DOI QR코드

DOI QR Code

Damping enhancement of the inerter on the viscous damper in mitigating cable vibrations

  • Gao, Hui (Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University) ;
  • Wang, Hao (Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University) ;
  • Li, Jian (Department of Civil, Environmental and Architectural Engineering, The University of Kansas) ;
  • Wang, Zhihao (School of Civil Engineering and Communication, North China University of Water Resources and Electric Power) ;
  • Ni, Youhao (Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University) ;
  • Liang, Ruijun (Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University)
  • 투고 : 2020.07.11
  • 심사 : 2021.03.31
  • 발행 : 2021.07.25

초록

This paper systematically investigates the effect of the inerter on the damping enhancement of a cable with a viscous damper (VD) installed close to the cable end. Three cases are considered, including the inerter installed parallel with the VD (PVID), the inerter placed in series with the VD (SVID), and the inerter installed at a higher location of the VD (HVID). The asymptotic solutions of the three cases are derived, which can predict the cable modal damping ratio when the inerter and the VD cause minimal perturbation in the undamped frequency of the cable. The effect of the inerter on the modal behavior of the cable with the VD is investigated. Based on the constrained static output LQR method, the effects of the inerter on the damping enhancement of the VD in mitigating cable multi-mode vibrations are further evaluated. The results show that the inerter can improve the control performance of the VD when the inertance is less than the optimum value. Further increasing the inertance beyond the optimum value, the optimum modal damping ratio of the cable decreases, and mode crossover is observed for the cable with PVID and HVID. Compared with the case where the VD and the inerter are located at the same location, the case of the HVID is more effective in mitigating cable multi-mode vibrations.

키워드

과제정보

The authors greatly acknowledge the financial support from the National Natural Science Foundation of China (51722804, 51878274, 51978155), the National Ten Thousand Talent Program for Young Top-notch Talents (W03070080), and the Project of Scientific Research and Development Plan of China-railway.

참고문헌

  1. Agrawal, A.K. and Yang, J.N. (1999), "Design of passive energy dissipation systems based on LQR control methods", J. Intell. Mater. Syst. Struct., 10(12), 933-944. https://doi.org/10.1106/FB58-N1DG-ECJT-B8H4
  2. Ahmad, J., Cheng, S.H. and Ghrib, F. (2018), "Combined effect of external damper and cross-tie on the modal response of hybrid two-cable networks", J. Sound Vib., 417, 132-148. https://doi.org/10.1016/j.jsv.2017.12.023
  3. Cai, C.S., Wu, W.J. and Araujo, M. (2007), "Cable vibration control with a TMD-MR damper system: experimental exploration", J. Struct. Eng., 133(5), 629-637. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:5(629)
  4. 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., Int. J., 7(5), 293-304. https://doi.org/10.12989/was.2004.7.5.293
  5. Chen, L., Sun, L.M. 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., Nagarajaiah, S. and Sun, L.M. (2021), "A unified analysis of negative stiffness dampers and inerter-based absorbers for multimode cable vibration control", J. Sound Vib., 494: 115814. https://doi.org/10.1016/j.jsv.2020.115814
  7. Christenson, R.E., Spencer, B.F. and Johnson, E.A. (2006), "Experimental verification of smart cable damping", J. Eng. Mech., 132(3), 268-278. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:3(268)
  8. Domenico, D.D. and Ricciardi, G. (2019), "An enhanced base isolation system equipped with optimal tuned mass damper inerter (TMDI)", Earthq. Eng. Struct. D., 47(5), 1169-1192. https://doi.org/10.1002/eqe.3011
  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. Civ. Inf., 20(6), 431-449. https://doi.org/10.1111/j.1467-8667.2005.00396.x
  10. Duan, Y., Ni, Y.Q., Zhang, H., Spencer Jr, B.F., Ko, J.M. and Dong, S. (2019), "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. Fournier, J.A. and Cheng, S.H. (2014), "Impact of damper stiffness and damper support stiffness on the efficiency of a linear viscous damper in controlling stay cable vibrations", J. Bridge Eng., 19(4), 04013022. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000562
  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. Gao, H., Wang, H., Li, J., Wang, Z., Liang, R., Xu, Z. and Ni, Y. (2021), "Optimum design of viscous inerter damper targeting multi-mode vibration mitigation of stay cables", Eng. Struct., 226, 111375. https://doi.org/10.1016/j.engstruct.2020.111375
  14. Giaralis, A. and Petrini, F. (2017), "Wind-induced vibration mitigation in tall buildings using the tuned mass-damperinerter", J. Struct. Eng., 143(9), 04017127. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001863
  15. He, X., Cai, C., Wang, Z., Jing, H. and Qin, C. (2018), "Experimental verification of the effectiveness of elastic cross-ties in suppressing wake-induced vibrations of staggered stay cables", Eng. Struct., 167, 151-165. https://doi.org/10.1016/j.engstruct.2018.04.033
  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. Hu, Y., Chen, M.Z., Shu, Z. and Huang, L. (2015), "Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution", J. Sound Vib., 346, 17-36. https://doi.org/10.1016/j.jsv.2015.02.041
  18. Huang, H.W., Liu, T.T. and Sun, L.M. (2019a), "Multi-mode cable vibration control using MR damper based on nonlinear modeling", Smart Struct. Syst., Int. J., 23(6), 565-577. https://doi.org/10.12989/sss.2019.23.6.565
  19. Huang, Z., Hua, X., Chen, Z. and Niu, H. (2019b), "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
  20. Ikago, K., Saito, K. and Inoue, N. (2012), "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
  21. Jamshidi, M., Chang, C.C. and Bakhshi, A. (2017), "Self-powered hybrid electromagnetic damper for cable vibration mitigation", Smart Struct. Syst., INt. J., 20(3), 285-301. https://doi.org/10.12989/sss.2017.20.3.285
  22. Javanbakht, M., Cheng, S.H. and Ghrib, F. (2020), "Multimode vibration control of stay cables using optimized negative stiffness damper", Struct. Control Health Monit., 27(4), e2503. https://doi.org/10.1002/stc.2503
  23. Jeong, S., Lee, J., Cho, S. and Sim, S.H. (2019), "Integrated cable vibration control system using Arduino", Smart Struct. Syst., Int. J., 23(6), 695-702. https://doi.org/10.12989/sss.2019.23.6.695
  24. Johnson, E.A., Christenson, R.E. and Spencer, B.F. (2003), "Semiactive damping of cables with sag", Comput-Aided. Civil Inf., 18(2), 132-146. https://doi.org/10.1111/1467-8667.00305
  25. Jung, H.J., Spencer Jr, B.F., Ni, Y.Q. and Lee, I.W. (2004), "State-of-the-art of semiactive control systems using MR fluid dampers in civil engineering applications", Struct. Eng. Mech., Int. J., 17(3-4), 493-526. https://doi.org/10.12989/sem.2004.17.3_4.493
  26. 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), 115027. https://doi.org/10.1088/0964-1726/19/11/115027
  27. Kleissl, K. and Georgakis, C.T. (2012), "Comparison of the aerodynamics of bridge cables with helical fillets and a pattern-indented surface", J. Wind Eng. Ind. Aerod., 104, 166-175. https://doi.org/10.1016/j.jweia.2012.02.031
  28. Kovacs, I. (1982), "Zur frage der seilschwingungen und der seildampfung", Die Bautechnik., 59, 325-32. [In German]
  29. 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
  30. Lazar, I.F., Neild, S.A. and Wagg, D.J. (2014), "Using an inerter-based device for structural vibration suppression", Earthq. Eng. Strut. D., 43(8), 1129-1147. https://doi.org/10.1002/eqe.2390
  31. Lazar, I.F., Neild, S.A. and Wagg, D.J. (2016), "Vibration suppression of cables using tuned inerter dampers", Eng. Struct., 122, 62-71. https://doi.org/10.1016/j.engstruct.2016.04.017
  32. Li, H., Liu, M. and Ou, J.P. (2008), "Negative stiffness characteristics of active and semi-active control systems for stay cables", Struct. Control Health Monit., 15(2), 120-142. https://doi.org/10.1002/stc.200
  33. Li, S., Chen, Z., Wu, T. and Kareem, A. (2013), "Rain-wind-induced in-plane and out-of-plane vibrations of stay cables", J. Eng. Mech., 139, 1688-1698. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000612
  34. Li, Y.M., Shen, W.A. and Zhu, H.P. (2019), "Vibration mitigation of stay cables using electromagnetic inertial mass dampers: fullscale experiment and analysis", Eng. Struct., 200, 109693. https://doi.org/10.1016/j.engstruct.2019.109693
  35. Li, J.Y., Zhu, S., Shi, X. and Shen, W. (2020), "Electromagnetic shunt damper for bridge cable vibration mitigation: full-scale experimental study", J. Struct. Eng., 146(1), 04019175. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002477
  36. Liu, M., Yang, W., Chen, W. and Li, H. (2019), "Experimental investigation on multi-mode vortex-induced vibration control of stay cable installed with pounding tuned mass dampers", Smart Struct. Syst., Int. J., 23(6), 579-587. https://doi.org/10.12989/sss.2019.23.6.579
  37. 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
  38. 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
  39. Luo, J.N., Jiang, J.Z. and Macdonald, J.H.G. (2019), "Cable vibration suppression with inerter-based absorbers", J. Eng. Mech., 145(2), 04018134. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001554
  40. Main, J.A. and Jones, N.P. (2002), "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)
  41. Mehrabi, A.B. and Tabatabai, H. (1998), "Unified finite difference formulation for free vibration of cables", J. Struct. Eng., 124(11), 1313-1322. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:11(1313)
  42. Ma, R.S., Bi, K.M. and Hao, H. (2020), "Using inerter-based control device to mitigate heave and pitch motions of semi-submersible platform in the shallow sea", Eng. Struct., 207, 110248. https://doi.org/10.1016/j.engstruct.2020.110248
  43. Ma, R.S., Bi, K.M., Hao, H. (2021), "A novel rotational inertia damper for amplifying fluid resistance: Experiment and mechanical model", Mech. Syst. Signal PR., 149, 107313. https://doi.org/10.1016/j.ymssp.2020.107313
  44. 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
  45. 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
  46. Ni, Y.Q., Wang, X.Y., Chen, Z.Q. and Ko, J.M. (2007), "Field observations of rain-wind-induced cable vibration in cable-stayed Dongting Lake Bridge", J. Wind Eng. Ind. Aerod., 95(5), 303-328. https://doi.org/10.1016/j.jweia.2006.07.001
  47. 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)
  48. Shen, X., Ma, R.J., Ge, C.X. and Hu, X.H. (2018), "Long-term monitoring of super-long stay cables on a cable-stayed bridge", Wind Struct., Int. J., 27(6), 357-368. https://doi.org/10.12989/was.2018.27.6.357
  49. Shi, X. and Zhu, S.Y. (2018), "Dynamic characteristics of stay cables with inerter dampers", J. Sound Vib., 423, 287-305. https://doi.org/10.1016/j.jsv.2018.02.042
  50. Shi, X., Zhu, S., Li, J.Y. and Spencer, B.F. (2016), "Dynamic behavior of stay cables with passive negative stiffness dampers", Smart Mater. Struct., 25(7), 075044. https://doi.org/10.1088/0964-1726/25/7/075044
  51. Shi, X., Zhu, S.Y. and Spencer, B.F. (2017), "Experimental study on passive negative stiffness damper for cable vibration mitigation", J. Eng. Mech., 143(9), 04017070. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001289
  52. Smith, M.C. (2002), "Synthesis of mechanical networks: the inerter", Ieee. T. On. Automat. Contr., 47(10), 1648-1662. https://doi.org/10.1109/TAC.2002.803532
  53. Sun, L.M., Hong, D.X. 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
  54. 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
  55. 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
  56. Wang, H., Mao, J.X. and Xu, Z.D. (2020), "Investigation of dynamic properties of a long-span cable-stayed bridge during typhoon events based on structural health monitoring", J. Wind Eng. Ind. Aerod., 201, 104172. https://doi.org/10.1016/j.jweia.2020.104172
  57. Weber, F. and Distl, H. (2015), "Semi-active damping with negative stiffness for multi-mode cable vibration mitigation: approximate collocated control solution", Smart Mater. Struct., 24(11), 115015. https://doi.org/10.1088/0964-1726/24/11/115015
  58. 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
  59. Zhang, R., Ni, Y.Q., Duan, Y. and Ko, J.M. (2019), "Development of a full-scale magnetorheological damper model for open-loop cable vibration control", Smart Struct. Syst., Int. J., 23(6), 553-564. https://doi.org/10.12989/sss.2019.23.6.553
  60. Zhang, R., Zhao, Z., Pan, C., Ikago, K. and Xue, S. (2020), "Damping enhancement principle of inerter system", Struct. Control Health Monit. 27(5), e2523. https://doi.org/10.1002/stc.2523
  61. 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
  62. Zhou, H., Huang, X., Xiang, N., He, J., Sun, L. and Xing, F. (2018a), "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
  63. Zhou, H., Xiang, N., Huang, X., Sun, L., Xing, F. and Zhou, R. (2018b), "Full-scale test of dampers for stay cable vibration mitigation and improvement measures", Struct. Monit. Maint., Int. J., 5(4), 489-506. https://doi.org/10.12989/smm.2018.5.4.489
  64. Zhu, H., Li, Y., Shen, W. and Zhu, S. (2019), "Mechanical and energy-harvesting model for electromagnetic inertial mass dampers", Mech. Syst. Signal PR., 120, 203-220. https://doi.org/10.1016/j.ymssp.2018.10.023