Title: Damping of a stay cable with two eddy‐current inertial mass dampers: Theoretical analysis, experimental study, and parameter optimization
Abstract: Structural Control and Health MonitoringVolume 29, Issue 11 e3085 RESEARCH ARTICLE Damping of a stay cable with two eddy-current inertial mass dampers: Theoretical analysis, experimental study, and parameter optimization Zhihao Wang, Corresponding Author Zhihao Wang [email protected] School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, China Correspondence Zhihao Wang, School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, China. Email: [email protected]Search for more papers by this authorZhipeng Cheng, Zhipeng Cheng School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSearch for more papers by this authorHao Wang, Hao Wang Key Laboratory of Concrete and Prestressed Concrete Structure Ministry of Education, Southeast University, Nanjing, ChinaSearch for more papers by this authorFangfang Yue, Fangfang Yue Engineering Vibration Control Technology Research Center, SINOMACH Academy of Science and Technology Co., Ltd, Beijing, ChinaSearch for more papers by this authorHui Gao, Hui Gao Key Laboratory of Concrete and Prestressed Concrete Structure Ministry of Education, Southeast University, Nanjing, ChinaSearch for more papers by this authorBuqiao Fan, Buqiao Fan School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSearch for more papers by this author Zhihao Wang, Corresponding Author Zhihao Wang [email protected] School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, China Correspondence Zhihao Wang, School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, China. Email: [email protected]Search for more papers by this authorZhipeng Cheng, Zhipeng Cheng School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSearch for more papers by this authorHao Wang, Hao Wang Key Laboratory of Concrete and Prestressed Concrete Structure Ministry of Education, Southeast University, Nanjing, ChinaSearch for more papers by this authorFangfang Yue, Fangfang Yue Engineering Vibration Control Technology Research Center, SINOMACH Academy of Science and Technology Co., Ltd, Beijing, ChinaSearch for more papers by this authorHui Gao, Hui Gao Key Laboratory of Concrete and Prestressed Concrete Structure Ministry of Education, Southeast University, Nanjing, ChinaSearch for more papers by this authorBuqiao Fan, Buqiao Fan School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, ChinaSearch for more papers by this author First published: 06 September 2022 https://doi.org/10.1002/stc.3085 Funding information: National Natural Science Foundation of China, Grant/Award Number: 51878274 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Recent studies have demonstrated that inerter-based dampers exhibit superior performance in mitigating cable vibration over conventional passive viscous dampers (VDs). This paper develops a new inerter-based damper called the eddy-current inertial mass damper (ECIMD), which consists of a rotary eddy-current damping element and a paralleled ball screw inertial mass element. Inspired by the advantages of two VDs on a single stay cable, the damping of a stay cable with two ECIMDs, either at opposite cable ends or the same cable end, was investigated through theoretical analysis, experimental study, and parameter optimization. First, the mechanical model of the ECIMD was derived from the geometrical configuration, and its effectiveness was verified through mechanical performance tests on two ECIMD prototypes. Subsequently, theoretical analysis models of the cable-ECIMD system were established by considering the cable sag, flexural stiffness, and boundary conditions. Furthermore, control performances of a model cable attached with two ECIMDs were experimentally evaluated. Finally, the multimode damping effect of two ECIMDs at the same cable end was highlighted through parameter optimization. Results show that when two ECIMDs are installed at opposite cable ends, the coupled single-mode damping effect of two ECIMDs is approximately the sum of individual contributions from each ECIMD. When mechanical properties of two ECIMDs at the same cable end can match well with each other, the coupled single-mode and multimode damping effect of two ECIMDs can be significantly enhanced compared with that of a single ECIMD installed at a further distance away from the cable anchorage. CONFLICT OF INTEREST The authors declare no conflict of interest. Open Research DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1Chen ZQ, Wang XY, Ko JM, et al. MR damping system for mitigating wind-rain induced vibration on Dongting Lake cable-stayed bridge. Wind Struct. 2004; 7(5): 293-304. doi:10.12989/was.2004.7.5.293 2Zhou HJ, Xu YL. Wind-rain-induced vibration and control of stay cables in a cable-stayed bridge. Struct Control Health Monit. 2007; 14(7): 1013-1033. doi:10.1002/stc.190 3Wang H, Tao TY, Gao YQ, Xu F. Measurement of wind effect on a kilometer-level cable-stayed bridge during typhoon Haikui. J Struct Eng. 2018; 144(9): 1-23. doi:10.1061/(ASCE)ST.1943-541X.0002138 4Chen L, Sun LM, Xu YY, Di F, Xu Y, Wang L. A comparative study of multi-mode cable vibration control using viscous and viscoelastic dampers through field tests on the Sutong bridge. Eng Struct. 2020; 224: 1-23. doi:10.1016/j.engstruct.2020.111226 5Gao H, Wang H, Li J, et al. Optimum design of viscous inerter damper targeting multi-mode vibration mitigation of stay cables. Eng Struct. 2021; 226: 1-17. doi:10.1016/j.engstruct.2020.111375 6Pacheco BM, Fujino Y, Sulekh A. Estimation curve for modal damping in stay cables with viscous damper. J Struct Eng. 1993; 119(6): 1961-1979. doi:10.1061/(ASCE)0733-9445(1993)119:6(1961) 7Fujino Y, Hoang N. Design formulas for damping of a stay cable with a damper. J Struct Eng. 2008; 134(2): 269-278. doi:10.1061/(ASCE)0733-9445(2008)134:2(269) 8Di FD, Sun LM, Chen L. Cable vibration control with internal and external dampers: theoretical analysis and field test. Smart Struct Syst. 2020; 26(5): 575-589. 9Li SY, Chen ZQ, Wu T, Kareem A. Rain-wind-induced in-plane and out-of-plane vibrations of stay cables. J Eng Mech. 2013; 139(12): 1688-1698. doi:10.1061/(ASCE)EM.1943-7889.0000612 10Weber F, Distl H. Amplitude and frequency independent cable damping of Sutong bridge and Russky bridge by magnetorheological dampers. Struct Control Health Monit. 2015; 22(2): 237-254. doi:10.1002/stc.1671 11Liu ZW, Shen JS, Li SQ, Chen Z, Ou Q, Xin D. Experimental study on high-mode vortex-induced vibration of stay cable and its aerodynamic countermeasures. J Fl Struct. 2021; 100: 1-20. doi:10.1016/j.jfluidstructs.2020.103195 12Johnson EA, Christenson RE, Spencer BF. Semi-active damping of cables with sag. Comput-Aided Civ Inf. 2003; 18(2): 132-146. doi:10.1111/1467-8667.00305 13Duan YF, Ni YQ, Ko JM. State-derivative feedback control of cable vibration using semiactive magnetorheological dampers. Comput-Aided Civ Inf. 2005; 20(6): 431-449. doi:10.1111/j.1467-8667.2005.00396.x 14Christenson RE, Spencer BF, Johnson EA. Experimental verification of smart cable damping. J Eng Mech-ASCE. 2006; 132(3): 268-278. doi:10.1061/(ASCE)0733-9399(2006)132:3(268) 15Weber F, Distl H. Semi-active damping with negative stiffness for multi-mode cable vibration mitigation: approximate collocated control solution. Smart Mater Struct. 2015; 24(11): 1-14. doi:10.1088/0964-1726/24/11/115015 16Huang HW, Liu TT, Sun LM. Multi-mode cable vibration control using MR damper based on nonlinear modeling. Smart Struct Syst. 2019; 23: 565-577. 17Li H, Liu M, Ou JP. Negative stiffness characteristics of active and semi-active control systems for stay cables. Struct Control Health Monit. 2008; 15(2): 120-142. doi:10.1002/stc.200 18Kim IH, Jung HJ, Koo JH. Experimental evaluation of a self-powered smart damping system in reducing vibration of a full-scale stay cable. Smart Mater Struct. 2010; 19(11): 1-10. doi:10.1088/0964-1726/19/11/115027 19Chen L, Sun LM, Nagarajaiah S. Cable with discrete negative stiffness device and viscous damper: passive realization and general characteristics. Smart Struct Syst. 2015; 15(3): 627-643. doi:10.12989/sss.2015.15.3.627 20Shi X, Zhu SY. Magnetic negative stiffness dampers. Smart Mater Struct. 2015; 24(7): 1-7. doi:10.1088/0964-1726/24/7/072002 21Shi X, Zhu SY, Nagarajaiah S. Performance comparison between passive negative stiffness damper and active control in cable vibration mitigation. J Bridg Eng. 2017; 22(9): 1-15. doi:10.1061/(ASCE)BE.1943-5592.0001088 22Zhou P, Li H. Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations. Struct Control Health Monit. 2016; 23(4): 764-782. doi:10.1002/stc.1809 23Shi X, Zhu SY, Spencer BF. Experimental study on passive negative stiffness damper for cable vibration mitigation. J Eng Mech. 2017; 143(9): 1-13. doi:10.1061/(ASCE)EM.1943-7889.0001289 24Shi X, Zhu SY, Li JY, Spencer BF Jr. Dynamic behavior of stay cables with passive negative stiffness dampers. Smart Mater Struct. 2016; 25(7): 1-14. doi:10.1088/0964-1726/25/7/075044 25Javanbakht M, Cheng SH, Ghrib F. Refined damper design formula for a cable equipped with a positive or negative stiffness damper. Struct Control Health Monit. 2018; 25(10): 1-23. doi:10.1002/stc.2236 26Smith MC. Synthesis of mechanical networks: the inerter. IEEE T Atomat Contr. 2002; 47(1): 1648-1662. doi:10.1109/TAC.2002.803532 27Lazar IF, Neild SA, Wagg DJ. Using an inerter-based device for structural vibration suppression. Earthq Eng Strut D. 2014; 43(8): 1129-1147. doi:10.1002/eqe.2390 28Sun HX, Zuo L, Wang XY, Peng J, Wang W. Exact H2 optimal solutions to inerter-based isolation systems for building structures. Struct Control Health Monit. 2019; 26(6): 1-21. doi:10.1002/stc.2357 29Luo JN, Jiang JZ, Macdonald JHG. Cable vibration suppression with inerter-based absorbers. J Eng Mech. 2019; 145(2): 1-15. doi:10.1061/(ASCE)EM.1943-7889.0001554 30Huang ZW, Hua XG, Chen ZQ, et al. Performance evaluation of inerter-based damping devices for structural vibration control of stay cables. Smart Struct Syst. 2019; 23(6): 615-626. 31Lu L, Duan YF, Spencer BF, et al. Inertial mass damper for mitigating cable vibration. Struct Control Health Monit. 2017; 24(10): 1-12. doi:10.1002/stc.1986 32Shi X, Zhu SY. Dynamic characteristics of stay cables with inerter dampers. J Sound Vib. 2018; 423: 287-305. doi:10.1016/j.jsv.2018.02.042 33Wang ZH, Yue FF, Gao H, et al. Refined study on free vibration of a cable with an inertial mass damper. Appl Sci. 2019; 9(11): 1-18. doi:10.3390/app9112271 34Wang ZH, Xu YW, Gao H. Vibration control of a stay cable with a rotary electromagnetic inertial mass damper. Smart Struct Syst. 2019; 23(6): 627-639. 35Li YM, Shen WA, Zhu HP. Vibration mitigation of stay cables using electromagnetic inertial mass dampers: full-scale experiment and analysis. Eng Struct. 2019; 200: 1-18. doi:10.1016/j.engstruct.2019.109693 36Ikago K, Saito K, Inoue N. Seismic control of single-degree-of-freedom structure using tuned viscous mass damper. Earthq Eng Struct D. 2012; 41(3): 453-474. doi:10.1002/eqe.1138 37Asai T, Watanabe Y. Outrigger tuned inertial mass electromagnetic transducers for high-rise buildings subject to long period earthquakes. Eng Struct. 2017; 153: 404-410. doi:10.1016/j.engstruct.2017.10.040 38Huang ZW, Hua XG, Chen ZQ, Niu H. Optimal design of TVMD with linear and nonlinear viscous damping for SDOF systems subjected to harmonic excitation. Struct Control Health Monit. 2019; 26(10): 1-15. doi:10.1002/stc.2413 39Shen WA, Niyitangamahoro A, Feng ZQ, Zhu H. Tuned inerter dampers for civil structures subjected to earthquake ground motions: optimum design and seismic performance. Eng Struct. 2019; 198: 1-17. doi:10.1016/j.engstruct.2019.109470 40Zhang RF, Zhao ZP, Dai KS. Seismic response mitigation of a wind turbine tower using a tuned parallel inerter mass system. Eng Struct. 2019; 180: 29-39. doi:10.1016/j.engstruct.2018.11.020 41Sun LM, Hong DX, Chen L. Cables interconnected with tuned inerter damper for vibration mitigation. Eng Struct. 2017; 151: 57-67. doi:10.1016/j.engstruct.2017.08.009 42Zhou HJ, Sun LM, Xing F. Damping of full-scale stay cable with viscous damper: experiment and analysis. Adv Struct Eng. 2014; 17(2): 265-274. doi:10.1260/1369-4332.17.2.265 43Cheng SH, Darivandi N, Ghrib F. The design of an optimal viscous damper for a bridge stay cable using energy-based approach. J Sound Vib. 2010; 329(22): 4689-4704. doi:10.1016/j.jsv.2010.05.027 44Wang XY, Ni YQ, Ko JM, Chen ZQ. Optimal design of viscous dampers for multi-mode vibration control of bridge cables. Eng Struct. 2005; 27(5): 792-800. doi:10.1016/j.engstruct.2004.12.013 45Weber F, Feltrin G, Malanka M, et al. Design of viscous dampers targeting multiple cable modes. Eng Struct. 2009; 31(11): 2797-2800. doi:10.1016/j.engstruct.2009.06.020 46Chen L, Di FD, Xu YY, et al. Multimode cable vibration control using a viscous-shear damper: case studies on the Sutong bridge. Struct Control Health Monit. 2020; 27(6): 1-20. 47Javanbakht M, Cheng SH, Ghrib F. Multimode vibration control of stay cables using optimized negative stiffness damper. Struct Control Health Monit. 2020; 27(4): 1-25. 48Chen L, Nagarajaiah S, Sun LM. A unified analysis of negative stiffness dampers and inerter-based absorbers for multimode cable vibration control. J Sound Vib. 2020; 494: 1-24. doi:10.1016/j.jsv.2020.115814 49Caracoglia L, Jones NP. Passive hybrid technique for the vibration mitigation of systems of interconnected stays. J Sound Vib. 2007; 307(3-5): 849-864. doi:10.1016/j.jsv.2007.07.022 50Caracoglia L, Zuo D. Effectiveness of cable networks of various configurations in suppressing stay-cable vibration. Eng Struct. 2009; 31(12): 2851-2864. doi:10.1016/j.engstruct.2009.07.012 51Zhou HJ, Sun LM, Xing F. Free vibration of taut cable with a damper and a spring. Struct Control Health Monit. 2014; 21(6): 996-1014. doi:10.1002/stc.1628 52Zhou HJ, Yang X, Sun LM, Xing F. Free vibrations of a two-cable network with near-support dampers and a cross-link. Struct Control Health Monit. 2015; 22(9): 1173-1192. doi:10.1002/stc.1738 53Ahmad J, Cheng SH, Ghrib F. Efficiency of an external damper in two-cable hybrid systems. J Bridg Eng. 2017; 23(2): 1-15. doi:10.1061/(ASCE)BE.1943-5592.0001185 54Ahmad J, Cheng SH, Ghrib F. Combined effect of external damper and cross-tie on the modal response of hybrid two-cable networks. J Sound Vib. 2018; 417: 132-148. doi:10.1016/j.jsv.2017.12.023 55Xu YL, Yu Z. Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers—II. Application. J Sound Vib. 1998; 214(4): 675-693. doi:10.1006/jsvi.1998.1630 56Caracoglia L, Jones NP. Damping of taut-cable systems: two dampers on a single stay. J Eng Mech. 2007; 133(10): 1050-1060. doi:10.1061/(ASCE)0733-9399(2007)133:10(1050) 57Hoang N, Fujino Y. Combined damping effect of two dampers on a stay cable. J Bridg Eng. 2008; 13(3): 299-303. doi:10.1061/(ASCE)1084-0702(2008)13:3(299) 58Cu VH, Han B. A stay cable with viscous damper and tuned mass damper. Austr J Struct Eng. 2015; 16(4): 316-323. doi:10.1080/13287982.2015.1092693 59Wang ZH, Yue FF, Gao H. Free vibration of a taut cable with two discrete inertial mass dampers. Appl Sci. 2019; 9(18): 1-16. doi:10.3390/app9183919 60Yang C, Chen ZQ, Wang WX, Hua X, Wang Y. Optimal design of two viscous dampers for multi-mode control of a cable covering broad frequency range. Eng Struct. 2021; 245: 1-17. doi:10.1016/j.engstruct.2021.112830 61Sun XQ, Chen L, Wang SH, Zhang XL, Yang XF. Performance investigation of vehicle suspension system with nonlinear ball-screw inerter. Int J Auto Tech-Kor. 2016; 17(3): 399-408. doi:10.1007/s12239-016-0041-x 62Zhang HY, Chen ZQ, Hua XG, Huang ZW, Niu HW. Design and dynamic characterization of a large-scale eddy current damper with enhanced performance for vibration control. Mech Sys Signal Pr. 2020; 145: 1-24. doi:10.1016/j.ymssp.2020.106879 63Loong CN, Shan JZ, Shi ZG, Chang CC. Approximate analysis of eddy-current force under time-varying velocity motion for structural control. J Sound Vib. 2020; 475: 1-13. doi:10.1016/j.jsv.2020.115295 64Mehrabi AB, Tabatabai H. Unified finite difference formulation for free vibration of cables. J Struct Eng. 1998; 124(11): 1313-1322. doi:10.1061/(ASCE)0733-9445(1998)124:11(1313) 65Hiroshi Z, Tohru S, Yoshio N. Practical formulas for estimation of cable tension by vibration method. J Struct Eng. 1996; 122(6): 651-656. doi:10.1061/(ASCE)0733-9445(1996)122:6(651) 66 PTI-DC45.1. Recommendations for stay cable design, testing and installation. Post-Tensioning Institute. 2018. 67Zhou HJ, Zhou XB, Yao GZ, et al. Free vibration of two taut cables interconnected by a damper. Struct Control Health Monit. 2019; 26(10): 1-17. Volume29, Issue11November 2022e3085 ReferencesRelatedInformation