Damping effects of a stay cable attached with a viscous damper and a high damping rubber damper considering cable bending stiffness and damper support flexibility

Abstract

To mitigate cable oscillations in cable-stayed bridges, a common approach involves using a strategically positioned viscous damper near the cable’s anchorage and bridge deck. However, for longer cables, this method may be insufficient due to installation constraints. In such cases, supplementing the damping system with a high-damping rubber (HDR) damper near the cable’s anchorage point on the bridge tower becomes imperative to enhance the cable’s damping ratio. Conventional designs often overlook crucial factors like viscous damper support stiffness and stay cable bending stiffness when integrating dampers into cable-stayed structures. This study presents findings on achieving an effective damping ratio in stay cables by using both a viscous damper and an HDR damper, considering the influence of viscous damper support stiffness and stay cable bending stiffness. The results indicate that the combined deployment of these dampers achieves a damping efficiency approximately equivalent to the sum of their individual effects. Importantly, decreased viscous damper support stiffness significantly affects the damping effectiveness, leading to a rapid decline in the stay cable’s damping ratio. While stay cable bending stiffness also influences the damping ratio, its impact is relatively less pronounced than that of viscous damper support stiffness. The study outcomes enable a more accurate prediction of the achievable damping ratio for a stay cable with additional components, considering both damper support stiffness and stay cable bending stiffness. Furthermore, the study explores parameters of both the viscous damper and HDR damper, such as the viscous coefficient, loss coefficient, HDR damper stiffness, and damper placement, evaluating their influence on the first damping ratio of the stay cable. The survey results provide valuable insights for determining optimal parameters for both dampers, maximizing the damping efficiency of cable-stayed bridges.

Keywords

Viscous damper / Cable damping ratio / High-damping rubber damper / Viscous damper support stiffness / Bending stiffness

References

[] Abdel-Ghaffar AM, Khalifa MA. Importance of cable vibration in dynamics of cable‐stayed bridges. J Eng Mech, 1991, 117: 2571-2589,

[] Beskhyroun S, Wegner LD, Sparling BF. Integral resonant control scheme for cancelling human-induced vibrations in light-weight pedestrian structures. Struct Control Heal Monit, 2011,

[] Caracoglia L, Jones NP. Damping of taut-cable systems: two dampers on a single stay. J Eng Mech, 2007, 133: 1050-1060,

[] Chen L, Sun L, Xu Y, et al.. 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,

[] Cu VH, Han B. High-damping rubber damper for taut cable vibration reduction. Aust J Struct Eng, 2015, 16: 283-291,

[] de Sá Caetano E (2007) Cable vibrations in Cable-stayed bridges. IABSE

[] Di F, Sun L, Chen L (2021) Suppression of vortex-induced high-mode vibrations of a cable-damper system by an additional damper. https://doi.org/10.1016/j.engstruct.2021.112495

[] Di F, Sun L, Chen L. Cable vibration control with internal and external dampers: theoretical analysis and field test validation. Smart Struct Syst, 2020, 26: 575-589,

[] Duan Y, Ni YQ, Zhang H et al (2019a) Design formulas for vibration control of taut cables using passive MR dampers. Smart Struct Syst 23:521–536. https://doi.org/10.12989/sss.2019.23.6.521

[] Duan Y, Ni YQ, Zhang H et al (2019b) Design formulas for vibration control of taut cables using passive MR dampers. Smart Struct Syst 23:521–536. https://doi.org/10.12989/sss.2019.23.6.521

[] Fujino Y, Hoang N. Design formulas for damping of a stay cable with a damper. J Struct Eng, 2008, 134: 269-278,

[] Fujino Y, Kimura K, Tanaka H (2014) Wind resistant design of bridges in Japan: developments and practices. Springer Science and Business Media

[] Gu M. On wind-rain induced vibration of cables of cable-stayed bridges based on quasi-steady assumption. J Wind Eng Ind Aerodyn, 2009, 97: 381-391,

[] Hoang N, Fujino Y. Combined damping effect of two dampers on a stay cable. J Bridg Eng, 2008, 13: 299-303,

[] Hung VD, Thao ND (2020a) A further study on stay cable galloping under dry weather condition BT - CIGOS 2019, innovation for sustainable infrastructure. In: Ha-Minh C, Dao D Van, Benboudjema F, et al. (eds). Springer Singapore, Singapore, p 191–196

[] Hung VD, Thao ND (2020b) A further study on stay cable galloping under dry weather condition. In: Lecture Notes in Civil Engineering. pp 191–196

[] Javanmardi A, Ghaedi K, Huang F, et al.. Application of structural control systems for the cables of cable-stayed bridges: state-of-the-art and state-of-the-practice. Arch Comput Methods Eng, 2022, 29: 1611-1641,

[] Kumarasena S, Jones NP, Irwin P, Taylor P. . Wind induced vibration of stay cables interim final report, 2005

[] Le LX, Katsuchi H, Yamada H. Damping of cable with HDR damper accounting for restraint boundary conditions. J Bridg Eng, 2020, 25: 4020105,

[] Liu Y, Xu YW, Wang ZH. Free vibration of a taut cable with internal high damping rubber dampers and an external negative stiffness damper. J Low Freq Noise Vib Act Control, 2023, 42: 1018-1034,

[] Main JA (2002) Modelling the vibrations of a stay cable with attached damper. The Johns Hopkins University

[] Main JA, Jones NP. influence of rubber bushings on stay-cable damper effectiveness. Angew Chemie Int Ed, 1967, 6(11): 951-952 5–24

[] Main JA, Jones NP (2002a) Free vibrations of taut cable with attached damper. I: linear viscous damper. J Eng Mech 128:1062–1071. https://doi.org/10.1061/(asce)0733-9399(2002)128:10(1062)

[] Main JA, Jones NP (2002b) Free vibrations of taut cable with attached damper. II: Nonlinear damper. J Eng Mech 128:1072–1081. https://doi.org/10.1061/(asce)0733-9399(2002)128:10(1072)

[] Main JA, Jones NP. Vibration of tensioned beams with intermediate damper. I: Formulation, influence of damper location. J Eng Mech, 2007, 133: 369-378,

[] Matsumoto M, Shirato H, Yagi T, et al.. Field observation of the full-scale wind-induced cable vibration. J Wind Eng Ind Aerodyn, 2003, 91: 13-26,

[] Matsumoto M, Yagi T, Shigemura Y, Tsushima D. Vortex-induced cable vibration of cable-stayed bridges at high reduced wind velocity. J Wind Eng Ind Aerodyn, 2001, 89: 633-647,

[] Nakamura A, Kasuga A, Arai H. The effects of mechanical dampers on stay cables with high-damping rubber. Constr Build Mater, 1998, 12: 115-123,

[] Nguyen DT, Vo DH (2020a) A study on combination of two friction dampers to control stayed-cable vibration under considering its bending stiffness BT - CIGOS 2019, innovation for sustainable infrastructure. In: Ha-Minh C, Dao D Van, Benboudjema F, et al. (eds). Springer Singapore, Singapore, p 87–92

[] Nguyen DT, Vo DH (2020b) A study on combination of two friction dampers to control stayed-cable vibration under considering its bending stiffness. In: Lecture Notes in Civil Engineering. 테크노프레스, p 87–92

[] Nguyen DT, Vo DH, Hai V, Haque MN. Optimization of multiple helical fillets surface to suppress rain-wind vibration of stay cables: a wind tunnel investigation. Open Civ Eng J, 2022, 16: 1-12,

[] Nguyen DT, Vo DH, Haque MN. Theoretical investigation on the impact of two HDR dampers on first modal damping ratio of stay cable. Appl Sci, 2021, 11,

[] Nielsen SRK, Krenk S. Whirling motion of a shallow cable with viscous dampers. J Sound Vib, 2003, 265: 417-435,

[] Pacheco BM, Fujino Y, Sulekh A. Estimation curve for modal damping in stay cables with viscous damper. J Struct Eng, 1993, 119: 1961-1979,

[] Sun L, Chen L. Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives. J Sound Vib, 2015, 335: 19-33,

[] Sun L, Huang H. Design, implementation and measurement of cable dampers for large cable-stayed bridges. In: 17th Congress of IABSE. Creating and Renewing Urban StructuresInternational Association for Bridge and Structural Engineering, 2008 242-243

[] Sun L, Xu Y, Chen L. Damping effects of nonlinear dampers on a shallow cable. Eng Struct, 2019, 196,

[] Vo HD, Katsuchi H, Yamada H, Nishio M. A wind tunnel study on control methods for cable dry-galloping. Front Struct Civ Eng, 2016, 10: 72-80,

[] Wang Z, Cheng Z, Wang H, et al.. Damping of a stay cable with two eddy-current inertial mass dampers: theoretical analysis, experimental study, and parameter optimization. Struct Control Heal Monit, 2022, 29: e3085,

[] Wang XY, Ni YQ, Ko JM, Chen ZQ. Optimal design of viscous dampers for multi-mode vibration control of bridge cables. Eng Struct, 2005, 27: 792-800,

[] Zhou Y, Sun L. Complex modal analysis of a taut cable with three-element Maxwell damper. Tongji Daxue Xuebao/Journal Tongji Univ, 2006, 34: 7-12