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TECHNICAL PAPERS

The Phenomenon of Steady-State String Motion

[+] Author and Article Information
R. Miroshnik

The Israel Electric Corporation, Ltd. R&D Division, Amir Bldg. Haifa 31000, Israele-mail: mir@iec.co.il

J. Appl. Mech 68(4), 568-574 (Nov 18, 2000) (7 pages) doi:10.1115/1.1380677 History: Received May 23, 2000; Revised November 18, 2000
Copyright © 2001 by ASME
Topics: Motion , String , Steady state
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References

Aitkin, J., 1878, “An Account of Some Experiments on Rigidity Produced by Centrifugal Forces,” Philos. Mag., 5.
Radinger, G., 1878, Dampfmachinen, 5.
Smith,  W. E., and Weathezchon,  R. C., 1961, “A New Type of Thermal Radiator of Space Vehicle,” ARS, 20, No. 1, pp. 32–36.
Burge,  H., 1962, “Revolving Bolt Space Radiator,” ARS, 32, No. 8, pp. 17–25.
Voevodin, A. A., 1965, “Dynamic Equilibrium of Closed String in Earth Conditions,” Proceedings of USSR Connection department, Vol. 2, pp. 89–108.
Kurkin,  V. I., and Lebedev,  I. P., 1965, “Calculation of String Air Resistance,” Izvestia Vuzov, Tehnologia Tekstilnoi Prom., 1, M., pp. 166–169.
Svetlicky,  V. A., and Gabruk,  V. I., 1966, “Critical Velocities of the Steady State Motion,” Soviet Applied Mechanics, 6, pp. 13–17.
Cohen,  H., and Epstein,  M., 1994, “On a Class of Planar Motions of Flexible Rods,” ASME J. Appl. Mech., 61, pp. 206–208.
Nordenholz,  T. R., and O’Reilly,  O. M., 1995, “On Kinematical Conditions for Steady Motion of Strings and Rods,” ASME J. Appl. Mech., 62, pp. 820–822.
Svetlicky,  V. A., and Miroshnik,  R. A., 1972, “Critical Velocities of the Steady State Motion of an Elastic Fiber in a Planar Homogeneous Flow,” Soviet Applied Mechanics, 6, pp. 52–57.
Kurkin,  V. A., and Miroshnik,  R. A., 1988, “The Spatial Stationary Movement of the Heavy Perfectly Flexible Bar,” Soviet Applied Mechanics, 24, pp. 113–116.
Healey,  T. J., and Papadopoulos,  J. N., 1990, “Steady Axial Motion of Strings,” ASME J. Appl. Mech., 57, pp. 785–787.
Schagerl,  M., Steiner,  W., and Troger,  H., 1997, “On the Paradox of the Free Falling Folded Chair,” Acta Mech., 125, pp. 155–168.
Perkins,  N. C., and Mote,  C. D., 1987, “Three-Dimensional Vibration of Travelling Elastic Cables,” J. Sound Vib., 114, No.2, pp. 305–340.
Perkins,  N. C., and Mote,  C. D., 1989, “Theoretical and Experimental Stability of Two Translating Cable Equilibria,” J. Sound Vib., 128, No. 3,pp 397–410.

Figures

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Schematic illustration of the phenomenon
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Three kinds of steady-state string motion
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The theoretical string modes for subcritical velocities
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The theoretical string tension for subcritical velocities
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The four possible solutions satisfying the given boundary conditions
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The theoretical string modes (α=45 deg) for small super critical velocities
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The theoretical string modes (α=45 deg) for large super and hyper critical velocities
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The theoretical string modes (μ=21 m/sec2) for different starting angles
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The schematic diagram of experimental apparatus
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The theoretical and experimental modes (μ=28.3 m/sec2) for different start angles
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The theoretical and experimental modes (α=45 deg) for different velocities
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The theoretical string tension for the modes of Fig. 9
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The theoretical string tension for the modes of Fig. 10
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The explanation of the phenomenon’s existence

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