Int. J., 23(6), 627-639. https://doi.org/10.12989/sss.2019.23.6.627.
  44. Weber, F., Feltrin, G., Maslanka, M., Fobo, W. and Distl, H. (2009), "Design of viscous dampers targeting multiple cable modes", Eng. Struct., 31(11), 2797-2800. https://doi.org/10.1016/j.engstruct.2009.06.020.
  45. Xu, Y.L. and Yu, Z. (1998a), "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).
  46. Xu, Y.L. and Yu, Z. (1998b), "Mitigation of three-dimensional vibration of inclined sag cable using disrete oil dampers-II. Application", J. Sound Vib., 214(4), 675-693. https://doi.org/10.1006/jsvi.1998.1630.
  47. Yoneda, M. and Maeda, K. (1989), "A study on practical estimation method for structural damping of stay cables with dampers", Doboku Gakkai Ronbunshu, 1989(410), 455-458. https://doi.org/10.2208/jscej.1989.410_455.
  48. Yoneda, M., Mochizuki, H. and Setouchi, H. (1995), "On the simplified method for estimating modal damping in stay cable with two types of dampers and its application to vibration control design", Doboku Gakkai Ronbunshu, 1995(516), 183-196. https://doi.org/10.2208/jscej.1995.516-183.
  49. Yu, Z. and Xu, Y.L. (1998), "Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers-I. Formulation", J. Sound Vib., 214(4), 659-673. https://doi.org/10.1006/jsvi.1998.1609.
  50. Zhou, P. and Li, H. (2016), "Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations", Struct. Control Health Monit., 23(4), 764-782. https://doi.org/10.1002/stc.1809.
  51. Zhou, Y. and Sun, L. (2006), "Complex modal analysis of a taut cable with three-element Maxwell damper", J. Tongji Univ., 34(1), 7-12. https://doi.org/10.3321/j.issn:0253-374X.2006.01.002
  52. Zhou, H., Sun, L. and Xing, F. (2014), "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.