FREE VIBRATIONS OF A SHALLOW CABLE WITH TWO VISCOUS DAMPERS
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摘要: 随着斜拉索长度的不断增加，在索近梁端单点安装阻尼器已经难以满足拉索减振的需要。同时，已有研究表明索垂度会减弱索端阻尼器的减振效果。因此，针对超长斜拉索，考虑垂度的影响，分析了斜拉索上两处安装粘滞阻尼器(拉索-双粘滞阻尼器)系统的复模态特性。考虑实际中阻尼器一般安装于近索锚固端位置，推导出了该情况下系统模态阻尼比的近似解析表达式，进行了阻尼器参数对索阻尼的影响分析和优化。结果表明：对于双阻尼器系统，垂度仍对拉索对称振动模态的阻尼比有减弱效果，对反对称振动模态无影响；阻尼器对称安装于索两端时，即使考虑垂度索所获得的最优阻尼相比于安装单个阻尼器时可以提高至2倍，能有效解决单阻尼器提供阻尼不足的问题。双阻尼器同端布置相比于仅安离索端较远的阻尼器时，索单阶最优模态阻尼无提高，但对于同时抑制拉索高、低阶振动具有优势。Abstract: With the continuous increase in the length of stay cables in cable-stayed bridges, a damper installed at a point near the cable-deck end is inadequate for cable vibration control. Meanwhile, previous studies have shown that cable sag effect weakens the damping effect of the damper. Therefore, it studies free vibrations of long cables with viscous dampers installed respectively on two points of a cable (cable-two-damper system) and performs complex modal analysis of the system with the sag effect taken into consideration. Asymptotic formulas for modal damping estimation has been derived considering the fact that each damper is close to one cable end in practice. Parametric studies on damper coefficients and locations are carried out to maximize cable damping. The results show that when a cable is equipped with two dampers, cable sag still has an negative effect on cable modal damping in nearly symmetric modes, but has no effect in nearly antisymmetric modes; When the two dampers are symmetrically installed on a cable near its ends, the total modal damping of the cable is approximately the sum of the contributions from each damper when installed separately. It is also found that the dampers both installed at the same cable end cannot improve the maximal attainable damping for a single mode, which can be achieved by only installing one damper farther from the cable end; however, they can achieve better multimode damping effects in terms of simultaneously suppressing high and low mode vibrations of the cable.
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Key words:
- stay cable /
- cable sag /
- double dampers /
- modal damping /
- parameter optimization
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图 2 不同
$ {\lambda ^2} $ 时系统模态阻尼曲线($ {{{l_1}} \mathord{\left/ {\vphantom {{{l_1}} L}} \right. } L} = 0.02 $ )Figure 2. Damping curves for
$ {{{l_1}} \mathord{\left/ {\vphantom {{{l_1}} L}} \right. } L} = 0.02 $ and varied values of$ {\lambda ^2} $ 
图 3 前五阶模态
$ {\lambda ^2} $ 与最大模态阻尼的关系曲线Figure 3. Dependence of maximum modal damping on the cable sag
图 4 两端安装阻尼器系统一阶模态阻尼曲线
Figure 4. First modal damping curves of cable equipped with two dampers at the opposite cable ends
图 5 同一端安装双阻尼器系统一阶模态阻尼曲线
Figure 5. First modal damping curves of cable equipped with two dampers at the same cable end
图 9 两端安装阻尼器系统模态阻尼曲线
Figure 9. Modal damping curves of cable equipped with two dampers at the opposite cable ends
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[1] Chen L, Di F, Xu Y, et al. Multimode cable vibration control using a viscous-shear damper: Case studies on the Sutong Bridge [J]. Structural Control and Health Monitoring, 2020, 27(6): e2536. [2] Di F, Sun L, Qin L, et al. Full-scale experimental study on vibration control of bridge suspenders using the Stockbridge damper [J]. Journal of Bridge Engineering, 2020, 25(8): 04020047. doi: 10.1061/(ASCE)BE.1943-5592.0001591 [3] 李寿英, 曾庆宇, 王世峰, 等. 阻尼器对悬索桥双吊索减振效果的理论研究[J]. 工程力学, 2018, 35(3): 186 − 192, 226. doi: 10.6052/j.issn.1000-4750.2016.12.0945Li Shouying, Zeng Qingyu, Wang Shifeng, et al. Theoretical investigation for the effectiveness of the dampers installed between the hangers of suspension bridges [J]. Engineering Mechanics, 2018, 35(3): 186 − 192, 226. (in Chinese) doi: 10.6052/j.issn.1000-4750.2016.12.0945 [4] 周颖, 刘晓芳, 汪盟. 不同耗能特征的黏弹性阻尼器性能对比试验研究[J]. 工程力学, 2021, 38(增刊): 167 − 177. doi: 10.6052/j.issn.1000-4750.2020.06.S030Zhou Ying, Liu Xiaofang, Wang Meng. Experimental study on mechanical properties of two types of viscoelastic dampers [J]. Engineering Mechanics, 2021, 38(Suppl): 167 − 177. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.S030 [5] Di F, Sun L, Chen L. In-plane dynamic behaviors of two-cable networks with a pretensioned cross-tie [J]. Structural Control and Health Monitoring, 2021, 28(7): e2755. [6] Garne T G. Guy cable design and damping for vertical axis wind turbines [R]. Albuquerque, Mexico: Technical Report, Sandia National Laboratories, 1981. [7] Kovacs I. Zur frage der seilschwingungen und der seildampfung [J]. Bautechnik, 1982, 59(10): 325 − 332. [8] Yoneda M, Maeda K. A study on practical estimation method for structural damping of stay cables with dampers [J]. Doboku Gakkai Ronbunshu, 1989, 1989(410): 455 − 458. [9] Uno K, Kitagawa S, Tsutsumi H, et al. A Simple method of designing cable vibration dampers of cable-stayed bridges [J]. JSCE Journal of Structural Engineering, 1991, 37: 789 − 798. [10] Pacheo B M, Fujino Y, Sulkh A. Estimation curve for modal damping in stay cable with viscous damper [J]. Journal of Structural Engineering, 1993, 119(6): 1961 − 1979. doi: 10.1061/(ASCE)0733-9445(1993)119:6(1961) [11] Mehrabi A B, Tabatabai H. Unified finite difference formulation for free vibration of cables [J]. Journal of Structural Engineering, 1998, 124(11): 1313 − 1322. doi: 10.1061/(ASCE)0733-9445(1998)124:11(1313) [12] Tabatabai H, Mehrabi A B. Design of mechanical viscous dampers for stay cables [J]. Journal of Bridge Engineering, 2000, 5(2): 114 − 123. doi: 10.1061/(ASCE)1084-0702(2000)5:2(114) [13] Xu Y L, Yu Z. Vibration of inclined sag cables with oil dampers in cable-stayed bridges [J]. Journal of Bridge Engineering, 1998, 3(4): 194 − 203. doi: 10.1061/(ASCE)1084-0702(1998)3:4(194) [14] Xu Y L, Zhan S, Yu Z, et al. Theoretical and experimental studies on vibration control of sag cables in cable-stayed bridge by oil damper [C]. Kyoto, Japan: Proceedings of the 2nd World Conference on Structural Control, 1999: 1031 − 1040. [15] Yu Z, Xu Y L. Mitigation of three-dimensional vibration of inclined sag cable using discrete oil damper-I. Formulation [J]. Journal of Sound and Vibration, 1998, 214(4): 659 − 673. doi: 10.1006/jsvi.1998.1609 [16] Yu Z, Xu Y L. Mitigation of three-dimensional vibration of inclined sag cable using discrete oil damper-II. Application [J]. Journal of Sound and Vibration, 1998, 214(4): 675 − 693. doi: 10.1006/jsvi.1998.1630 [17] Krenk S, Hogsberg J R. Damping of cables by a transverse force [J]. Journal of Engineering Mechanics, 2005, 131(4): 340 − 348. doi: 10.1061/(ASCE)0733-9399(2005)131:4(340) [18] Krenk S. Vibration of a Taut cable with an external damper [J]. Journal of Applies Mechanics, 2000, 67(4): 772 − 776. doi: 10.1115/1.1322037 [19] Krenk S, Nielsen S. Vibration of a shallow cable with a viscous damper [J]. Proceeding of the Royal Society of London Series A:Mathematical Physical and Engineering Sciences, 2002, 458(2018): 339 − 357. doi: 10.1098/rspa.2001.0879 [20] Main J A, Jones N P. Evaluation of viscous dampers for stay-cable vibration mitigation [J]. Journal of Bridge Engineering, 2001, 6(6): 385 − 388. doi: 10.1061/(ASCE)1084-0702(2001)6:6(385) [21] Main J A, Jones N P. Free Vibration of taut cable with attaches damper Ⅰ: Linear viscous damper [J]. Journal of Engineering Mechanics, 2002, 128(10): 1062 − 1071. doi: 10.1061/(ASCE)0733-9399(2002)128:10(1062) [22] Main J A, Jones N P. Free vibration of taut cable with attaches damper Ⅱ: Nonlinear damper [J]. Journal of Engineering Mechanics, 2002, 128(10): 1072 − 1081. doi: 10.1061/(ASCE)0733-9399(2002)128:10(1072) [23] Sun L, Chen L. Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives [J]. Journal of Sound and Vibration, 2015, 335: 19 − 33. doi: 10.1016/j.jsv.2014.09.016 [24] 张瑞甫, 曹嫣如, 潘超. 惯容减震(振)系统及其研究进展[J]. 工程力学, 2019, 36(10): 8 − 27. doi: 10.6052/j.issn.1000-4750.2018.09.0496Zhang Ruifu, Cao Yanru, Pan Chao. Inerter system and its state-of-the-art [J]. Engineering Mechanics, 2019, 36(10): 8 − 27. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.09.0496 [25] Chen L, Sun L, Nagarajaiah S. Cable with discrete negative stiffness and viscous damper: passive realization and general characteristics [J]. Smart Structures and Systems, 2015, 15(3): 627 − 643. doi: 10.12989/sss.2015.15.3.627 [26] Zhou P, Li H. Modeling and control performance of a negative stiffness damper for suppressing stay cable vibrations [J]. Structural Control and Health Monitoring, 2016, 23(4): 764 − 782. doi: 10.1002/stc.1809 [27] Chen L, Sun L, Nagarajaiah S. Cable vibration control with both lateral and rotational dampers attached at an intermediate location [J]. Journal of Sound and Vibration, 2016, 377: 38 − 57. doi: 10.1016/j.jsv.2016.04.028 [28] Caracogla L, Jones N P. Damping of taut-cable system: Two dampers on a single stay [J]. Journal of Engineering Mechanics, 2007, 133(10): 1050 − 1060. doi: 10.1061/(ASCE)0733-9399(2007)133:10(1050) [29] Hoang N, Fujino Y. Combined damping effect of two dampers on a stay cable [J]. Journal of Bridge Engineering, 2008, 13(3): 299 − 303. doi: 10.1061/(ASCE)1084-0702(2008)13:3(299) [30] Wang Z, Yue F, Gao H. Free vibration of a taut cable with two discrete inertial mass dampers [J]. Applied Sciences, 2019, 9(18): 3919. doi: 10.3390/app9183919 [31] Irvine H M, Caughey T K. The linear theory of free vibrations of a suspended cable [J]. Proceedings of the Royal Society of London Series A:Mathematical and Physical Sciences, 1974, 341(1626): 299 − 315. [32] Di F, Sun L, Chen L. Cable vibration control with internal and external dampers: Theoretical analysis and field test validation [J]. Smart Structures and Systems, 2020, 26(5): 575 − 589. [33] Di F, Sun L, Chen L. Suppression of vortex-induced high-mode vibrations of a cable-damper system by an additional damper [J]. Engineering Structures, 2021, 242: 112495. doi: 10.1016/j.engstruct.2021.112495 -
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