Abstract
Nonlinear dynamic analysis of a cable-stayed bridge has been a hot topic due to its structural flexibility. Based on integro-partial differential equations of a double-cable-stayed shallow-arch model, in-plane 2:2:1 internal resonance among three first in-plane modes of two cables and a shallow arch under external primary or subharmonic resonance is considered. Galerkin's method and the method of multiple scales are used to derive averaged equations of this cable-stayed bridge system. Nonlinear dynamic behaviors of the system are investigated via numerical simulation. Results show rich nonlinear phenomena of the cable-stayed bridge system and some new phenomena are observed. Two identical cables that are symmetrically located above the shallow arch can have different dynamic behaviors even when initial conditions of the system are symmetrically given. Two cables with some differences between their parameters can exhibit either softening or hardening characteristics.
Issue Section:
Research Papers
References
1.
Kang
, H.
,
Guo
, T.
,
Zhu
, W.
,
Su
, J.
, and
Zhao
, B.
, 2019
, “Dynamical Modeling and Non-Planar Coupled Behavior of Inclined CFRP Cable Under Simultaneous Internal and External Resonances
,” Appl. Math. Mech.-Engl.
, 40
(5
), pp. 649
–678
.10.1007/s10483-019-2472-6
2.
Kang
, H. J.
,
Zhao
, Y. Y.
, and
Zhu
, H. P.
, 2015
, “Linear and Nonlinear Dynamics of Suspended Cable Considering Bending Stiffness
,” J. Vib. Control
, 21
(8
), pp. 1487
–1505
.10.1177/1077546313499390
3.
Rega
, G.
, and
Srinil
, N.
, 2007
, “Nonlinear Hybrid-Mode Resonant Forced Oscillations of Sagged Inclined Cables at Avoidances
,” ASME J. Comput. Nonlin. Dyn.
, 2
(4
), pp. 324
–336
.10.1115/1.2756064
4.
Ding
, H.
,
Huang
, L.
,
Mao
, X.
, and
Chen
, L.
, 2017
, “Primary Resonance of Traveling Viscoelastic Beam Under Internal Resonance
,” Appl. Math. Mech.-Engl.
, 38
(1
), pp. 1
–14
.10.1007/s10483-016-2152-6
5.
Yi
, Z.
, and
Stanciulescu
, I.
, 2016
, “Nonlinear Normal Modes of a Shallow Arch With Elastic Constraints for Two-to-One Internal Resonances
,” Nonlinear Dyn.
, 83
(3
), pp. 1577
–1600
.10.1007/s11071-015-2432-3
6.
Tripathi
, A.
, and
Bajaj
, A. K.
, 2016
, “Topology Optimization and Internal Resonances in Transverse Vibrations of Hyperelastic Plates
,” Int. J. Solids Struct.
, 81
, pp. 311
–328
.10.1016/j.ijsolstr.2015.11.029
7.
Rossikhin
, Y. A.
, and
Shitikova
, M. V.
, 2015
, “Nonlinear Dynamic Response of a Fractionally Damped Cylindrical Shell With a Three-To-One Internal Resonance
,” Appl. Math. Comput.
, 257
, pp. 498
–525
.8.
Gattulli
, V.
, and
Lepidi
, M.
, 2003
, “Nonlinear Interactions in the Planar Dynamics of Cable-Stayed Beam
,” Int. J. Solids Struct.
, 40
(18
), pp. 4729
–4748
.10.1016/S0020-7683(03)00266-X
9.
Gattulli
, V.
,
Morandini
, M.
, and
Paolone
, A.
, 2002
, “A Parametric Analytical Model for Non-Linear Dynamics in Cable-Stayed Beam
,” Earthquake Eng. Struct. Dyn.
, 31
(6
), pp. 1281
–1300
.10.1002/eqe.162
10.
Huang
, K.
,
Feng
, Q.
, and
Yin
, Y.
, 2014
, “Nonlinear Vibration of the Coupled Structure of Suspended- Cable-Stayed Beam—1:2 Internal Resonance
,” Act. Mec. Sol.
, 27
(5
), pp. 467
–476
.10.1016/S0894-9166(14)60055-0
11.
Wang
, Y.
, and
Zhu
, W.
, 2021
, “Nonlinear Transverse Vibration of a Hyperelastic Beam Under Harmonically Varying Axial Loading
,” ASME J. Comput. Nonlinear Dyn.
, 16
(3
), p. 031006
.10.1115/1.4049562
12.
Nayfeh
, A. H.
, 2000
,
Nonlinear Interactions
,” Willey
, New York
.13.
Irvine
, H. M.
, 1981
,
Cable Structures
,” The MIT Press
, Cambridge, MA and London, UK
.14.
Rega
, G.
, 2004
, “Nonlinear Vibrations of Suspended Cables—Part I: Modeling and Analysis
,” ASME Appl. Mech. Rev.
, 57
(6
), pp. 443
–478
.10.1115/1.1777224
15.
Rega
, G.
, 2004
, “Nonlinear Vibrations of Suspended Cables—Part II: Deterministic Phenomena
,” ASME Appl. Mech. Rev.
, 57
(6
), pp. 479
–514
.10.1115/1.1777225
16.
Emam
, S. A.
, and
Nayfeh
, A. H.
, 2013
, “Non-Linear Response of Buckled Beams to 1:1 and 3:1 Internal Resonances
,” Int. J. Non-Linear Mech.
, 52
(6
), pp. 12
–25
.10.1016/j.ijnonlinmec.2013.01.018
17.
Gattulli
, V.
,
Lepidi
, M.
,
Macdonald
, J. H. G.
, and
Taylor
, C. A.
, 2005
, “One-To-Two Global-Local Interaction in a Cable-Stayed Beam Observed Through Analytical, Finite Element and Experimental Models
,” Int. J. Non-Linear Mech.
, 40
(4
), pp. 571
–588
.10.1016/j.ijnonlinmec.2004.08.005
18.
Lilien
, J. L.
, and
Costa
, A. P. D.
, 1994
, “Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structures
,” J. Sound Vib.
, 174
(1
), pp. 69
–90
.10.1006/jsvi.1994.1261
19.
Gattulli
, V.
,
Martinelli
, L.
,
Perotti
, F.
, and
Vestroni
, F.
, 2004
, “Non-Linear Oscillations of Cables Under Harmonic Loading Using Analytical and Finite Element Models
,” Comput. Methods Appl. Mech. Eng.
, 193
(1–2
), pp. 69
–85
.10.1016/j.cma.2003.09.008
20.
Srinil
, N.
,
Rega
, G.
, and
Chucheepsakul
, S.
, 2007
, “Two-To-One Resonant Multi-Modal Dynamics of Horizontal/Inclined Cables—Part I: Theoretical Formulation and Model Validation
,” Nonlinear Dyn.
, 48
(3
), pp. 231
–252
.10.1007/s11071-006-9086-0
21.
Srinil
, N.
, and
Rega
, G.
, 2007
, “Two-to-One Resonant Multi-Modal Dynamics of Horizontal/Inclined Cables—Part II: Internal Resonance Activation, Reduced-Order Models and Nonlinear Normal Modes
,” Nonlinear Dyn.
, 48
(3
), pp. 253
–274
.10.1007/s11071-006-9087-z
22.
Marsico
, M. R.
,
Tzanov
, V.
,
Wagg
, D. J.
,
Neild
, S. A.
, and
Krauskopf
, B.
, 2011
, “Bifurcation Analysis of a Parametrically Excited Inclined Cable Close to Two-To-One Internal Resonance
,” J. Sound Vib.
, 330
(24
), pp. 6023
–6035
.10.1016/j.jsv.2011.07.027
23.
Warnitchai
, P.
,
Fujino
, Y.
,
Pacheco
, B. M.
, and
Agret
, R.
, 1993
, “An Experimental Study on Active Tendon Control of Cable-Stayed Bridges
,” Earthquake Eng. Struct. Dyn.
, 22
(2
), pp. 93
–111
.10.1002/eqe.4290220202
24.
Warnitchai
, P.
,
Fujino
, Y.
, and
Susumpow
, T.
, 1995
, “A Non-Linear Dynamic Model for Cables and Its Application to a Cable–Structure System
,” J. Sound Vib.
, 187
(4
), pp. 695
–712
.10.1006/jsvi.1995.0553
25.
Wei
, M. H.
,
Xiao
, Y. Q.
,
Liu
, H. T.
, and
Lin
, K.
, 2014
, “Nonlinear Responses of a Cable-Beam Coupled System Under Parametric and External Excitations
,” Arch. Appl. Mech.
, 84
(2
), pp. 173
–185
.10.1007/s00419-013-0792-z
26.
Yi
, Z.
,
Wang
, L.
,
Kang
, H.
, and
Tu
, G.
, 2014
, “Modal Interaction Activations and Nonlinear Dynamic Response of Shallow Arch With Both Ends Vertically Elastically Constrained for Two-To-One Internal Resonance
,” J. Sound Vib.
, 333
(21
), pp. 5511
–5524
.10.1016/j.jsv.2014.05.052
27.
Wei
, M. H.
,
Xiao
, Y. Q.
, and
Liu
, H. T.
, 2012
, “Bifurcation and Chaos of a Cable–Beam Coupled System Under Simultaneous Internal and External Resonances
,” Nonlinear Dyn.
, 67
(3
), pp. 1969
–1984
.10.1007/s11071-011-0122-3
28.
Caetano
, E.
,
Cunha
, A.
, and
Taylor
, C. A.
, 2000
, “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
), pp. 481
–498
.10.1002/(SICI)1096-9845(200004)29:4<481::AID-EQE918>3.0.CO;2-1
29.
Ren
, W. X.
,
Peng
, X. L.
, and
Lin
, Y. Q.
, 2005
, “Experimental and Analytical Studies on Dynamic Characteristics of a Large Span Cable-Stayed Bridge
,” Biomed. Res. Trace Elem.
, 27
(4
), pp. 535
–548
.30.
Kang
, H. J.
,
Guo
, T. D.
,
Zhao
, Y. Y.
,
Fu
, W. B.
, and
Wang
, L. H.
, 2017
, “Dynamic Modeling and In-Plane 1:1:1 Internal Resonance Analysis of Cable-Stayed Bridge
,” Eur. J. Mech. A-Solid.
, 62
, pp. 94
–109
.10.1016/j.euromechsol.2016.10.016
31.
Cong
, Y.
,
Kang
, H.
, and
Guo
, T.
, 2019
, “Analysis of In-Plane 1:1:1 Internal Resonance of a Double Cable-Stayed Shallow Arch Model With Cables' External Excitations
,” Appl. Math. Mech.-Engl.
, 40
(7
), pp. 977
–1000
.10.1007/s10483-019-2497-8
32.
Caetano
, E.
,
Cunha
, A.
, and
Taylor
, C. A.
, 2000
, “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
), pp. 499
–521
.10.1002/(SICI)1096-9845(200004)29:4<499::AID-EQE919>3.0.CO;2-A
33.
Su
, X.
,
Kang
, H.
,
Chen
, J.
,
Guo
, T.
,
Sun
, C.
, and
Zhao
, Y.
, 2019
, “Experimental Study on In-Plane Nonlinear Vibrations of the Cable-Stayed Bridge
,” Nonlinear Dyn.
, 98
(2
), pp. 1247
–1266
.10.1007/s11071-019-05259-0
34.
Caetano
, E.
,
Cunha
, A.
,
Gattulli
, V.
, and
Lepidi
, M.
, 2008
, “Cable-Deck Dynamic Interactions at the International Guadiana Bridge: On-Site Measurements and Finite Element Modelling
,” Struct. Control Health
, 15
(3
), pp. 237
–264
.10.1002/stc.241
35.
Cao
, D. Q.
,
Song
, M. T.
,
Zhu
, W. D.
,
Tucker
, R. W.
, and
Wang
, H. T.
, 2012
, “Modeling and Analysis of the In-Plane Vibration of a Complex Cable-Stayed Bridge
,” J. Sound Vib.
, 331
(26
), pp. 5685
–5714
.10.1016/j.jsv.2012.07.010
36.
Mettler
, E.
, 1962
, “Dynamic Buckling
,”
Handbook of Engineering Mechanics
,
S.
Flügge
, ed., McGraw-Hill
, New York
.37.
Malhotra
, N.
, and
Namachchivaya
, N. S.
, 1997
, “Chaotic Dynamics of Shallow Arch Structures Under 1:2 Resonance
,” J. Eng. Mech.-ASCE
, 123
(6
), pp. 612
–619
.10.1061/(ASCE)0733-9399(1997)123:6(612)
38.
Luongo
, A.
,
Rega
, G.
, and
Vestroni
, F.
, 1984
, “Planar Nonlinear Free Vibrations of an Elastic Cable
,” Int. J. Non-Linear Mech.
, 19
(1
), pp. 39
–52
.10.1016/0020-7462(84)90017-9
39.
Wu
, Q.
,
Takahashi
, K.
,
Okabayashi
, T.
, and
Nakamura
, S.
, 2003
, “Response Characteristics of Local Vibrations in Stay Cables on an Existing Cable-Stayed Bridge
,” J. Sound Vib.
, 261
(3
), pp. 403
–420
.10.1016/S0022-460X(02)01088-X
40.
Nayfeh
, A. H.
, and
Mook
, D. T.
, 1979
,
Nonlinear Oscillations
, Wiley
, New York
.41.
Zhou
, Y.
, and
Chen
, S.
, 2015
, “Framework of Nonlinear Dynamic Simulation of Long-Span Cable-Stayed Bridge and Traffic System Subjected to Cable-Loss Incidents
,” J. Struct. Eng.-ASCE
, 36
(2
), pp. 124
–136
.https://doi.org/10.1061/(ASCE)ST.1943-541X.0001440
42.
Kang
, H. J.
,
Zhao
, Y. Y.
,
Zhu
, H. P.
, and
Yi
, Z.
, 2013
, “In-Plane Non-Linear Dynamics of the Stay Cables
,” Nonlinear Dyn.
,73
(3
), pp. 1385
–1398
.10.1007/s11071-013-0871-2
43.
Seydel
, R.
, 2009
,
Practical Bifurcation and Stability Analysis
,” Springer
, New York
.44.
Nayfeh
, A. H.
,
Mook
, D. T.
, and
Marshall
, L. R.
, 1973
, “Nonlinear Coupling of itch and Roll Modes in Ship Motions
,” AIAA-J. Hydronautics
, 7
(4
), pp. 145
–152
.10.2514/3.62949
45.
Guo
, T.
,
Kang
, H.
,
Wang
, L.
, and
Zhao
, Y.
, 2016
, “A Boundary Modulation Formulation for Cable's Non-Planar Coupled Dynamics Under Out-of-Plane Support Motion
,” Arch. Appl. Mech.
, 86
(4
), pp. 1
–13
.10.1007/s00419-015-1058-8
Copyright © 2021 by ASME
You do not currently have access to this content.
