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Research Papers

Post-Critical Behavior of Suspension Bridges Under Nonlinear Aerodynamic Loading

[+] Author and Article Information
Andrea Arena

Department of Structural
and Geotechnical Engineering,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: andrea.arena@uniroma1.it

Walter Lacarbonara

Department of Structural
and Geotechnical Engineering,
Sapienza University of Rome,
Rome 00184, Italy
e-mail: walter.lacarbonara@uniroma1.it

Pier Marzocca

Professor
Department of Aerospace, Mechanical and Manufacturing Engineering,
RMIT University,
Melbourne VIC 3001, Australia
e-mail: pier.marzocca@rmit.edu.au
Department of Mechanical and Aeronautical
Engineering,
Clarkson University,
8 Clarkson Avenue,
Potsdam, NY 13699
e-mail: pmarzocc@clarkson.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 3, 2014; final manuscript received March 11, 2015; published online June 30, 2015. Assoc. Editor: D. Dane Quinn.

J. Comput. Nonlinear Dynam 11(1), 011005 (Jun 30, 2015) (11 pages) Paper No: CND-14-1087; doi: 10.1115/1.4030040 History: Received April 03, 2014; Revised March 11, 2015

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.

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References

Figures

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Fig. 1

Schematic 3D view of the single-span suspension bridge model in its reference configuration

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Fig. 2

Aerodynamic loads acting on the bridge deck section

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Fig. 3

Aerodynamic coefficients for the deck section of the Runyang suspension bridge [27,31]: (top) lift and drag and (bottom) aerodynamic moment

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Fig. 4

Convergence of the eigenvalues with increasing numbers of trial functions: (top) real parts and (bottom) imaginary parts. The gray lines indicate the symmetric bending–torsional mode while the solid black lines indicate the skew-symmetric mode.

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Fig. 5

Convergence of the LCO response at the post-critical speed U = 68 m/s, with ζ = 0.5%: (top) torsional rotation φ3 and (center) vertical displacement u2 at quarter-span, (bottom) FFT of the torsional rotation φ3 at quarter-span

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Fig. 10

LCO at the post-flutter speed U = 55 m/s, with ζ = 0.5%. (a) Deck torsional rotation φ3, (b) vertical displacement u2, and (c) horizontal displacement u1.

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Fig. 11

LCO at the post-flutter speed U = 55 m/s, with ζ = 0.5% (critical mode shape)

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Fig. 9

Variations with the wind speed U (top) of the real parts (damping) and (bottom) of the imaginary parts (frequency) at selected initial wind angles of attack, αw=6 deg. The gray lines indicate the symmetric mode while the solid black lines indicate the skew-symmetric mode.

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Fig. 8

Variations with the wind speed U (top) of the real parts (damping) and (bottom) of the imaginary parts (frequency) at selected initial wind angles of attack, αw=3 deg. The gray lines indicate the symmetric mode while the solid black lines indicate the skew-symmetric mode.

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Fig. 7

Variations with the wind speed U (top) of the real parts (damping) and (bottom) of the imaginary parts (frequency) at selected initial wind angles of attack, αw=0 deg. The gray lines indicate the symmetric mode while the solid black lines indicate the skew-symmetric mode.

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Fig. 6

Variation of the lowest two critical speeds with the initial angle of attack. The gray line indicates the symmetric bending–torsional mode while the solid black line indicates the skew-symmetric mode. The inserts show the skew-symmetric and symmetric bridge mode shapes.

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Fig. 12

Stable branches (solid lines) and unstable branches (dashed lines) of the bifurcation curves: comparison with direct time integration results (represented by the circles). (Top) Maximum torsional rotation φ3 max and (bottom) maximum vertical displacement u2 max at quarter-span.

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Fig. 13

Bifurcation curves at selected values of damping ratio ζ. Stable branches (solid lines) and unstable branches (dashed lines). (Top) Maximum torsional rotation φ3 max and (bottom) maximum vertical displacement u2 max at quarter-span.

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Fig. 14

Bifurcation curves at selected angles of attack αw. Stable branches (solid lines) and unstable branches (dashed lines). (Top) Maximum torsional rotation φ3 max and (bottom) maximum vertical displacement u2 max at quarter-span.

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Fig. 15

Range of stability of LCOs: (top) variation with the damping ratio ζ for αw=0 deg and (bottom) variation with the angle of attack αw for ζ = 0.5%

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