Enhancing vibration control in stay cables: a modified damping formulation with NS-HDR damper
Email:
luusbvl@utc.edu.vn
Từ khóa:
Negative stiffness HDR damper (NS-HDR); damping ratio; modification factor; field measurement.
Tóm tắt
Cables in cable-stayed bridges have low intrinsic damping, and dampers are often used as a countermeasure for cable vibration control. This paper presents an innovative asymptotic formula for calculating the additional damping in stay cables equipped with Negative Stiffness High Damping Rubber dampers (NS-HDR). The NS-HDR damper incorporates negative stiffness through a pre-compressed spring. The analysis employs models of flexural cables with fixed-fixed or hinged-hinged ends to derive the formulation of attainable damping ratio. The results of the study reveal that the NS-HDR damper, with its negative stiffness feature, exhibits a significantly higher added damping ratio in comparison to the conventional HDR damper configuration. To quantify this increased added damping resulting from negative stiffness, a modification factor is proposed. The accuracy and effectiveness of the proposed damping formula are successfully validated using the Finite Difference Method (FDM). Subsequently, the methodology is applied to design the damping of two existing stay cables (137.82m and 167.18m in length). Field measurements reveal that the damping in these cables falls below the required threshold of 0.5%. The proposed NS-HDR damper offers a viable solution to achieve the required damping ratio. These findings contribute significantly to the understanding and optimization of damping in stay cables employing HDR dampers, presenting potential applications in the field of bridge engineering. The research opens up new possibilities for enhancing vibration control and safety in cable-stayed bridges.Tài liệu tham khảo
[1] Y. Fujino, N. Hoang, Design formulas for damping of a stay cable with a damper, J. Struct. Eng., 134 (2008) 269-278. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:2(269
[2] B.M. Pacheco, Y. Fujino, A. Sulekh, Estimation curve for modal damping in stay cables with viscous damper, J. Struct. Eng., 119 (1993) 1961-1979. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(19
[3] N.J. Gimsing, C.T. Georgakis, Cable supported bridges: Concept and design, John Wiley & Sons, 2011.
[4] PTI, Recommendations for stay cable design, testing and installation, in, Cable-Stayed Bridges Committee Phoenix, 2007.
[5] S. Krenk, Vibrations of a taut cable with an external damper, J. Appl. Mech., 67 (2000) 772-776. https://doi.org/10.1115/1.1322037
[6] J. Main, N. Jones, Free vibrations of taut cable with attached damper. II: Nonlinear damper, J. Eng. Mech., 128 (2002) 1072-1081. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(107
[7] J. Main, N. Jones, Free vibrations of taut cable with attached damper. I: Linear viscous damper, J. Eng. Mech., 128 (2002) 1062-1071. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1062)
[8] H. Tabatabai, A.B. Mehrabi, Design of mechanical viscous dampers for stay cables, J. Bridge Eng., 5 (2000) 114-123. https://doi.org/10.1061/(ASCE)1084-0702(2000)5:2(11
[9] L. Chen, L. Sun, S. Nagarajaiah, Cable with discrete negative stiffness device and viscous damper: passive realization and general characteristics, Smart Struct. Syst., 15 (2015) 627-643. https://doi.org/10.12989/sss.2015.15.3.627
[10] P. Zhou, H. Li, Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations, Struct Control Health Monit., 23 (2016) 764-782. https://doi.org/10.1002/stc.1809
[11] X. Shi, S. Zhu, J.-Y. Li, B.F. Spencer, Dynamic behavior of stay cables with passive negative stiffness dampers, Smart Mater. Struct., 25 (2016) 075044. https://doi.org/10.1088/0964-1726/25/7/075044
[12] X. Shi, S. Zhu, B.F. Spencer Jr, Experimental study on passive negative stiffness damper for cable vibration mitigation, J. Eng. Mech., 143 (2017) 04017070. https://doi.org/10.1061/(ASCE)EM.1943-7889.00012
[13] M. Javanbakht, S. Cheng, F. Ghrib, Impact of support stiffness on the performance of negative stiffness dampers for vibration control of stay cables, Struct Control Health Monit., 27 (2020) e2610. https://doi.org/10.1002/stc.2610
[14] L.X. Le, H. Katsuchi, H. Yamada, Effect of rotational restraint at damper location on damping of a taut cable with a viscous damper, J. Bridge Eng., 25 (2020) 04019139. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001520
[15] L.X. Le, H. Katsuchi, H. Yamada, Damping of cable with HDR damper accounting for restraint boundary conditions, J. Bridge Eng., 25 (2020) 04020105. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001641
[16] A.K. Chopra, Dynamics of structures, Pearson Education India, 2007.
[17] S. Butterworth, On the theory of filter amplifiers, Wirel. Eng., 7 (1930) 536-541.
[18] S.G. Kelly, Mechanical vibrations: theory and applications, Cengage learning, 2012.
[2] B.M. Pacheco, Y. Fujino, A. Sulekh, Estimation curve for modal damping in stay cables with viscous damper, J. Struct. Eng., 119 (1993) 1961-1979. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:6(19
[3] N.J. Gimsing, C.T. Georgakis, Cable supported bridges: Concept and design, John Wiley & Sons, 2011.
[4] PTI, Recommendations for stay cable design, testing and installation, in, Cable-Stayed Bridges Committee Phoenix, 2007.
[5] S. Krenk, Vibrations of a taut cable with an external damper, J. Appl. Mech., 67 (2000) 772-776. https://doi.org/10.1115/1.1322037
[6] J. Main, N. Jones, Free vibrations of taut cable with attached damper. II: Nonlinear damper, J. Eng. Mech., 128 (2002) 1072-1081. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(107
[7] J. Main, N. Jones, Free vibrations of taut cable with attached damper. I: Linear viscous damper, J. Eng. Mech., 128 (2002) 1062-1071. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1062)
[8] H. Tabatabai, A.B. Mehrabi, Design of mechanical viscous dampers for stay cables, J. Bridge Eng., 5 (2000) 114-123. https://doi.org/10.1061/(ASCE)1084-0702(2000)5:2(11
[9] L. Chen, L. Sun, S. Nagarajaiah, Cable with discrete negative stiffness device and viscous damper: passive realization and general characteristics, Smart Struct. Syst., 15 (2015) 627-643. https://doi.org/10.12989/sss.2015.15.3.627
[10] P. Zhou, H. Li, Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations, Struct Control Health Monit., 23 (2016) 764-782. https://doi.org/10.1002/stc.1809
[11] X. Shi, S. Zhu, J.-Y. Li, B.F. Spencer, Dynamic behavior of stay cables with passive negative stiffness dampers, Smart Mater. Struct., 25 (2016) 075044. https://doi.org/10.1088/0964-1726/25/7/075044
[12] X. Shi, S. Zhu, B.F. Spencer Jr, Experimental study on passive negative stiffness damper for cable vibration mitigation, J. Eng. Mech., 143 (2017) 04017070. https://doi.org/10.1061/(ASCE)EM.1943-7889.00012
[13] M. Javanbakht, S. Cheng, F. Ghrib, Impact of support stiffness on the performance of negative stiffness dampers for vibration control of stay cables, Struct Control Health Monit., 27 (2020) e2610. https://doi.org/10.1002/stc.2610
[14] L.X. Le, H. Katsuchi, H. Yamada, Effect of rotational restraint at damper location on damping of a taut cable with a viscous damper, J. Bridge Eng., 25 (2020) 04019139. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001520
[15] L.X. Le, H. Katsuchi, H. Yamada, Damping of cable with HDR damper accounting for restraint boundary conditions, J. Bridge Eng., 25 (2020) 04020105. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001641
[16] A.K. Chopra, Dynamics of structures, Pearson Education India, 2007.
[17] S. Butterworth, On the theory of filter amplifiers, Wirel. Eng., 7 (1930) 536-541.
[18] S.G. Kelly, Mechanical vibrations: theory and applications, Cengage learning, 2012.
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Nhận bài
06/08/2023
Nhận bài sửa
10/12/2023
Chấp nhận đăng
10/01/2024
Xuất bản
15/01/2024
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Kiểu trích dẫn
Luu Xuan, L., Hiroshi, K., Binh Xuan, L., Linh Ngoc, V., & Quan Van, H. (1705251600). Enhancing vibration control in stay cables: a modified damping formulation with NS-HDR damper. Tạp Chí Khoa Học Giao Thông Vận Tải, 75(1), 1198-1212. https://doi.org/10.47869/tcsj.75.1.8
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