Research Papers

Nonlinear Dynamics of Stockbridge Dampers

[+] Author and Article Information
O. Barry

Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada
e-mail: oumar.barry@utoronto.ca

J. W. Zu

Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada

D. C. D. Oguamanam

Department of Mechanical
and Industrial Engineering,
Ryerson University,
Toronto, ON M5B 2K3, Canada

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 7, 2013; final manuscript received December 29, 2014; published online February 9, 2015. Assoc. Editor: Jiong Tang.

J. Dyn. Sys., Meas., Control 137(6), 061017 (Jun 01, 2015) (7 pages) Paper No: DS-13-1346; doi: 10.1115/1.4029526 History: Received September 07, 2013; Revised December 29, 2014; Online February 09, 2015

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Chan, J., 2006, Transmission Line Reference Book: Wind-Induced Conductor Motion, Electrical Power Research Institute, Palo Alto, CA.
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. [CrossRef]
Nigol, O., and Houston, H. J., 1985, “Aeolian Vibration of Single Conductor and Its Control,” IEEE Trans. Power Delivery, 104(11), pp. 3245–3254. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Rawlins, C. B., 1958, “Recent Developments in Conductor Vibration,” Alcoa Technical Paper No. 13.
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. [CrossRef]
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.
Claren, R., and Diana, G., 1969, “Mathematical Analysis of Transmission Line Vibration,” IEEE Trans. Power Delivery, 60(2), pp. 1741–1771. [CrossRef]
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. [CrossRef]
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.
Wagner, H., Ramamurti, V., Sastry, R., and Hartman, K., 1973, “Dynamic of Stockbridge Dampers,” J. Sound Vib., 30(2), pp. 207–220. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Barbieri, N., and Barbieri, R., 2012, “Dynamic Analysis of Stockbridge Damper,” Adv. Acoust. Vib., 2012(2012), p. 659398. [CrossRef]
Burgreen, D., 1951, “Free Vibrations of Pin-Ended Column With Constant Distance Between Pin-Ends,” ASME J. Appl. Mech., 18, pp. 135–139.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.
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. [CrossRef]
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. [CrossRef]
Ozkaya, E., 2001, “Non-Linear Vibrations of a Simply-Supported Carrying Concentrated Masses,” J. Sound Vib., 257(3), pp. 413–424. [CrossRef]
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. [CrossRef]
Pakdemirli, M., and Nayfeh, A. H., 1994, “Nonlinear Vibration of a Beam-Spring-Mass System,” ASME J. Vib. Acoust., 166(4), pp. 433–438. [CrossRef]
Nayfeh, A. H., 1981, Introduction to Perturbation Techniques, Wiley, New York.
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.


Grahic Jump Location
Fig. 2

Schematic of two cantilevered beams with tip masses

Grahic Jump Location
Fig. 1

Photograph of Stockbridge damper

Grahic Jump Location
Fig. 3

Schematic of experimental setup

Grahic Jump Location
Fig. 4

Damper 1 mode shapes

Grahic Jump Location
Fig. 5

Damper 2 mode shapes

Grahic Jump Location
Fig. 6

Damper 3 mode shapes

Grahic Jump Location
Fig. 7

Variation of fundamental nonlinear frequency with vibration amplitude

Grahic Jump Location
Fig. 8

Frequency-response curve for varying f0 and constant damping

Grahic Jump Location
Fig. 9

Frequency-response curve for varying μ1 and constant force

Grahic Jump Location
Fig. 10

Effect of the counterweight mass and rotational inertia



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In