The paper examines the phenomenon of steady-state motion for a string traveling with constant velocity along an invariant curve under gravity in a viscous medium. This technically important phenomenon has been known in the literature for about 120 years and may be applied in high-speed turbines, the textile industry, etc. The conditions for the phenomenon’s existence are found. Concepts of two critical string velocities as well as sub, super, and hypercritical domains are introduced. The analytical solutions for the nonlinear differential equations and arbitrary constants for the general boundary conditions are found. The theoretical results are very close to the experimental ones.

Issue Section:
Technical Papers
Keywords:
nonlinear differential equations, boundary-value problems, drag, dynamics, turbines, textile industry, force
Topics:
String, Steady state
1.
Aitkin, J., 1878, “An Account of Some Experiments on Rigidity Produced by Centrifugal Forces,” Philos. Mag., 5.
2.
Radinger, G., 1878, Dampfmachinen, 5.
3.
Smith
,
W. E.
, and
Weathezchon
,
R. C.
,
1961
, “
A New Type of Thermal Radiator of Space Vehicle
,”
ARS
,
20
, No.
1
, pp.
32
–
36
.
4.
Burge
,
H.
,
1962
, “
Revolving Bolt Space Radiator
,”
ARS
,
32
, No.
8
, pp.
17
–
25
.
5.
Voevodin, A. A., 1965, “Dynamic Equilibrium of Closed String in Earth Conditions,” Proceedings of USSR Connection department, Vol. 2, pp. 89–108.
6.
Kurkin
,
V. I.
, and
Lebedev
,
I. P.
,
1965
, “
Calculation of String Air Resistance
,”
Izvestia Vuzov, Tehnologia Tekstilnoi Prom.
,
1
, M., pp.
166
–
169
.
7.
Svetlicky
,
V. A.
, and
Gabruk
,
V. I.
,
1966
, “
Critical Velocities of the Steady State Motion
,”
Soviet Applied Mechanics
,
6
, pp.
13
–
17
.
8.
Cohen
,
H.
, and
Epstein
,
M.
,
1994
, “
On a Class of Planar Motions of Flexible Rods
,”
ASME J. Appl. Mech.
,
61
, pp.
206
–
208
.
9.
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
.
10.
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
.
11.
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
.
12.
Healey
,
T. J.
, and
Papadopoulos
,
J. N.
,
1990
, “
Steady Axial Motion of Strings
,”
ASME J. Appl. Mech.
,
57
, pp.
785
–
787
.
13.
Schagerl
,
M.
,
Steiner
,
W.
, and
Troger
,
H.
,
1997
, “
On the Paradox of the Free Falling Folded Chair
,”
Acta Mech.
,
125
, pp.
155
–
168
.
14.
Perkins
,
N. C.
, and
Mote
,
C. D.
, Jr.,
1987
, “
Three-Dimensional Vibration of Travelling Elastic Cables
,”
J. Sound Vib.
,
114
, No.
2
, pp.
305
–
340
.
15.
Perkins
,
N. C.
, and
Mote
,
C. D.
, Jr.,
1989
, “
Theoretical and Experimental Stability of Two Translating Cable Equilibria
,”
J. Sound Vib.
,
128
, No.
3
,pp
397
–
410
.
Copyright © 2001
 by ASME
You do not currently have access to this content.