DOI QR코드

DOI QR Code

Experimental evaluation of an inertial mass damper and its analytical model for cable vibration mitigation

  • Lu, Lei (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Fermandois, Gaston A. (Department of Civil & Environmental Engineering, University of Illinois at Urbana-Champaign) ;
  • Lu, Xilin (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University) ;
  • Spencer, Billie F. Jr. (Department of Civil & Environmental Engineering, University of Illinois at Urbana-Champaign) ;
  • Duan, Yuan-Feng (College of Civil Engineering and Architecture, Zhejiang University) ;
  • Zhou, Ying (State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University)
  • Received : 2016.10.18
  • Accepted : 2018.02.24
  • Published : 2019.06.25

Abstract

Cables are prone to vibration due to their low inherent damping characteristics. Recently, negative stiffness dampers have gained attentions, because of their promising energy dissipation ability. The viscous inertial mass damper (termed as VIMD hereinafter) can be viewed as one realization of the inerter. It is formed by paralleling an inertial mass part with a common energy dissipation element (e.g., viscous element) and able to provide pseudo-negative stiffness properties to flexible systems such as cables. A previous study examined the potential of IMD to enhance the damping of stay cables. Because there are already models for common energy dissipation elements, the key to establish a general model for IMD is to propose an analytical model of the rotary mass component. In this paper, the characteristics of the rotary mass and the proposed analytical model have been evaluated by the numerical and experimental tests. First, a series of harmonic tests are conducted to show the performance and properties of the IMD only having the rotary mass. Then, the mechanism of nonlinearities is analyzed, and an analytical model is introduced and validated by comparing with the experimental data. Finally, a real-time hybrid simulation test is conducted with a physical IMD specimen and cable numerical substructure under distributed sinusoidal excitation. The results show that the chosen model of the rotary mass part can provide better estimation on the damper's performance, and it is better to use it to form a general analytical model of IMD. On the other hand, the simplified damper model is accurate for the preliminary simulation of the cable responses.

Keywords

stay cable;inerter;inertial mass damper;performance test;nonlinearities;real-time hybrid simulation test

Acknowledgement

Supported by : China Scholarship Council, National Natural Science Foundation of China, Universidad Tecnica Federico Santa Maria

References

  1. Audet, C. and Dennis Jr, J.E. (2002), "Analysis of generalized pattern searches", SIAM J. Optim., 13(3), 889-903. https://doi.org/10.1137/S1052623400378742. https://doi.org/10.1137/S1052623400378742
  2. Cai, C.S., Wu, W.J. and Shi, X.M. (2006), "Cable vibration reduction with a hung-on TMD system. Part I: Theoretical study", J. Vib. Control, 12(7), 801-814. https://doi.org/10.1177/1077546306065857. https://doi.org/10.1177/1077546306065857
  3. Carrie, T.G. (1980), "Guy cable design and damping for vertical axis wind turbines", SAND80-2669, National Technical Information Service, US Department of Commerce.
  4. Chen, L., Liu, C., Liu, W., Nie, J., Shen, Y. and Chen, G. (2016a), "Network synthesis and parameter optimization for vehicle suspension with inerter", Adv. Mech. Eng., 9(1), https://doi.org/10.1177/1687814016684704.
  5. Chen, L., Sun, L.M. and Nagarajaiah, S. (2015a), "Cable with discrete negative stiffness device and viscous damper: passive realization and general characteristics", Smart Struct. Syst., 15(3), 627-643. http://dx.doi.org/10.12989/sss.2015.15.3.627. https://doi.org/10.12989/sss.2015.15.3.627
  6. Chen, M.Z., Hu, Y., Li, C. and Chen, G. (2016b), "Application of semi-active inerter in semi-active suspensions via force tracking", J. Vib. Acoust., 138(4), 041014. doi:10.1115/1.4033357. https://doi.org/10.1115/1.4033357
  7. Chen, M.Z., Papageorgiou, C., Scheibe, F., Wang, F.C. and Smith, M.C. (2009), "The missing mechanical circuit element", IEEE Circuits Syst. Magazine, 9(1). doi: 10.1109/MCAS.2008.931738
  8. Chen, Z.Q., Huang, Z.W. and Hua, X.G. (2015b), "Inerter-damperspring passive vibraiton control: its system reliazation with eddy-current mass dampers", Proceedings of the 14th World Conference on Seismic Isolation, Energy dissipation and Active Control of Structures, San Diego, USA.
  9. 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. https://doi.org/10.12989/was.2004.7.5.293
  10. Duan, Y., Tao, J., Zhang, H., Wang, S. and Yun, C. (2019a), "Realtime 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 https://doi.org/10.1002/stc.2277
  11. 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. https://doi.org/10.1111/j.1467-8667.2005.00396.x
  12. Duan, Y.F., Ni, Y.Q. and Ko, J.M. (2006), "Cable vibration control using magnetorheological dampers", J. Intel. Mat. Syst. Struct., 17(4), 321-325. https://doi.org/10.1177/1045389X06054997
  13. Duan, Y.F., Ni, Y.Q., Ko, J.M. and Dong, S.L. (2007), "Design of MR dampers for open-loop vibration control of stay cables on cable supported structures", Spatial Struct., 13(2), 58-64. https://doi.org/10.3969/j.issn.1006-6578.2007.02.012
  14. Duan, Y.F., Ni, Y.Q., Zhang, H.M., Spencer, B.F. Jr. and Ko, J.M. (2019b), "Design formulas for vibration control of sagged cables using passive MR dampers", Smart Struct. Syst., Accepted.
  15. Duan, Y.F., Ni, Y.Q., Zhang, H.M., Spencer, B.F. Jr. and Ko, J.M. (2019c), "Design formulas for vibration control of taut cables using passive MR dampers", Smart Struct. Syst., Accepted.
  16. Firestone, F.A. (1933), "A new analogy between mechanical and electrical systems", J. Acoust. Soc. Am., 4(3), 249-267. https://doi.org/10.1121/1.1915605. https://doi.org/10.1121/1.1915605
  17. 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). https://doi.org/10.1061/(ASCE)0733-9445(2008)134:2(269)
  18. Giaralis, A. and Marian, L. (2016), "Use of inerter devices for weight reduction of tuned mass-dampers for seismic protection of multi-story building: the Tuned Mass-Damper-Interter (TMDI)", SPIE Smart Structures and Materials+Nondestructive Evaluation and Health Monitoring.
  19. Giaralis, A. and Petrini, F. (2017), "Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter (TMDI)", J. Struct. Eng., 143(9), https://doi.org/10.1061/(ASCE)ST.1943-541X.0001863
  20. Gonzalez-Buelga, A., Lazar, I.F., Jiang, J.Z., Neild, S.A. and Inman, D.J. (2017), "Assessing the effect of nonlinearities on the performance of a tuned inerter damper", Struct. Control Health Monit., 24(3), https://doi.org/10.1002/stc.1879.
  21. Gonzalez-Buelga, A., Clare, L., Neild, S., Burrow, S. and Inman, D. (2015), "An electromagnetic vibration absorber with harvesting and tuning capabilities", Struct. Control Health Monit., 22(11), 1359-1372. https://doi.org/10.1002/stc.1748. https://doi.org/10.1002/stc.1748
  22. Gu, M., Xiang, H.F. and Chen, A.R. (1994), "A practical method of passive TMD for suppressing wind-induced vertical buffeting of long-span cable-stayed bridges and its application", J. Wind Eng. Ind. Aerod., 51(2), 203-213. https://doi.org/10.1016/0167-6105(94)90004-3. https://doi.org/10.1016/0167-6105(94)90004-3
  23. Hogsberg, J. and Krenk, S. (2017), "Calibration of piezoelectric RL shunts with explicit residual mode correction", J. Sound Vib., 386, 65-81. https://doi.org/10.1016/j.jsv.2016.08.028. https://doi.org/10.1016/j.jsv.2016.08.028
  24. Hessabi, R.M. and Mercan, O. (2016), "Investigations of the application of gyro-mass dampers with various types of supplemental dampers for vibration control of building structures", Eng. Struct., 126, 174-186. https://doi.org/10.1016/j.engstruct.2016.07.045. https://doi.org/10.1016/j.engstruct.2016.07.045
  25. Horiuchi, T., Nakagawa, M., Sugano, M. and Konno, T. (1996), "Development of a real-time hybrid experimental system with actuator delay compensation", Proceedings of the 11th World Conf. Earthquake Engineering.
  26. Hwang, J.S., Kim, J. and Kim, Y.M. (2007), "Rotational inertia dampers with toggle bracing for vibration control of a building structure", Eng. Struct., 29(6), 1201-1208. https://doi.org/10.1016/j.engstruct.2006.08.005. https://doi.org/10.1016/j.engstruct.2006.08.005
  27. Hjgsberg, J. and Krenk, S. (2016), "Accurate calibration of RL shunts for piezoelectric vibration damping of flexible structures", Proceedings of the 27th International Conference on Adaptive Structures and Technologies (icast 2016).
  28. Ikago, K., Saito, K. and Inoue, N. (2012a), "Seismic control of single-degree-of-freedom structure using tuned viscous mass damper", Earthq. Eng. Struct. D., 41(3), 453-474. https://doi.org/10.1002/eqe.1138. https://doi.org/10.1002/eqe.1138
  29. Ikago, K., Sugimura, Y., Saito, K. and Inoue, N. (2012b), "Modal response characteristics of a multiple-degree-of-freedom structure incorporated with tuned viscous mass dampers", J. Asian Architect. Build. Eng., 11(2), 375-382. https://doi.org/10.3130/jaabe.11.375. https://doi.org/10.3130/jaabe.11.375
  30. Kawaguchi, O., Kanoh, T., Akino, K., Kato, M. and Sunakoda, K. (1991), "Research and development of seismic restraint snubbers,(1)", Nippon Genshiryoku Gakkai-Shi, 33(1), 76-89.
  31. Kawamata, S. (1989), Liquid type mass damper with elongated discharge tube, Google Patents
  32. Kelly, J. (1997), "Experimental study of mechanical pipe snubber seismic behavior".
  33. Kovacs, I. (1982), "Zur frage der seilschwingungen und der seildampfung", Bautechnik, 59(10).
  34. Krenk, S. and Hogsberg, J.R. (2005), "Damping of cables by a transverse force", J. Eng. Mech., 131(4), 340-348. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(340). https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(340)
  35. Krenk, S. and Nielsen, S.R. (2002), "Vibrations of a shallow cable with a viscous damper", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.
  36. Lazar, I., Neild, S. and Wagg, D. (2014a), "Inerter-based vibration suppression systems for laterally and base-excited structures", Proceedings of EURODYN 2014.
  37. Lazar, I., Neild, S. and Wagg, D. (2014b), "Using an inerter-based device for structural vibration suppression", Earthq. Eng. Struct. D., 43(8), 1129-1147. https://doi.org/10.1002/eqe.2390. https://doi.org/10.1002/eqe.2390
  38. Lazar, I., Neild, S. and Wagg, D. (2016), "Vibration suppression of cables using tuned inerter dampers", Eng. Struct., 122, 62-71. https://doi.org/10.1016/j.engstruct.2016.04.017. https://doi.org/10.1016/j.engstruct.2016.04.017
  39. Lazar, I.F., Neild, S.A. and Wagg, D.J. (2014c), Design and performance analysis of inerter-based vibration control systems, Dynamics of Civil Structures, Volume 4, Springer
  40. Lazar, I.F., Neild, S.A. and Wagg, D.J. (2015), Performance analysis of cables with attached tuned-inerter-dampers, Dynamics of Civil Structures, Volume 2, Springer
  41. Liu, Y., Chen, M.Z. and Tian, Y. (2015), "Nonlinearities in landing gear model incorporating inerter", Information and Automation, 2015 IEEE International Conference on.
  42. Lu, L., Duan, Y.F., Spencer, B.F. Jr., Lu, X.L. and Zhou, Y. (2017), "Inertial mass damper for mitigating cable vibration", Struct. Control Health Monit., 24(10), https://doi.org/10.1002/stc.1986.
  43. Luo, J., Jiang, J.Z. and Macdonald, J.H. (2016), "Damping Performance of Taut Cables with Passive Absorbers Incorporating Inerters", J. Phys.: Conference Series.
  44. Main, J. and Jones, N. (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). https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1062)
  45. Main, J. and Jones, N. (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). https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1072)
  46. Makris, N. and Kampas, G. (2016), "Seismic Protection of Structures with Supplemental Rotational Inertia", J. Eng. Mech., 142(11), 04016089. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001152. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001152
  47. Marian, L. and Giaralis, A. (2013), "Optimal design of inerter devices combined with TMDs for vibration control of buildings exposed to stochastic seismic excitations", Proceedings of the 11th International Conference on Structural Safety and Reliability for Integrating Structural Analysis, Risk and Reliability (ICOSSAR 2013).
  48. Marian, L. and Giaralis, A. (2014), "Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems", Probabilist. Eng. Mech., 38, 156-164. https://doi.org/10.1016/j.probengmech.2014.03.007. https://doi.org/10.1016/j.probengmech.2014.03.007
  49. Nakamura, Y., Fukukita, A., Tamura, K., Yamazaki, I., Matsuoka, T., Hiramoto, K. and Sunakoda, K. (2014), "Seismic response control using electromagnetic inertial mass dampers", Earthq. Eng. Struct. D., 43(4), 507-527. https://doi.org/10.1002/eqe.2355. https://doi.org/10.1002/eqe.2355
  50. Nakamura, Y., Hanzawa, T. and Isoda, K. (2013), "Performancebased placement design of tuned inertial mass dampers", Proceedings of the 13th World Conference on Seismic Isolation, Sendai, Japan.
  51. Nakamura, Y., Watanabe, H. and Kawamata, S. (1988), "Seismic response control of structures by accelerated liquid mass damper", Proceedings of the 9th World Conference on Earthquake Engineering.
  52. Nakashima, M., Kato, H. and Takaoka, E. (1992), "Development of real-time pseudo dynamic testing", Earthq. Eng. Struct. D., 21(1), 79-92. https://doi.org/10.1002/eqe.4290210106. https://doi.org/10.1002/eqe.4290210106
  53. Ohtake, T., Sunakoda, K. and Matsuoka, T. (2006), "Study on vibration control device using power generator", Proceedings of the ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference.
  54. Okamoto, M., Tsuyuki, Y. and Matsui, K. (2017), "Development and application example of rotational inertia mass damper", Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile.
  55. 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. https://doi.org/10.1177/1045389X07085673
  56. 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). https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(1961)
  57. Papageorgiou, C., Houghton, N.E. and Smith, M.C. (2009), "Experimental testing and analysis of inerter devices", J. Dyn. Syst. Meas. Control, 131(1), 011001. doi:10.1115/1.3023120. https://doi.org/10.1115/1.3023120
  58. Papageorgiou, C. and Smith, M.C. (2005), "Laboratory experimental testing of inerters", Proceedings of the Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC'05. 44th IEEE Conference on.
  59. Phillips, B.M. and Spencer, B.F. Jr. (2012), "Model-based feedforward-feedback actuator control for real-time hybrid simulation", J. Struct. Eng., 139(7), 1205-1214. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000606.
  60. Pietrosanti, D., De Angelis, M. and Basili, M. (2017), "Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)", Earthq. Eng. Struct. D., 46(8), 1367-1388. https://doi.org/10.1002/eqe.2861. https://doi.org/10.1002/eqe.2861
  61. Saito, K., Yogo, K., Sugimura, Y., Nakaminami, S. and Park, K. (2004), "Application of rotary inertia to displacement reduction for vibration control system", Proceedings of the 13th World Conference on Earthquake Engineering.
  62. Saitoh, M. (2012), "On the performance of gyro-mass devices for displacement mitigation in base isolation systems", Struct. Control Health Monit., 19(2), 246-259. https://doi.org/10.1002/stc.419. https://doi.org/10.1002/stc.419
  63. Severud, L. and Summers, G. (1980), Design considerations for mechanical snubbers, Hanford Engineering Development Lab., Richland, WA (USA)
  64. Shen, Y., Chen, L., Liu, Y. and Zhang, X. (2016a), "Modeling and optimization of vehicle suspension employing a nonlinear fluid inerter", J. Shock Vib., 2016. http://dx.doi.org/10.1155/2016/2623017. https://doi.org/10.1155/2016/2623017
  65. Shen, Y., Chen, L., Yang, X., Shi, D. and Yang, J. (2016b), "Improved design of dynamic vibration absorber by using the inerter and its application in vehicle suspension", J. Sound Vib., 361, 148-158. https://doi.org/10.1016/j.jsv.2015.06.045. https://doi.org/10.1016/j.jsv.2015.06.045
  66. Smith, M.C. (2002), "Synthesis of mechanical networks: The inerter", IEEE T. Autom. Control, 47(10), 1648-1662. doi:10.1109/TAC.2002.803532. https://doi.org/10.1109/TAC.2002.803532
  67. Sun, X.Q., Chen, L., Wang, S.H., Zhang, X.L. and Yang, X.F. (2016), "Performance investigation of vehicle suspension system with nonlinear ball-screw inerter", Int. J. Autom. Techn., 17(3), 399-408. https://doi.org/10.1007/s12239-016-0041-x
  68. Swift, S., Smith, M.C., Glover, A., Papageorgiou, C., Gartner, B. and Houghton, N.E. (2013), "Design and modelling of a fluid inerter", Int. J. Control, 86(11), 2035-2051. https://doi.org/10.1080/00207179.2013.842263 https://doi.org/10.1080/00207179.2013.842263
  69. 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). https://doi.org/10.1061/(ASCE)1084-0702(2000)5:2(114)
  70. Wang, F.C., Chen, Y.C. and Lee, C.H. (2016), "Design and optimization of inerter layouts for a multi-layers building model", Proceedings of the 2016 55th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE).
  71. Wang, F.C., Hong, M.F. and Lin, T.C. (2011), "Designing and testing a hydraulic inerter", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(1), 66-72. https://doi.org/10.1243/09544062JMES2199
  72. Wang, F.C. and Su, W.J. (2008a), "Inerter nonlinearities and the impact on suspension control", Proceedings of the American Control Conference, 2008.
  73. Wang, F. and Su, W. (2008b), "Impact of inerter nonlinearities on vehicle suspension control", Vehicle Syst. Dyn., 46(7), 575-595. https://doi.org/10.1080/00423110701519031. https://doi.org/10.1080/00423110701519031
  74. 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. https://doi.org/10.1016/j.engstruct.2004.12.013
  75. Watanabe, Y., Ikago, K., Inoue, N., Kida, H., Nakaminami, S., Tanaka, H., Sugimura, Y. and Saito, K. (2012), "Full-scale dynamic tests and analytical verification of a force-restricted tuned viscous mass damper", Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon, Portugal.
  76. Watson, S.C. and Stafford, D.G. (1988), "Cables in trouble", Civil Eng. - ASCE, 58(4), 38-41.
  77. Weber, F., Hogsberg, J. and Krenk, S. (2010), "Optimal tuning of amplitude proportional Coulomb friction damper for maximum cable damping", J. Struct. Eng., 136(2), 123-134. https://doi.org/10.1061/(ASCE)0733-9445(2010)136:2(123). https://doi.org/10.1061/(ASCE)0733-9445(2010)136:2(123)
  78. Wen, Y., Chen, Z. and Hua, X. (2016), "Design and evaluation of tuned inerter-based dampers for the seismic control of MDOF structures", J. Struct. Eng., 04016207.
  79. Wu, W.J. and Cai, C.S. (2006), "Cable vibration reduction with a hung-on TMD system, Part II: parametric study", J. Vib. Control, 12(8), 881-899. https://doi.org/10.1177/1077546306065858. https://doi.org/10.1177/1077546306065858
  80. Xu, Y.L. and Yu, Z. (1998), "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. https://doi.org/10.1006/jsvi.1998.1630
  81. Yamaguchi, H. and Fujino, Y. (1998), "Stayed cable dynamics and its vibration control", Bridge Aerod., 235-254.
  82. 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
  83. Zhang, S.Y., Jiang, J.Z. and Neild, S. (2016), "Passive vibration suppression using inerters for a multi-storey building structure", Journal of Physics: Conference Series.
  84. Zhang, S.Y., Jiang, J.Z. and Neild, S. (2017), "Optimal configurations for a linear vibration suppression device in a multi-storey building", Struct. Control Health Monit., 24(3), https://doi.org/10.1002/stc.1887.
  85. 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. https://doi.org/10.1260/1369-4332.17.2.265