The limit cycle oscillations (LCOs) exhibited by long-span suspension bridges in post-flutter condition are investigated. A parametric dynamic model of prestressed long-span suspension bridges is coupled with a nonlinear quasi-steady aerodynamic formulation to obtain the governing aeroelastic partial differential equations adopted herewith. By employing the Faedo–Galerkin method, the aeroelastic nonlinear equations are reduced to their state-space ordinary differential form. Convergence analysis for the reduction process is first carried out and time-domain simulations are performed to investigate LCOs while continuation tools are employed to path follow the post-critical LCOs. A supercritical Hopf bifurcation behavior, confirmed by a stable LCO, is found past the critical flutter condition. The analysis shows that the LCO amplitude increases with the wind speed up to a secondary critical speed where it terminates with a fold bifurcation. The stability of the LCOs within the range bracketed by the Hopf and fold bifurcations is evaluated by performing parametric analyses regarding the main design parameters that can be affected by uncertainties, primarily the structural damping and the initial wind angle of attack.

References

References
1.
Nayfeh
,
A.
, and
Pai
,
P.
,
2004
,
Linear and Nonlinear Structural Mechanics
,
Wiley-Interscience
,
New York
.
2.
Pai
,
P.
,
2007
,
Highly Flexible Structures: Modeling, Computation and Experimentation
,
AIAA Education Series
, Reston, VA.
3.
Irvine
,
H. M.
,
1981
,
Cable Structures
,
MIT Press
,
Cambridge, MA
.
4.
Abdel-Ghaffar
,
A. M.
,
1982
, “
Suspension Bridge Vibration: Continuum Formulation
,”
J. Eng. Mech. Div. ASCE
,
108
(
6
), pp.
1215
1232
.
5.
Abdel-Ghaffar
,
A. M.
, and
Rubin
,
L. I.
,
1983
, “
Nonlinear Free Vibrations of Suspension Bridges: Theory
,”
J. Eng. Mech. Div. ASCE
,
109
(
1
), pp.
313
329
.
6.
Abdel-Ghaffar
,
A. M.
, and
Rubin
,
L. I.
,
1983
, “
Nonlinear Free Vibrations of Suspension Bridges: Application
,”
J. Eng. Mech. Div. ASCE
,
109
, pp.
330
345
.
7.
Abdel-Rohman
,
M.
, and
Nayfeh
,
A. H.
,
1987
, “
Passive Control of Nonlinear Oscillations in Bridges
,”
J. Eng. Mech. Div. ASCE
,
113
, pp.
1694
1708
.
8.
Abdel-Rohman
,
M.
, and
Nayfeh
,
A. H.
,
1987
, “
Active Control of Nonlinear Oscillations in Bridges
,”
J. Eng. Mech. Div. ASCE
,
113
(
3
), pp.
335
349
.
9.
Casalotti
,
A.
,
Arena
,
A.
, and
Lacarbonara
,
W.
,
2014
, “
Mitigation of Post-Flutter Oscillations in Suspension Bridges by Hysteretic Tuned Mass Dampers
,”
Eng. Struct.
,
69
, pp.
62
71
.
10.
Çevika
,
M.
, and
Pakdemirli
,
M.
,
2005
, “
Non-Linear Vibrations of Suspension Bridges With External Excitation
,”
Int. J. Nonlinear Mech.
,
40
(
6
), pp.
901
923
.
11.
Malík
,
J.
,
2006
, “
Nonlinear Models of Suspension Bridges
,”
J. Math. Anal. Appl.
,
321
(
2
), pp.
828
850
.
12.
Malík
,
J.
,
2006
, “
Generalized Nonlinear Models of Suspension Bridges
,”
J. Math. Anal. Appl.
,
324
(
2
), pp.
1288
1296
.
13.
McKenna
,
P. J.
,
1999
, “
Large Torsional Oscillations in Suspension Bridges Revised: Fixing an Old Approximation
,”
Am. Math. Mon.
,
106
(
1
), pp.
1
18
.
14.
Drábek
,
P.
, and
Holubová
,
G.
,
1999
, “
Bifurcation of Periodic Solutions in Symmetric Models of Suspension Bridges
,”
Topol. Methods Nonlinear Anal.
,
14
, pp.
39
58
.
15.
Lepidi
,
M.
, and
Piccardo
,
G.
,
2015
, “
Aeroelastic Stability of a Symmetric Multi-Body Section Model
,”
Meccanica
,
50
(
3
), pp.
731
749
.
16.
Pascoletti
,
A.
, and
Zanolin
,
F.
,
2008
, “
Example of a Suspension Bridge ODE Model Exhibiting Chaotic Dynamics: A Topological Approach
,”
J. Math. Anal. Appl.
,
339
(
2
), pp.
1179
1198
.
17.
Tian
,
R.
, and
Yiang
,
X.
,
2011
, “
Nonlinear Vibration Characteristics of Flexible Suspension Bridge Under Moving Load
,”
Adv. Mater. Res.
,
179–180
, pp.
1025
1030
.
18.
Drábek
,
P.
,
Holubová
,
G.
,
Matas
,
A.
, and
Nečesal
,
P.
,
2003
, “
Nonlinear Models of Suspension Bridges: Discussion of the Results
,”
Appl. Math.
,
48
(
6
), pp.
497
514
.
19.
Lacarbonara
,
W.
, and
Arena
,
A.
,
2011
, “
Flutter of an Arch Bridge Via a Fully Nonlinear Continuum Formulation
,”
J. Aerosp. Eng.
,
24
(
1
), pp.
112
123
.
20.
Arena
,
A.
, and
Lacarbonara
,
W.
,
2012
, “
Nonlinear Parametric Modeling of Suspension Bridges Under Aeroelastic Forces: Torsional Divergence and Flutter
,”
Nonlinear Dyn.
,
70
(
4
), pp.
2487
2510
.
21.
Bisplinghoff
,
R.
,
Ashley
,
H.
, and
Halfman
,
R.
,
1955
,
Aeroelasticity
,
Dover Publication
,
New York
.
22.
Salvatori
,
L.
, and
Borri
,
C.
,
2007
, “
Frequency- and Time-Domain Methods for the Numerical Modeling of Full-Bridge Aeroelasticity
,”
Comput. Struct.
,
85
(
11–14
), pp.
675
687
.
23.
Petrini
,
F.
,
Giuliano
,
F.
, and
Bontempi
,
F.
,
2007
, “
Comparison of Time Domain Techniques for the Evaluation of the Response and the Stability in Long Span Suspension Bridges
,”
Comput. Struct.
,
85
(
11–14
), pp.
1032
1048
.
24.
Lacarbonara
,
W.
,
2013
,
Nonlinear Structural Mechanics. Theory, Dynamical Phenomena and Modeling
,
Springer
,
New York
.
25.
Arena
,
A.
,
Lacarbonara
,
W.
,
Valentine
,
D. T.
, and
Marzocca
,
P.
,
2014
, “
Aeroelastic Behavior of Long-Span Suspension Bridges Under Arbitrary Wind Profiles
,”
J. Fluids Struct.
,
50
, pp.
105
119
.
26.
Scanlan
,
R. H.
, and
Tomko
,
J.
,
1971
, “
Airfoil and Bridge Deck Flutter Derivatives
,”
J. Eng. Mech.
,
97
(
6
), pp.
1717
1737
.
27.
Farsani
,
H. Y.
,
Valentine
,
D. T.
,
Arena
,
A.
,
Lacarbonara
,
W.
, and
Marzocca
,
P.
,
2014
, “
Indicial Functions in the Aeroelasticity of Bridge Decks
,”
J. Fluids Struct.
,
48
, pp.
203
215
.
28.
Zhang
,
X.
,
Xiang
,
H.
, and
Sun
,
B.
,
2002
, “
Nonlinear Aerostatic and Aerodynamic Analysis of Long-Span Suspension Bridges Considering Wind–Structure Interactions
,”
J. Wind Eng. Ind. Aerodyn.
,
90
(
9
), pp.
1065
1080
.
29.
Miyata
,
T.
,
Yamada
,
H.
,
Boonyapinyo
,
V.
, and
Stantos
,
J. C.
,
1995
, “
Analytical Investigation on the Response of a Very Long Suspension Bridge Under Gusty Wind
,”
Proceedings of the 9th International Conference on Wind Engineering
, Paper No. 10061017.
30.
Chen
,
X.
, and
Kareem
,
A.
,
2002
, “
Advances in Modeling of Aerodynamic Forces on Bridge Decks
,”
J. Eng. Mech.
,
128
(
11
), pp.
1193
1205
.
31.
Arena
,
A.
,
2012
, “
Aeroelasticity of Suspension Bridges Using Nonlinear Aerodynamics and Geometrically Exact Structural Models
,” Ph.D., thesis, Sapienza University of Rome, Rome, Italy.
32.
Wolfram Research
,
I.
,
2008
,
Mathematica, Version 7.0 ed.
,
Wolfram Research
,
Champaign, IL
.
33.
Dankowicz
,
H.
, and
Schilder
,
F.
,
2011
, “
An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints
,”
ASME J. Comput. Nonlinear Dyn.
,
6
(
3
), p.
031003
.
34.
Formica
,
G.
,
Arena
,
A.
,
Lacarbonara
,
W.
, and
Dankowicz
,
H.
,
2013
, “
Coupling FEM With Parameter Continuation for Analysis of Bifurcations of Periodic Responses in Nonlinear Structures
,”
ASME J. Comput. Nonlinear Dyn.
,
8
, p.
021013
.
This content is only available via PDF.
You do not currently have access to this content.