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REVIEW ARTICLES

Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow

[+] Author and Article Information
Raouf A Ibrahim

Department of Mechanical Engineering, Wayne State University, Detroit MI 48202

Appl. Mech. Rev 57(6), 515-549 (Feb 16, 2005) (35 pages) doi:10.1115/1.1804541 History: Online February 16, 2005
Copyright © 2004 by ASME
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References

Figures

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Three potentials with different wells and saddle points for α=γ=1.0
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Schematic diagram of a suspended cable showing the unperturbed and perturbed configurations and coordinate system
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Dependence of Cable natural frequencies on the cable parameter λ/π points Ci indicate 1:1 internal resonance 75
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Bifurcation diagrams and stability boundaries 76a) Region I: unimodal response of the first in-plane mode; region II: first in-plane and first out-of-plane mixed mode interaction; region III: first in-plane, first and second out-of-plane mixed mode interaction; region IV four-mode interaction b) Stability boundaries of equilibria of the second in-plane, first and second out-of-plane modes, light shaded region indicates two-mode interactio, medium shaded is three-mode interaction, and dark shaded if four-mode interaction
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Normalized time history records of mean square responses of cable modes 76
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Dependece of mean square response on excitation level ζ1=0.004,ζ2=0.00011,ζ3=0.0001 and ζ4=0.0001,ωa1a2b1b2=2:2:1:276
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Depenence of normalized mean square responses on internal detuning parameter for ζ1=0.004,ζ2=0.00011,ζ3=0.001,ζ40.0001, and σw2=0.01576
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Probability density functions and power spectra of a) first in-plane mode, b) second in-plane mode, c) first out-of-plane mode, and d) second out-of-plane mode for ζ1=0.004,ζ2=0.00011,ζ3=0.001,ζ4=0.0001, and σw2=0.01576
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a) Taut oceanographic mooring system, and b) Inverse-catenary mooring system 155
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Tension power spectra of a taut oceanographic mooring system (– predicted, [[dashed_line]]measured) 155
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Tension power spectra in inverse-catenary mooring system for two different sea waves a) ηs=2.89 m,fp=0.11 Hz,b) ηs=6.26 m,fp=0.081 Hz155
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Dependence of the root mean square displacement response on the flow speed 182
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Time history records of vertical and torsion cable motion including additional lift related to torsional motion 226
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Probability density function of the short-circuit current 227
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Schematic diagram of a mooring line analyzed by Sarkar and Eatok Taylor 240
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Dynamic and quasi-static drag distribution over the cable length –Dynamic, –⋅– Quasi-dynamic 240
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a) Drag distribution, b) power spectral density of cable surge response, c) power spectral density of cable tension for three excitation band-widths: –0.5–2.5 rad/s, [[dashed_line]]1–2 rad/s, –⋅– 1.25–1.75 rad/s 240
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Power spectral density of out-of-plane cable response at s=L/2, –with friction, –⋅– without friction 240
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Time history records and configuration diagrams for two different values of flow speed parameter a) less than the critical speed, b) greater than the critical speed 247
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Definition of stretching, ξ, and transverse, ψ, coordinates 247
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Time history records of the stretching motions as estimated by integrating Eq. (47) shown by dashed curves, and by the asymptotic approach shown by solid curves for two different values of the gravity parameter κ 247
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Time history records of the stretching and transverse coordinates (ξ,ψ), the configuration diagrams and time history records of modal coordinates (W1,W2) for two different values of flow speed a) V=0.29, and b) V=0.3247
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Time history records, spectra of stretching and transverse coordinates, configuration diagrams and time history records of modal coordinates for three different values of fluid flow speed a) V=0.4,b) V=0.7, and c) V=1.0248
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Time history records and statistics of the fluid flow and cable motion under random fluid flow with mean flow speed E[Vf]=0.5, and standard deviation σΔVf=0.005 for μ=0.3,κ=1.0,248: a) Magnification sections of time history records of random fluid flow velocity, transverse and stretching motions, and stretching mean square; b) time history records of modal amplitudes and configuration diagram under random fluid flow speed; and c) power spectra and probability density functions of fluid flow speed and stretching displacement of the cable under random fluid flow
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Bridge vibration amplitude dependence on wind velocity of bridges of main span length a) 365 m, b) 465 m 269
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Recorded cable vibration showing cable acceleration in a) time domain, b) time and frequency domain (Wavelet) 269
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a) Schematic diagram of a cable represented by a taut string with attached damper considered in reference 297b) dependence of rms displacement on damper location for passive, semi-active, and fully active dampers 297

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