The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

References

References
1.
Chan
,
J.
,
2006
,
Transmission Line Reference Book: Wind-Induced Conductor Motion
,
Electrical Power Research Institute
,
Palo Alto, CA.
2.
Lu
,
M. L. C.
, and
Chan
,
J. K.
,
2007
, “
An Efficient Algorithm for Aeolian Vibration of Single Conductor With Multiple Dampers
,”
IEEE Trans. Power Delivery
,
22
(
3
), pp.
1822
1829
.10.1109/TPWRD.2007.899779
3.
Nigol
,
O.
, and
Houston
,
H. J.
,
1985
, “
Aeolian Vibration of Single Conductor and Its Control
,”
IEEE Trans. Power Delivery
,
104
(
11
), pp.
3245
3254
.
4.
Kraus
,
M.
, and
Hagedorn
,
P.
,
1991
, “
Aeolian Vibration: Wind Energy Input Evaluated From Measurements on an Energized Transmission Lines
,”
IEEE Trans. Power Delivery
,
6
(
3
), pp.
1264
1270
.10.1109/61.85875
5.
Verma
,
H.
, and
Hagedorn
,
P.
,
2004
, “
Wind Induced Vibration of Long Electrical Overhead Transmission Line Spans: A Modified Approach
,”
J. Wind Struct.
,
8
(
2
), pp.
89
106
.
6.
Rawlins
,
C. B.
,
1958
, “
Recent Developments in Conductor Vibration
,” Alcoa Technical Paper No. 13.
7.
Vecchiarelly
,
J.
,
Curries
, I
. G.
, and
Havard
,
D. G.
,
2000
, “
Computational Analysis of Aeolian Conductor Vibration With a Stockbridge-Type Damper
,”
J. Fluids Struct.
,
14
(
4
), pp.
489
509
.10.1006/jfls.1999.0279
8.
Havard
,
D. G.
,
1994
, “
Weakness in the Forced Response Method for Testing Vibration Dampers
,” Institute of Electrical and Electronics Engineers, San Francisco, CA, p.
664
.
9.
Claren
,
R.
, and
Diana
,
G.
,
1969
, “
Mathematical Analysis of Transmission Line Vibration
,”
IEEE Trans. Power Delivery
,
60
(
2
), pp.
1741
1771
.
10.
Diana
,
G.
,
Cigada
,
A.
,
Belloli
,
M.
, and
Vanali
,
M.
,
2003
, “
Stokbridge Type-Damper Effectiveness Evaluation: Part 1. Comparison Between Tests on Span and on the Shaker
,”
IEEE Trans. Power Delivery
,
18
(
4
), pp.
1462
1469
.10.1109/TPWRD.2003.817797
11.
Wiendl
,
S.
,
Hagedorn
,
P.
, and
Hochlenert
,
V.
,
2009
, “
Control of a Test Rig for Vibration Measurement of Overhead Transmission Lines
,”
Proceedings of the IEEE Conference on Control and Automation
, pp.
2129
2135
.
12.
Wagner
,
H.
,
Ramamurti
,
V.
,
Sastry
,
R.
, and
Hartman
,
K.
,
1973
, “
Dynamic of Stockbridge Dampers
,”
J. Sound Vib.
,
30
(
2
), pp.
207
220
.10.1016/S0022-460X(73)80114-2
13.
Barry
,
O.
,
Oguamanam
,
D. C. D.
, and
Lin
,
D. C.
,
2013
, “
Aeolian Vibration of a Single Conductor With a Stockbridge Damper
,”
Proc. Inst. Mech. Eng., Part C
,
227
(
5
), pp.
935
945
.10.1177/0954406212452064
14.
Barry
,
O.
,
Zu
,
J. W.
, and
Oguamanam
,
D. C. D.
,
2014
, “
Forced Vibration of Overhead Transmission Line: Analytical and Experimental Investigation
,”
ASME J. Vib. Acoust.
,
136
(
4
), p.
041012
.10.1115/1.4027578
15.
Barry
,
O.
,
Zu
,
J. W.
, and
Oguamanam
,
D. C. D.
,
2014
, “
Forced Vibration of Overhead Transmission Line: Analytical and Experimental Investigation
,”
ASME J. Vib. Control
,
136
(4), p.
041012
. 10.1115/1.4027578
16.
Barbieri
,
N.
, and
Barbieri
,
R.
,
2012
, “
Dynamic Analysis of Stockbridge Damper
,”
Adv. Acoust. Vib.
,
2012
(
2012
), p.
659398
.10.1155/2012/659398
17.
Burgreen
,
D.
,
1951
, “
Free Vibrations of Pin-Ended Column With Constant Distance Between Pin-Ends
,”
ASME J. Appl. Mech.
,
18
, pp.
135
139
.
18.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1979
,
Nonlinear Oscillations
,
Wiley
,
New York
.
19.
Ozkaya
,
E.
, and
Pakdemirli
,
M.
,
1999
, “
Non-Linear Vibrations of a Beam-Mass System With Both Ends Clamped
,”
J. Sound Vib.
,
221
(
3
), pp.
491
503
.10.1006/jsvi.1998.2003
20.
Ozkaya
,
E.
,
Pakdemirli
,
M.
, and
Oz
,
H. R.
,
1999
, “
Non-Linear Vibrations of a Beam-Mass System Under Various Boundary Conditions
,”
J. Sound Vib.
,
199
(
4
), pp.
679
696
.10.1006/jsvi.1996.0663
21.
Ozkaya
,
E.
,
2001
, “
Non-Linear Vibrations of a Simply-Supported Carrying Concentrated Masses
,”
J. Sound Vib.
,
257
(
3
), pp.
413
424
.10.1006/jsvi.2002.5042
22.
Cartmell
,
M. P.
,
Ziegler
,
S. W.
,
Khanin
,
R.
, and
Forehand
,
D. I. M.
,
2003
, “
Multiple Scales Analyses of the Dynamics of Weakly Nonlinear Mechanical Systems
,”
ASME Appl. Mech. Rev.
,
56
(
5
), pp.
455
492
.10.1115/1.1581884
23.
Pakdemirli
,
M.
, and
Nayfeh
,
A. H.
,
1994
, “
Nonlinear Vibration of a Beam-Spring-Mass System
,”
ASME J. Vib. Acoust.
,
166
(
4
), pp.
433
438
.10.1115/1.2930446
24.
Nayfeh
,
A. H.
,
1981
,
Introduction to Perturbation Techniques
,
Wiley
,
New York
.
25.
IEEE Committee 664,
1993
,
IEEE Guide on the Measurement of the Performance of Aeolian Vibration Dampers for Single Conductors (IEEE Std.)
,
IEEE
, pp.
664
1993
.
You do not currently have access to this content.