This paper examines the nonlinear vibration of a single conductor with Stockbridge dampers. The conductor is modeled as a simply supported beam and the Stockbridge damper is reduced to a mass–spring–damper–mass system. The nonlinearity of the system stems from the midplane stretching of the conductor and the cubic equivalent stiffness of the Stockbridge damper. The derived nonlinear equations of motion are solved by the method of multiple scales. Explicit expressions are presented for the nonlinear frequency, solvability conditions, and detuning parameter. The present results are validated via comparisons with those in the literature. Parametric studies are conducted to investigate the effect of variable control parameters on the nonlinear frequency and the frequency response curves. The findings are promising and open a horizon for future opportunities to optimize the design of nonlinear absorbers.
Issue Section:
Research Papers
References
1.
Chan
, J.
, Harvard
, D.
, Rawlins
, C.
, Diana
, G.
, Cloutier
, L.
, Lilien
, J.
, Hardy
, C.
, Wang
, J.
, and Goel
, A.
, 2009
, EPRI Transmission Line Reference Book: Wind-Induced Conductor Motion
, Electric Power Research Institute, Palo Alto, CA.2.
Barry
, O.
, Zu
, J. W.
, and Oguamanam
, D. C. D.
, 2015
, “Analytical and Experimental Investigation of Overhead Transmission Line Vibration
,” J. Vib. Control
, 21
(14
), pp. 2825
–2837
.3.
Barry
, O.
, Oguamanam
, D. C.
, 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
.4.
Oliveira
, A. R.
, and Freire
, D. G.
, 1994
, “Dynamical Modelling and Analysis of Aeolian Vibrations of Single Conductors
,” IEEE Trans. Power Delivery
, 9
(3
), pp. 1685
–1693
.5.
Verma
, H.
, and Hagedorn
, P.
, 2005
, “Wind Induced Vibrations of Long Electrical Overhead Transmission Line Spans: A Modified Approach
,” Wind Struct.
, 8
(2
), pp. 89
–106
.6.
Schfer
, B.
, 1984
, “Dynamical Modelling of Wind-Induced Vibrations of Overhead Lines
,” Int. J. Non-Linear Mech.
, 19
(5
), pp. 455
–467
.7.
Kraus
, M.
, and Hagedorn
, P.
, 1991
, “Aeolian Vibrations: Wind Energy Input Evaluated From Measurements on an Energized Transmission Line
,” IEEE Trans. Power Delivery
, 6
(3
), pp. 1264
–1270
.8.
Tompkins
, J. S.
, Merrill
, L. L.
, and Jones
, B. L.
, 1956
, “Quantitative Relationships in Conductor Vibration Damping
,” Trans. Am. Inst. Electr. Eng. Part III
, 75
(3
), pp. 879
–896
.9.
Nigol
, O.
, Heics
, R. C.
, and Houston
, H. J.
, 1985
, “Aeolian Vibration of Single Conductors and Its Control
,” IEEE Trans. Power Apparatus Syst.
, PAS-104
(11
), pp. 3245
–3254
.10.
Rawlins
, C. B.
, 1958
, “Recent Developments in Conductor Vibration Research
,” Alcoa Research Laboratories, Pittsburgh, PA, Technical Paper No. 13.11.
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
.12.
Barry
, O.
, Long
, R.
, and Oguamanam
, D. C. D.
, 2016
, “Simplified Vibration Model and Analysis of a Single-Conductor Transmission Line With Dampers
,” Proc. Inst. Mech. Eng., Part C
, 231
(11), pp. 4150–4162.13.
Nayfeh
, A. H.
, and Mook
, D. T.
, 1979
, Nonlinear Oscillations
, Wiley
, New York
.14.
Nayfeh
, A. H.
, 1981
, Introduction to Perturbation Techniques
, Wiley
, New York
.15.
Dowell
, E. H.
, 1980
, “Component Mode Analysis of Nonlinear and Nonconservative Systems
,” ASME J. Appl. Mech.
, 47
(1
), pp. 172
–176
.16.
Pakdemirli
, M.
, and Nayfeh
, A. H.
, 1994
, “Nonlinear Vibrations of a Beam-Spring-Mass System
,” ASME J. Vib. Acoust.
, 116
(4
), pp. 433
–439
.17.
Barry
, O. R.
, Oguamanam
, D. C. D.
, and Zu
, J. W.
, 2014
, “Nonlinear Vibration of an Axially Loaded Beam Carrying Multiple Massspringdamper Systems
,” Nonlinear Dyn.
, 77
(4
), pp. 1597
–1608
.18.
Low
, K. H.
, 1997
, “Comments on ‘Non-Linear Vibrations of a Beam-Mass System Under Different Boundary Conditions’(With Authors' Reply)
,” J. Sound Vib.
, 207
(2
), pp. 284
–287
.19.
Mestrom
, R. M. C.
, Fey
, R. H. B.
, Phan
, K. L.
, and Nijmeijer
, H.
, 2010
, “Simulations and Experiments of Hardening and Softening Resonances in a Clampedclamped Beam MEMS Resonator
,” Sens. Actuators A: Phys.
, 162
(2
), pp. 225
–234
.20.
Ozkaya
, E.
, and Pakdemirli
, M.
, 1999
, “Non-Linear Vibrations of a Beammass System With Both Ends Clamped
,” J. Sound Vib.
, 221
(3
), pp. 491
–503
.21.
Ozkaya
, E.
, Pakdemirli
, M.
, and Öz
, H. R.
, 1997
, “Non-Linear Vibrations of a Beam-Mass System Under Different Boundary Conditions
,” J. Sound Vib.
, 199
(4
), pp. 679
–696
.22.
Ozkaya
, E.
, 2002
, “Non-Linear Transverse Vibrations of a Simply Supported Beam Carrying Concentrated Masses
,” J. Sound Vib.
, 257
(3
), pp. 413
–424
.23.
Lin
, H. Y.
, and Tsai
, Y. C.
, 2007
, “Free Vibration Analysis of a Uniform Multi-Span Beam Carrying Multiple Springmass Systems
,” J. Sound Vib.
, 302
(3
), pp. 442
–456
.24.
Hassanpour
, P. A.
, Cleghorn
, W. L.
, Mills
, J. K.
, and Esmailzadeh
, E.
, 2007
, “Exact Solution of the Oscillatory Behavior Under Axial Force of a Beam With a Concentrated Mass Within Its Interval
,” J. Vib. Control
, 13
(12
), pp. 1723
–1739
.25.
Naguleswaran
, S.
, 2001
, “Transverse Vibrations of an EulerBernoulli Uniform Beam Carrying Two Particles In-Span
,” Int. J. Mech. Sci.
, 43
(12
), pp. 2737
–2752
.26.
Wu
, J. S.
, and Lin
, T. L.
, 1990
, “Free Vibration Analysis of a Uniform Cantilever Beam With Point Masses by an Analytical-and-Numerical-Combined Method
,” J. Sound Vib.
, 136
(2
), pp. 201
–213
.27.
Grgze
, M.
, 1998
, “On the Alternative Formulations of the Frequency Equation of a BernoulliEuler Beam to Which Several Spring-Mass Systems Are Attached in-Span
,” J. Sound Vib.
, 217
(3
), pp. 585
–595
.28.
Barry
, O. R.
, Zhu
, Y.
, Zu
, J. W.
, and Oguamanam
, D. C. D.
, 2012
, “Free Vibration Analysis of a Beam Under Axial Load Carrying a Mass-Spring-Mass
,” ASME
Paper No. DETC2012-70144.29.
Kirk
, C. L.
, and Wiedemann
, S. M.
, 2002
, “Natural Frequencies and Mode Shapes of a Freefree Beam With Large End Masses
,” J. Sound Vib.
, 254
(5
), pp. 939
–949
.30.
Wu
, J. S.
, and Huang
, C. G.
, 1995
, “Free and Forced Vibrations of a Timoshenko Beam With Any Number of Translational and Rotational Springs and Lumped Masses
,” Int. J. Numer. Methods Biomed. Eng.
, 11
(9
), pp. 743
–756
.31.
Wu, J.-S., and Chou, H.-M., 1998, “
Free Vibration Analysis of a Cantilever Beam Carrying any Number of Elastically Mounted Point Masses With the Analytical-And-Numerical-Combined Method
,” J. Sound Vib.
, 213
(2), pp. 317–332.32.
Bokaian
, A.
, 1990
, “Natural Frequencies of Beams Under Tensile Axial Loads
,” J. Sound Vib.
, 142
(3
), pp. 481
–498
.33.
Samani
, F. S.
, Pellicano
, F.
, and Masoumi
, A.
, 2013
, “Performances of Dynamic Vibration Absorbers for Beams Subjected to Moving Loads
,” Nonlinear Dyn.
, 73
(1–2
), pp. 1065
–1079
.34.
Boisseau
, S.
, Despesse
, G.
, and Seddik
, B. A.
, 2013
, “Nonlinear H-Shaped Springs to Improve Efficiency of Vibration Energy Harvesters
,” ASME J. Appl. Mech.
, 80
(6
), p. 061013
.35.
Bukhari
, M. A.
, Barry
, O.
, and Tanbour
, E.
, 2017
, “On the Vibration Analysis of Power Lines With Moving Dampers
,” J. Vib. Control
, epub.36.
Barry
, O.
, Long
, R.
, and Oguamanam
, D. C. D.
, 2017
, “Rational Damping Arrangement Design for Transmission Lines Vibrations: Analytical and Experimental Analysis
,” ASME J. Dyn. Syst. Meas. Control
, 139
(5
), p. 051012
.Copyright © 2018 by ASME
You do not currently have access to this content.
