The exact, closed-form, three-dimensional solutions for the steady motion of traveling, sagged, elastic cables under arbitrarily distributed and concentrated loading are developed in this paper. Three components of displacement describing two equilibrium states of an extensible traveling elastic cable are derived. These exact solutions apply to straight and sagged cables traveling under their own weight and uniformly distributed loading. The exact solutions are also used to investigate the steady motion of three-dimensional traveling cables under the uniformly distributed and concentrated loading. Traveling elastic cables with large sag can be modeled approximately through the inextensible cable model when both the loading and the translation speed are very small. A slightly sagged cable must be modeled as extensible, rather than inextensible, even though both the loading and transport speed are very small. These solutions can be applied to multispan cable structures. [S0021-8936(00)02601-5]

Issue Section:
Technical Papers
Keywords:
elasticity, load distribution, structural engineering, vibrations
Topics:
Cables, Displacement, Equilibrium (Physics), Tension, Stress
1.
Rohrs
,
J. H.
,
1851
, “
On the Oscillations of a Suspension Cable
,”
Trans. Cambridge Philos. Soc.
,
9
, pp.
379
–
398
.
2.
Routh E. J., 1884, The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, 4th Ed., MacMillan and Co., London.
3.
Pugsley
,
A. G.
,
1949
, “
On Natural Frequencies of Suspension Chain
,”
Q. J. Mech. Appl. Math.
,
2
, pp.
412
–
418
.
4.
Saxon
,
D. S.
, and
Cahn
,
A. S.
,
1953
, “
Modes of Vibration of a Suspended Chain
,”
Q. J. Mech. Appl. Math.
,
6
, pp.
273
–
285
.
5.
Simpson
,
A.
,
1966
, “
Determination of the Inplane Natural Frequencies of Multispan Transmission Lines by a Transfer Matrix Method
,”
Proc. Inst. Electr. Eng.
,
113
, pp.
870
–
878
.
6.
Irvine
,
H. M.
, and
Caughey
,
T. K.
,
1974
, “
The Linear Theory of Free Vibrations of a Suspended Cable
,”
Proc. R. Soc. London, Ser. A
,
341A
, pp.
299
–
315
.
7.
Hagedorn
,
P.
, and
Schafer
,
B.
,
1980
, “
On Nonlinear Free Vibrations of an Elastic Cable
,”
Int. J. Non-Linear Mech.
,
15
, pp.
333
–
340
.
8.
Luongo
,
A.
,
Rega
,
G.
, and
Vestroni
,
F.
,
1984
, “
Planar Non-linear Free Vibrations of an Elastic Cable
,”
Int. J. Non-Linear Mech.
,
19
, pp.
39
–
52
.
9.
Perkins
,
N. C.
,
1992
, “
Modal Interactions in the Nonlinear Response of Elastic Cables Under Parametric/External Excitation
,”
Int. J. Non-Linear Mech.
,
27
, No.
2
, pp.
233
–
250
.
10.
Simpson
,
A.
,
1972
, “
On the Oscillatory Motions of Translating Elastic Cables
,”
J. Sound Vib.
,
20
, No.
2
, pp.
177
–
189
.
11.
Triantafyllou
,
M. S.
,
1985
, “
The Dynamics of Translating Cables
,”
J. Sound Vib.
,
103
, No.
2
, pp.
171
–
182
.
12.
Perkins
,
N. C.
, and
Mote
, Jr.,
C. D.
,
1987
, “
Three-Dimensional Vibration of Traveling Elastic Cables
,”
J. Sound Vib.
,
114
, No.
3
, pp.
325
–
340
.
13.
Perkins
,
N. C.
, and
Mote
, Jr.,
C. D.
,
1989
, “
Theoretical and Experimental Stability of Two Translating Cable Equilibria
,”
J. Sound Vib.
,
128
, No.
3
, pp.
397
–
410
.
14.
Dickey
,
R. W.
,
1969
, “
The Nonlinear String Under a Vertical Force
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
17
, No.
1
, pp.
172
–
178
.
15.
Antman
,
S. S.
,
1979
, “
Multiple Equilibrium States of Nonlinear Elastic Strings
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
37
, No.
3
, pp.
588
–
604
.
16.
O’Reilly
,
O. M.
, and
Varadi
,
P.
,
1995
, “
Elastic Equilibria of Translating Cables
,”
Acta Mech.
,
108
, pp.
189
–
206
.
17.
Healey
,
T. J.
, and
Papadopoulos
,
J. N.
,
1990
, “
Steady Axial Motions of Strings
,”
ASME J. Appl. Mech.
,
57
, pp.
785
–
787
.
18.
O’Reilly
,
O. M.
,
1996
, “
Steady Motions of a Drawn Cable
,”
ASME J. Appl. Mech.
,
63
, pp.
180
–
189
.
19.
Irvine, H. M., 1974, Cable Structures, The MIT Press, Cambridge, MA.
20.
Yu
,
P.
,
Wong
,
P. S.
, and
Kaempffer
,
F.
,
1995
, “
Tension of Conductor Under Concentrated Loads
,”
ASME J. Appl. Mech.
,
62
, pp.
802
–
809
.
21.
Luo
,
A. C. J.
,
Han
,
R. P. S.
,
Tyc
,
G.
,
Modi
,
V. J.
, and
Misra
,
A. K.
,
1996
, “
Analytical Vibration and Resonant Motion of a Stretched, Spinning, Nonlinear Tether
,”
AIAA J. Guidance, Control Dyn.
,
19
, No.
5
, pp.
1162
–
1171
.
Copyright © 2000
 by ASME
You do not currently have access to this content.