Browse > Article
http://dx.doi.org/10.12989/sem.2020.76.3.293

Analytical study on free vertical and torsional vibrations of two- and three-pylon suspension bridges via d'Alembert's principle  

Zhang, Wen-ming (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Wang, Zhi-wei (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Zhang, Hao-qing (China Railway Major Bridge Reconnaissance & Design Institute Co., Ltd)
Lu, Xiao-fan (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Liu, Zhao (The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University)
Publication Information
Structural Engineering and Mechanics / v.76, no.3, 2020 , pp. 293-310 More about this Journal
Abstract
This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.
Keywords
suspension bridge; continuum model; free vibration; differential equation; vertical bending; torsion; natural vibration frequency; vibration mode;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Li, J.Z., Yan, J. and Peng, T.B. (2015), "Shake table studies of seismic structural systems of a Taizhou Changjiang highway bridge model", J. Bridge Eng., 20(3), 04014065. http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0000650   DOI
2 Pizarro, D., Hube, M.A., Valenzuela, M. and Márquez, M. (2015), "Dynamic characteristics of a longitudinally asymmetrical multi-span suspension bridge: the Chacao Bridge", Proceedings of IABSE Conference - Structural Engineering: Providing Solutions to Global Challenges, Geneva, Switzerland, September. http://dx.doi.org/10.2749/222137815818203971
3 Sun, Y., Zhu, H.P. and Xu, D. (2016), "A specific rod model based efficient analysis and design of hanger installation for self-anchored suspension bridges with 3D curved cables", Eng. Struct., 110, 184-208. http://dx.doi.org/10.1016/j.engstruct.2015.11.040   DOI
4 Ubertini, F. (2014), "Effects of cables damage on vertical and torsional eigenproperties of suspension bridges", J. Sound Vibr., 333(11), 2404-2421. http://dx.doi.org/10.1016/j.jsv.2014.01.027   DOI
5 Wu, C. and Jiang, C. (2016), "Fatigue behavior of hangers on a three-tower suspension bridge", Proceedings of International Conference on Sustainable Energy, Environment and Information Engineering (SEEIE), Bangkok, Thailand, March. http://dx.doi.org/10.12783/dteees/seeie2016/4680
6 Zhang, W.M. and Ge, Y.J. (2014), "Flutter mode transition of a double-main-span suspension bridge in full aeroelastic model testing", J. Bridge Eng., 19(7), 06014004. http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0000625   DOI
7 Zhang, W.M. and Ge, Y.J. (2017), "Wind tunnel investigation on flutter and buffeting of a three-tower suspension bridge", Wind Struct., 24(4), 367-384. http://dx.doi.org/10.12989/was.2017.24.4.367   DOI
8 Zhang, W.M., Shi, L.Y., Li, L. and Liu, Z. (2018), "Methods to correct unstrained hanger lengths and cable clamps' installation positions in suspension bridges", Eng. Struct., 171, 202-213. http://dx.doi.org/10.1016/j.engstruct.2018.05.039   DOI
9 Abdel-Ghaffar, A.M. (1979), "Free torsional vibrations of suspension bridges", J. Struct. Div., ASCE, 105(4), 767-788.   DOI
10 Abdel-Ghaffar, A.M. (1980), "Vertical vibration analysis of suspension bridges", J. Struct. Div., ASCE, 106(10), 2053-2075.   DOI
11 Cao, H.Y., Zhou, Y.L., Chen, Z.J. and Wahab, M.A. (2017), "Form-finding analysis of suspension bridges using an explicit iterative approach", Struct. Eng. Mech., 62(1), 85-95. http://dx.doi.org/10.12989/sem.2017.62.1.085   DOI
12 Abdel-Ghaffar, A.M. (1978), "Free lateral vibrations of suspension bridges", J. Struct. Div., ASCE, 104(3), 503-525.   DOI
13 Abdel-Ghaffar, A.M. and Rubin, L.I. (1983a), "Nonlinear free vibrations of suspension bridges: application", J. Eng. Mech., 109(1), 330-345.   DOI
14 Abdel-Ghaffar, A.M. and Rubin, L.I. (1983b), "Nonlinear free vibrations of suspension bridges: theory", J. Eng. Mech., 109(1), 313-329.   DOI
15 Capsoni, A., Ardito, R. and Guerrieri, A. (2017), "Stability of dynamic response of suspension bridges", J. Sound Vibr., 393, 285-307. http://dx.doi.org/10.1016/j.jsv.2017.01.009   DOI
16 Cheng, J. and Dong, F.H. (2016), "A simplified method for free vibration analysis of cable-stayed bridges", Int. J. Steel Struct., 16(1), 151-162. http://dx.doi.org/10.1007/s13296-016-3012-1   DOI
17 Castellani, A. and Felotti, P. (1986), "Lateral vibration of suspension bridges", J. Struct. Eng., ASCE, 112(9), 2169-2173. http://dx.doi.org/10.1061/(ASCE)0733-9445(1986)112:9(2169)   DOI
18 Chen, R.F. (2015), Theory of Long-span Suspension Bridges, Southwest Jiaotong University Press, Chengdu, Sichuan, China. (in Chinese)
19 Chen, Z.J., Cao, H.Y. and Zhu, H.P. (2013), "An iterative calculation method for suspension bridge's cable system based on exact catenary theory", Baltic J. Road Bridge Eng., 8(3), 196-204. http://dx.doi.org/10.3846/bjrbe.2013.25   DOI
20 Gorman, D.J. and Garibaldi, L. (2000), "A highly accurate and efficient analytical approach to bridge deck free vibration analysis", Shock Vibr., 7(6), 399-412. http://dx.doi.org/10.1155/2000/896361   DOI
21 Hayashikawa, T. (1997), "Torsional vibration analysis of suspension bridges with gravitational stiffness", J. Sound Vibr., 204(1), 117-129. http://dx.doi.org/10.1006/jsvi.1997.0948   DOI
22 Gorman, D.J. and Garibaldi, L. (2006), "Accurate analytical type solutions for free vibration frequencies and mode shapes of multi-span bridge decks: the span-by-span approach", J. Sound Vibr., 290(1-2), 321-336. http://dx.doi.org/10.1016/j.jsv.2005.03.020   DOI
23 Grigorjeva, T. and Kamaitis, Z. (2015), "Numerical analysis of the effects of the bending stiffness of the cable and the mass of structural members on free vibrations of suspension bridges", J. Civ. Eng. Manag., 21(7), 948-957. http://dx.doi.org/10.3846/13923730.2015.1055787   DOI
24 Gwon, S.G. and Choi, D.H. (2017), "Improved continuum model for free vibration analysis of suspension bridge", J. Eng. Mech., 143(7), 04017038. http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0001244   DOI
25 Gwon, S.G. and Choi, D.H. (2018a), "Continuum model for static and dynamic analysis of suspension bridges with a floating girder", J. Bridge Eng., 23(10), 04018079. http://dx.doi.org/10.1061/(ASCE)BE.1943-5592.0001282   DOI
26 Gwon, S.G. and Choi, D.H. (2018b), "Static and dynamic analyses of a suspension bridge with three-dimensionally curved main cables using a continuum model", Eng. Struct., 161, 250-264. http://dx.doi.org/10.1016/j.engstruct.2018.01.062   DOI
27 Hayashikawa, T. and Watanabe, N. (1984), "Vertical vibration in Timoshenko beam suspension bridges", J. Eng. Mech., 110(3), 341-356. http://dx.doi.org/10.1061/(ASCE)0733-9399(1984)110:3(341)   DOI
28 Irvine, M. (1974), "Torsional vibrations in boxgirder suspension bridges", Earthq. Eng. Struct. Dyn., 3(2), 203-213. http://dx.doi.org/10.1002/eqe.4290030208   DOI
29 Kim, M.Y., Kwon, S.D. and Kim, N.I. (2000), "Analytical and numerical study on free vertical vibration of shear-flexible suspension bridges", J. Sound. Vibr., 238(1), 65-84. http://dx.doi.org/10.1006/jsvi.2000.3079   DOI