The near resonant response of suspended elastic cables driven by harmonic, planar excitation is investigated experimentally. Measurements of large amplitude cable motions confirm previous theoretical predictions of fundamental classes of internally-resonant responses. For particular magnitudes of equilibrium curvature, strong modal interactions arise through isolated (two-mode) or simultaneous (three-mode) internal resonances. Four qualitatively different periodic responses are observed: (1) pure planar response, (2) 2:1 internally resonant nonplanar response, (3) 1:1 internally resonant nonplanar response, and (4) simultaneous, 2:2:1 internally resonant nonplanar response. Quasiperiodic responses are also observed.

1.
Bux
S. L.
, and
Roberts
J. W.
,
1986
, “
Non-Linear Vibratory Interactions in Systems of Coupled Beams
,”
Journal of Sound and Vibration
, Vol.
104
, No.
3
, pp.
497
520
.
2.
Haddow
A. G.
,
Barr
A. D. S.
, and
Mook
D. T.
,
1984
, “
Theoretical and Experimental Study of Modal Interaction in a Two-Degree-of-Freedom Structure
,”
Journal of Sound and Vibration
, Vol.
97
, No.
3
pp
451
473
.
3.
Ibrahim
R. A.
,
1976
, “
Multiple Internal Resonance in a Structure-Liquid System
,”
ASME Journal of Engineering for Industry
, Vol.
98
, pp.
1092
1098
.
4.
Irvine
H. M.
, and
Caughey
T. K.
,
1974
, “
The Linear Theory of Free Vibrations of a Suspended Cable
,”
Proceedings of the Royal Society of London, Series A
, Vol.
341
, pp.
299
315
.
5.
Lee, C. L., 1992, “Modal Interactions in the Nonlinear Oscillations of Elastic Cables,” Ph.D. Dissertation, The University of Michigan, Ann Arbor, MI.
6.
Lee
C. L.
, and
Perkins
N. C.
,
1992
a, “
Nonlinear Oscillations of Suspended Cables Containing a Two-to-One Internal Resonance
,”
Nonlinear Dynamics
, Vol.
3
, No.
6
, pp.
465
490
.
7.
Lee
C. L.
, and
Perkins
N. C.
,
1992
b, “
Three Dimensional Oscillations of a Suspended Cable Containing Simultaneous Internal Resonances
,”. And to appear in
Nonlinear Dynamics
Nonlinear Vibrations, 1992 ASME Winter Annual Meeting, DE-Vol. 50/AMD-Vol.
144
, pp.
59
67
.
8.
Luongo
A.
,
Rega
G.
, and
Vestroni
F.
,
1987
, “
On Large-Amplitude Vibrations of Cables
,”
Journal of Sound and Vibration
, Vol.
116
, No.
3
, pp.
573
575
.
9.
Nayfeh
A. H.
, and
Balachandran
B.
,
1989
, “
Modal Interactions in Dynamical and Structural Systems
,”
ASME Applied Mechanics Review
, Vol.
42
, No.
11
, Part II, pp.
S175–S202
S175–S202
.
10.
Nayfeh
A. H.
,
Balachandran
B.
,
Colbert
M. A.
, and
Nayfeh
M. A.
,
1989
, “
An Experimental Investigation of Complicated Responses of a Two-Degree-of-Freedom Structure
,”
ASME Journal of Applied Mechanics
, Vol.
56
, pp.
960
967
.
11.
Oh, I. G., 1992, “Theoretical and Experimental Nonlinear Dynamics of Floating Oscillatory Systems,” Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA.
12.
O’Reilly
O.
, and
Holmes
P. J.
,
1992
, “
Non-linear, Non-planar and Non-periodic Vibrations of a String
,”
Journal of Sound and Vibration
, Vol.
153
, No.
3
, pp.
413
435
.
13.
Perkins, N. C., 1986, “Three Dimensional Theory and Analysis of Travelling Sagged Cable Dynamics,” Ph.D. Dissertation, University of California, Berkeley, CA.
14.
Perkins
N. C.
,
1992
, “
Modal Interactions in the Nonlinear Response of Elastic Cables Under Parametric/External Excitation
,”
International Journal of Non-Linear Mechanics
, Vol.
27
, No.
2
, pp.
233
250
.
15.
Rao
G. v.
, and
Iyengar
R. N.
,
1991
, “
Internal Resonance and Non-Linear Response of a Cable Under Periodic Excitation
,”
Journal of Sound and Vibration
, Vol.
149
, No.
1
, pp.
25
41
.
This content is only available via PDF.
You do not currently have access to this content.