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TECHNICAL PAPERS

Bouncing-Ball Model of ‘Dry’ Motions of a Tethered Buoy

[+] Author and Article Information
R. H. Plaut, A. L. Farmer, M. M. Holland

The Charles E. Via, Jr. Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0105

J. Vib. Acoust 123(3), 333-339 (Dec 01, 2000) (7 pages) doi:10.1115/1.1375164 History: Received July 01, 2000; Revised December 01, 2000
Copyright © 2001 by ASME
Topics: Force , Motion , Cables , Buoys
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References

Carpenter,  E. B., Leonard,  J. W., and Yim,  S. C. S., 1995, “Experimental and Numerical Investigations of Tethered Spar and Sphere Buoys in Irregular Waves,” Ocean Eng., 22, pp. 765–784.
Idris,  K., Leonard,  J. W., and Yim,  S. C. S., 1997, “Coupled Dynamics of Tethered Buoy Systems,” Ocean Eng., 24, pp. 445–464.
Govardhan,  R., and Williamson,  C. H. K., 1997, “Vortex-Induced Motions of a Tethered Sphere,” J. Wind. Eng. Ind. Aerodyn., 69-71, pp. 375–385.
Williamson,  C. H. K., and Govardhan,  R., 1997, “Dynamics and Forcing of a Tethered Sphere in a Fluid Flow,” J. Fluids Struct., 11, pp. 293–305.
Gottlieb,  O., 1997, “Bifurcations of a Nonlinear Small-Body Ocean-Mooring System Excited by Finite-Amplitude Waves,” ASME J. Offshore Mech. Arct. Eng., 119, pp. 234–238.
Gottlieb, O., and Perlin, M., 1998, “Period-Doubling of an Elastically Tethered Sphere: Theory and Experiment,” Proceedings, 17th International OMAE Conference, ASME, New York, Paper OMAE98-0324.
Adrezin,  R., and Benaroya,  H., 1999, “Non-Linear Stochastic Dynamics of Tension Leg Platforms,” J. Sound Vib., 220, pp. 27–65.
Bar-Avi,  P., 1999, “Nonlinear Dynamic Response of a Tension Leg Platform,” ASME J. Offshore Mech. Arct. Eng., 121, pp. 219–226.
Bezverkhii,  A. I., 1998, “On Oscillations of Anchored Buoys on Waves,” International Applied Mechanics, 34, pp. 398–403.
Tjavaras,  A. A., Zhu,  Q., Liu,  Y., Triantafyllou,  M. S., and Yue,  D. K. P., 1998, “The Mechanics of Highly-Extensible Cables,” J. Sound Vib., 213, pp. 709–737.
Zhu,  Q., Liu,  Y., Tjavaras,  A. A., Triantafyllou,  M. S., and Yue,  D. K. P., 1999, “Mechanics of Nonlinear Short-Wave Generation by a Moored Near-Surface Buoy,” J. Fluid Mech., 381, pp. 305–335.
Virgin, L. N., 2000, An Introduction to Experimental Nonlinear Dynamics, Cambridge University Press, Cambridge, England.
Tufillaro, N. B., Abbott, T., and Reilly, J., 1992, An Experimental Approach to Nonlinear Dynamics and Chaos, Addison-Wesley, Redwood City, California.
Plaut,  R. H., and Farmer,  A. L., 2000, “Large Motions of a Moored Floating Breakwater Modeled as an Impact Oscillator,” Nonlinear Dyn., 23, pp. 319–334.
Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, New York.
Plaut, R. H., Farmer, A. L., and Holland, M. M., 2000, “A Simple Model for Slack/Taut Behavior of the Mooring Line of a Buoy,” Proceedings, Ocean Engineering Symposium, ETCE/OMAE 2000 Joint Conference, ASME, New York, Paper OMAE2000-8008, pp. 55–62.

Figures

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Geometry of buoy under (a) equilibrium, (b) slack, and (c) taut conditions
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Elliptical forcing in xy plane
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Trajectory for Case A: b=0.3,e=0.9,fo=0.1, Ω=0.9, y(0)=0.1
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Time histories for Case A
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Phase portraits for Case A
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Impact Poincaré plots for Case A
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Trajectory for Case B: b=0.1,e=0.9,fo=0.1, Ω=0.5, y(0)=0.1
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Time histories for Case B
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Trajectory for point mass: e=0.95,fo=1, Ω=0.9, y(0)=0.1,z(0)=0.1
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Impact velocity versus time for point mass
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Critical forcing amplitude versus forcing frequency
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Critical forcing amplitude versus coefficient of restitution
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Phase portraits for Case B

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