Stability and Dynamics Analysis of In-Plane Parametric Vibration of Stay Cables in a Cable-Stayed Bridge with Superlong Spans Subjected to Axial Excitation
Publication: Journal of Aerospace Engineering
Volume 33, Issue 1
Abstract
Stay cables are prone to parametric vibrations, which might severely affect the serviceability and safety of cable-stayed bridges. This paper investigates the stability and dynamic characteristics of in-plane parametric vibrations for stay cables in cable-stayed bridges with superlong span under axial excitations. First, the nonlinear motion equation of a stay cable under axial harmonic excitation is derived on the basis of an established cable sag curve equation with the chord component of cable self-weight considered. Next, the equation is solved theoretically using a multiscale method, which reveals the conditions for the existence of the constant solution in parametric resonances. Subsequently, the sufficient conditions for the existence of the asymptotic steady solution are further obtained according to the Lyapunov’s first approximate stability criterion. Moreover, a numerical analysis is performed to assess the influences of the cable’s damping ratio, excitation frequency, and amplitude on the cable vibration using the longest cable, S36, in the Hutong Yangtze River Railway Bridge. The results show that the minimum external excitation amplitude exists for parametrical vibrations of stay cables, while the damping does not effectively suppress the amplitude of large-scale parametrical vibrations. Therefore, controlling the excitation amplitude may be an effective way to inhibit the parametrical vibrations of stay cables.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some data and all codes used during the study are available from the corresponding author by request, as are items for Figs. 2–10.
Acknowledgments
This study was financially supported by the National Natural Science Foundations of China with Grant Nos. 51678198 and 51808175, the National Key Research and Development Program of China with Grants Nos. 2016YFC0701102 and 2018YFC0705603, and the Transportation Science and Technology Program of Hubei province with Grant No. 2016600207.
References
Caetano, E., A. Cunha, and C. A. Taylor. 2000a. “Investigation of dynamic cable-deck interaction in a physical model of a cable-stayed bridge. Part I: Modal analysis.” Earthquake Eng. Struct. Dyn. 29 (4): 484–498. https://doi.org/10.1002/(SICI)1096-9845(200004)29:4%3C481::AID-EQE918%3E3.0.CO;2-1.
Caetano, E., A. Cunha, and C. A. Taylor. 2000b. “Investigation of dynamic cable-deck interaction in a physical model of a cable-stayed bridge. Part II: Seismic response.” Earthquake Eng. Struct. Dyn. 29 (4): 499–521. https://doi.org/10.1002/(SICI)1096-9845(200004)29:4%3C499::AID-EQE919%3E3.0.CO;2-A.
Chen, S. S. 2002. “Vibration passive and semi-active control of cables for large-span cable-stayed bridge.” Ph.D. dissertation, College of Civil Engineering and Architecture, Zhejiang Univ.
Chen, W. L., X. J. Wang, F. Xu, and H. Li. 2017 “A passive jet flow control method for suppressing unsteady vortex shedding from a circular cylinder.” J. Aerosp. Eng. 30 (1): 04016063. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000661.
Costa, A. P. D., J. A. C. Martins, F. A. Branco, and J. L. Lilien. 1996. “Oscillation of bridge stay cables induced by periodic motions of deck and/or towers.” J. Eng. Mech. 122 (7): 613–622. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:7(613).
Gattulli, V., M. Morandini, and A. Paolone. 2002. “A parametric analytical model for non-linear dynamics in cable-stayed beam.” Earthquake Eng. Struct. Dyn. 31 (6): 1281–1300. https://doi.org/10.1002/eqe.162.
Huang, P., X. Y. Wang, Q. Wen, W. X. Wang, and H. X. Sun. 2018. “Active control of stay cable vibration using a giant magneto-strictive actuator.” J. Aerosp. Eng. 31 (5): 04018074. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000905.
Irvine, H. M. 1981. Cable structures: Dynamics of a suspended cable. Cambridge, UK: MIT Press.
Kang, Z., K. S. Xu, and Z. Luo. 2011. “A numerical study on nonlinear vibration of an inclined cable coupled with the deck in cable-stayed bridges.” J. Vib. Control 18 (3): 404–416. https://doi.org/10.1177/1077546311407648.
Liu, M., P. Zhou, and H. Li. 2018. “Novel self-centering negative stiffness damper based on combination of shape memory alloy and prepressed spring.” J. Aerosp. Eng. 31 (6): 04018100. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000926.
Macdonald, J. H. G. 2016. “Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation.” J. Sound Vib. 363 (Feb): 473–494. https://doi.org/10.1016/j.jsv.2015.11.012.
Mahfoud, J., and J. D. Hagopian. 2011. “Fuzzy active control of flexible structures by using electromagnetic actuators.” J. Aerosp. Eng. 24 (3): 329–337. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000067.
Mei, K. H., Z. T. Lu, and S. J. Sun. 2007. “Property of nonlinear parametric vibration of CFRP cables.” [In Chinese.] China J. Highway Trans. 20 (1): 52–57.
Ouni, M. H. E., N. B. Kahla, and A. Preumont. 2012. “Numerical and experimental dynamic analysis and control of a cable stayed bridge under parametric excitation.” Eng. Struct. 45 (15): 244–256. https://doi.org/10.1016/j.engstruct.2012.06.018.
Qian, C. Z., C. P. Chen, and G. W. Zhou. 2014. “Nonlinear dynamical analysis for the cable excited with parametric and forced excitation.” J. Appl. Math. 2014: 1–6. https://doi.org/10.1155/2014/183257.
Sun, C. S., H. J. Kang, Y. B. Zhao, and Y. Y. Zhao. 2015. “Experimental research on jumping course of inclined cable in nonlinear vibration.” [In Chinese.] J. Solid Mech. 36 (5): 429–435.
Tagata, G. 1977. “Harmonically forced, finite amplitude vibration of a string.” J. Sound Vib. 51 (4): 483–492. https://doi.org/10.1016/S0022-460X(77)80046-1.
Virlogeux, M. 1998. “Cable vibration in cable-stayed bridges.” J. Bridge Dyn. 127 (3): 213–233.
Wang, W. X., X. G. Hua, Z. Q. Chen, X. Y. Wang, and G. Song. 2019. “Modeling, simulation and validation of a pendulum pounding tuned mass damper (PPTMD) for vibration control.” Struct. Control Health Monit. 23 (4): e2326. https://doi.org/10.1002/stc.2326.
Wang, W. X., X. Y. Wang, X. G. Hua, G. B. Song, and Z. Q. Chen. 2018a. “Vibration control of vortex-induced vibrations of a bridge deck by a single-side pounding tuned mass damper.” J. Eng. Struct. 173 (Oct): 61–75. https://doi.org/10.1016/j.engstruct.2018.06.099.
Wang, W. X., X. Y. Wang, X. G. Hua, J. L. Wu, H. X. Sun, and G. B. Song. 2018b. “Mechanical behavior of magneto-rheological dampers after long-term operation in a cable vibration control system.” Struct. Control Health Monit. 26 (1): e2280. https://doi.org/10.1002/stc.2280.
Wei, M. H., Y. Q. Xiao, H. T. Liu, and K. Lin. 2014. “Nonlinear responses of a cable-beam coupled system under parametric and external excitations.” Arch. Appl. Mech. 84 (2): 173–185. https://doi.org/10.1007/s00419-013-0792-z.
Wu, Q., K. Takahashi, T. Okabayashi, and S. Nakamura. 2003. “Response characteristics of local vibrations in stay cables on an existing cable-stayed bridge.” J. Sound Vib. 261 (3): 403–420. https://doi.org/10.1016/S0022-460X(02)01088-X.
Xia, Y., and Y. Fujino. 2006. “Auto-parametric vibration of a cable-stayed-beam structure under random excitation.” J. Eng. Mech. 132 (3): 279–286. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:3(279).
Yang, Y. Q., X. Wang, and Z. S. Wu. 2015. “Experimental study of vibration characteristics of FRP cables for long-span cable-stayed bridges.” J. Bridge Eng. 20 (4): 04014074. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000656.
Yin, X. F., G. B. Song, and L. Yang. 2019. “Vibration suppression of wind/traffic/bridge coupled system using multiple pounding tuned mass dampers.” Sensors 19 (5): 1133. https://doi.org/10.3390/s19051133.
Yuan, C. S., R. L. Shen, L. Y. Zhou, W. D. Li, and K. Guan. 2015. “Nonlinear free vibration of inclined cables taking into account the effect of chord component of gravity.” [In Chinese.] J. Vib. Shock 34 (12): 201–206.
Zhang, L. N., F. C. Li, X. Y. Wang, and P. F. Cui. 2017. “Theoretical and numerical analysis of 1:1 main parametric resonance of stayed cable considering cable-beam coupling.” Adv. Mater. Sci. Eng. 2017: 1–10. https://doi.org/10.1155/2017/6948081.
Zhang, L. N., F. C. Li, X. Yu, P. F. Cui, and X. Y. Wang. 2016. “Experimental research on 2:1 parametric vibration of stay cable model under support excitation.” Adv. Mater. Sci. Eng. 2016: 1–9. https://doi.org/10.1155/2016/9804159.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 33 • Issue 1 • January 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 5, 2018
Accepted: Aug 26, 2019
Published online: Oct 25, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 25, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.