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The strumming vibrations of marine cables : state of the art online

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ASME, Journal of Fluids Engineering, Vol. 98, 19-27, 1976.

E9. M. Kennedy and J.K. Vandiver, "A Random Vibration Model for Cable Strumming Prediction,"
CIVIL ENGINEERING IN THE OCEANS IV, Vol. I, 273-292, ASCE: New York, September
1979.

ElO. J.F. Howell, "Soil-Structure Interaction Under Wind Loading," Ph.D. Thesis, University of
Western Ontario, London, Ont., April 1978.

Ell. K.C.S. Kwok and W.H. Melbourne, "Cross- Wind Response Due to the Cross-Stream Vibration of
Circular Cylinders in Uniform and Shear Flows," in Proc. Fifth Int. Conf. on Wind Engrg. (Pre-
prints), Vol. II, Fort Collins, CO, Paper VI-4, July 1979.

E12. T. Sarpkaya and R.L. Shoaflf, "Discrete Vortex Analysis of Transverse Oscillations of a Circular
Cylinder in Uniform Flow," Naval Postgraduate School Report NPS-69SL79011, January 1979.

El 3. T. Sarpkaya and R.L. Shoaff, "Numerical Modelling of Vortex-Excited Oscillations," CIVIL
ENGINEERING IN THE OCEANS IV, Vol. I, 504-517, ASCE: New York, September 1979.



172



E14. D.J. Maull, "An Introduction to the Discrete Vortex Model," Cambridge University Engineering
Department Report CUED/A-Aero/TR8, 1979.

El 5. R.R. Clements and D.J. Maull, "The Representation of Sheets of Vorticity by Discrete Vortices,"
Progress in Aerospace Science, Vol. 16, No. 2, 129-146, 1975.

E16. P.K. Stansby, "An inviscid model of vortex shedding from a circular cylinder in steady and oscilla-
tory far flows," Proceedings of the Institution of Civil Engineers, Vol. 63, 865-880, 1977.

E17. S.E. Hurlbut, M.L. Spaulding and P.M. White, "Numerical Solution of the Time Dependent
Navier-Stokes Equations in the Presence of an Oscillating Cylinder," in Numerical Solution of Non-
Steady Flows, ASME: New York, 201-206, 1978.

El 8. S.E. Hurlbut and M.L. Spaulding, "A Numerical Model of Fluid-Structure Interaction for Circular
Cylinders," University of Rhode Island, Department of Ocean Engineering Contract Report,
November 1978.

El 9. P.M. Greshko, R.L. Lee and CD. Upson, "FEM solution of the Navier-Stokes equations for the
vortex shedding behind a cylinder: experiments with the four-node element," in Proceedings of the
Third International Conference on Finite Elements in Water Resources (Preprints), The University of
Mississippi: Oxford, Vol. 2, 4.48-4.65, 1980.



173



Table El. Normal Modes t//,(z) and Corresponding
Values of /,~'^^ for Various Structural Forms

I. Pivoted Rigid Rod

Normal modes: <//] = z/L, i//,;^i =

lr\l^ ■ : (5/3)'^= = 1.2910

11. Taut String

Normal modes: i/», = smivz/ L

ir^'^ : (4/3)'/' = 1.1547

III. Pinned-Pinned Beam
Normal modes: »//, = sini-n-z/ L

/-'/2 : (4/3)'/== 1.1547

IV. Cantilevered Beam

Normal modes; i//, = cosh \,z/L - cos X,z/L - a,(sinh kiz/L - sin X/z/L)

i A., a, /,""•=

1 1.87510410 0.73409550 0.6525

2 4.19409113 1.01846644 0.7494

3 7.85475743 0.99922450 0.7686

V. Clamped-Clamped Beam

Normal modes; i//, = cosh K,z/ L — cos \,z/ L — u,(sinh k,z/ L — sin \,zl L)
i \, a, /,-"^

1 4.75300408 0.98250222 0.7348

2 7.8532046 1.00077731 0.7694

3 10.9956078 0.99996645 0.7817

VI. Clamped-Pinned Beam

Normal modes: i|/, = coshX,z/L - cos \,z/L - a,(sinh X;z/L - sinX,z/L)
/ \, a, /, "'



1


3.92660230


1.00077730


0.7694


2


7.06858275


1.00000144


0.7891


3


10.21027613


1.00000000


0.7972



VII. Free-Pinned Beam
Normal modes: i//, = cosh X,(z/L) + cos X,(z/L) - a,[sinh X,(z/L) + sin X,(z/L)]

/ \, a, J,-'"



1 3.92660


1.000773


0.7628


2 7.06858


1.000000


0.7890


3 10.2102


1 .000000


0.7972



174






LJ
O
<

_J
Q-
CO



0.01




0.2



1.0 10.0

REDUCED DAMPING, ( 27r St )^k<



100.0



Figure El Predicled cross flow displacemcnl amplitude Yl D plolled againsi Ihe reduced damping (.l-nSl)^k; for llic sine
mode resonani response of a flexible siruclurc; from BIcvins and Burlon (E8). The aspect ratio of the structure, i.e., a ca-
ble, is given by LID.



175




Figure E2 Evolution with time of the vortex shedding in the wake of an oscillating cylinder; from
Sarpkaya and Shoaff (E12). The vortex sheets emanating from the cylinder are calculated with the
discrete vortex method (DVM). The arrow represents the direction of the incident flow relative to
the instantaneous position of the cylinder.



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Online LibraryOwen M GriffinThe strumming vibrations of marine cables : state of the art → online text (page 12 of 12)