A solution is presented of the problem of vibrations of a taut cable equipped with a concentrated viscous damper. The solution is expressed in terms of damped complex-valued modes, leading to a transcendental equation for the complex eigenfrequencies. A simple iterative solution of the frequency equation for all complex eigenfrequencies is proposed. The damping ratio of the vibration modes, determined from the argument of the complex eigenfrequency, are typically determined to within one percent in two iterations. An accurate asymptotic approximation of the damping ratio of the lower modes is obtained. This formula permits explicit determination of the optimal location of the viscous damper, depending on its damping parameter. [S0021-8936(00)00404-9]

Issue Section:
Technical Papers
Keywords:
vibrations, damping, eigenvalues and eigenfunctions, iterative methods
Topics:
Cables, Dampers, Damping, Vibration, Mode shapes
1.
Irvine, H. M., 1981, Cable Structures, M.I.T. Press, Cambridge, MA.
2.
Watson
,
S. C.
, and
Stafford
,
D.
,
1988
, “
Cables in Trouble
,”
Civil Engineering ASCE
,
58
, No.
4
, pp.
38
–
41
.
3.
Yamaguchi, H., and Fujino, Y., 1998, “Stayed Cable Dynamics and Its Vibration Control,” Bridge Aerodynamics, A. Larsen and S. Esdahl, eds., Balkma, Rotterdam, pp. 235–253.
4.
Yamaguchi
,
H.
, and
Jayawardena
,
L.
,
1992
, “
Analytical Estimation of Structural Damping in Cable Structures
,”
Journal of Wind Engineering and Industrial Aerodynamics
,
43
, pp.
1961
–
1972
.
5.
Gimsing, N. J., 1997, Cable Supported Bridges, 2nd Ed., Wiley, Chichester,
6.
Kovacs
,
I.
,
1982
, “
Zur Frage der Seilschwigungen und der Seildampfung
,”
Die Bautechnik
,
59
, No.
10
, pp.
325
–
332
.
7.
Pacheco
,
B. N.
,
Fujino
,
Y.
, and
Sulekh
,
A.
,
1993
, “
Estimation Curve for Modal Damping in Stay Cables With Viscous Damper
,”
J. Struct. Eng.
,
119
, pp.
1961
–
1979
.
8.
Baker, G. A., Johnson, E. A., Spencer, B. F., and Fujino, Y. 1999, “Modeling and Semiactive Damping of Stay Cables,” 13’th ASCE Engineering Mechanics Division Conference, Johns Hopkins University, Baltimore MD, June 13–16.
9.
Singh
,
R.
,
Lyons
,
W. M.
, and
Prater
,
G.
,
1989
, “
Complex Eigensolution for Longitudinally Vibrating Bars With a Viscously Damped Boundary
,”
J. Sound Vib.
,
133
, pp.
364
–
367
.
10.
Hull
,
A. J.
,
1994
, “
A Closed Form Solution of a Longitudinal Bar With a Viscous Boundary Layer
,”
J. Sound Vib.
,
169
, pp.
19
–
28
.
11.
Oliveto
,
G.
,
Santini
,
A.
, and
Tripodi
,
E.
,
1997
, “
Complex Modal Analysis of a Flexural Vibrating Beam With Viscous End Conditions
,”
J. Sound Vib.
,
200
, pp.
327
–
345
.
12.
Yang
,
B.
, and
Wu
,
X.
,
1997
, “
Transient Response of One-Dimensional Distributed Systems: A Closed Form Eigenfunction Expansion Realization
,”
J. Sound Vib.
,
208
, pp.
763
–
776
. UK.
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