Existing analytical models for railway tracks consider only one rail supported by a continuous foundation or periodic concentrated supports (called the periodically supported beam). This paper presents an analytical model for a railway track which includes two rails connected by sleepers. By considering the sleepers as Euler–Bernoulli beams resting on a Kelvin–Voigt foundation, we can obtain a dynamic equation for a sleeper subjected to the reaction forces of the rails. Then, by using the relation between the rail forces and displacements from the periodically supported beam model, we can calculate the sleeper responses with the help of Green's function. The numerical applications show that the sleeper is in flexion where the displacement at the middle of the sleeper is greater than those at the rail seats. Moreover, the deformed shape of the sleeper is nonsymmetric when the loads on the two rails are different. The model result agrees well with measurements performed using instrumented sleeper in situ
Issue Section:
Research Papers
References
1.
Mead
, D.
, 1970
, “Free Wave Propagation in Periodically Supported, Infinite Beams
,” J. Sound Vib.
, 11
(2
), pp. 181
–197
.2.
Mead
, D.
, and Yaman
, Y.
, 1991
, “The Response of Infinite Periodic Beams to Point Harmonic Forces: A Flexural Wave Analysis
,” J. Sound Vib.
, 144
(3
), pp. 507
–529
.3.
Mead
, D.
, 1996
, “Wave Propagation in Continuous Periodic Structures: Research Contributions From Southampton, 1964-1995
,” J. Sound Vib.
, 190
(3
), pp. 495
–524
.4.
Metrikine
, A.
, and Popp
, K.
, 1999
, “Vibration of a Periodically Supported Beam on an Elastic Half-Space
,” Eur. J. Mech.—A/Solids
, 18
(4
), pp. 679
–701
.5.
Vostroukhov
, A.
, and Metrikine
, A.
, 2003
, “Periodically Supported Beam on a Visco-Elastic Layer as a Model for Dynamic Analysis of a High-Speed Railway Track
,” Int. J. Solids Struct.
, 40
(21
), pp. 5723
–5752
.6.
Sheng
, X.
, Jones
, C.
, and Thompson
, D.
, 2005
, “Responses of Infinite Periodic Structures to Moving or Stationary Harmonic Loads
,” J. Sound Vib.
, 282
(1–2
), pp. 125
–149
.7.
Sheng
, X.
, Li
, M.
, Jones
, C.
, and Thompson
, D.
, 2007
, “Using the Fourier-Series Approach to Study Interactions Between Moving Wheels and a Periodically Supported Rail
,” J. Sound Vib.
, 303
(3–5
), pp. 873
–894
.8.
Hoang
, T.
, Duhamel
, D.
, Foret
, G.
, Yin
, H.
, Joyez
, P.
, and Caby
, R.
, 2017
, “Calculation of Force Distribution for a Periodically Supported Beam Subjected to Moving Loads
,” J. Sound Vib.
, 388
, pp. 327
–338
.9.
Nordborg
, A.
, 1998
, “Vertical Rail Vibrations: Parametric Exication
,” Acustica
, 84
, pp. 289
–300
.http://www.ingentaconnect.com/contentone/dav/aaua/1998/00000084/00000002/art0001010.
Hoang
, T.
, Duhamel
, D.
, Foret
, G.
, Yin
, H.-P.
, and Cumunel
, G.
, 2016
, “Response of a Periodically Supported Beam on a Nonlinear Foundation Subjected to Moving Loads
,” Nonlinear Dyn.
, 86
(2
), pp. 953
–961
.11.
Fryba
, L.
, 1972
, Vibration of Solids and Structures Under Moving Load
(Mechanics of Structural Systems, Vol. 1), Springer, Dordrecht, The Netherlands.12.
Nguyen
, V.-H.
, and Duhamel
, D.
, 2006
, “Finite Element Procedures for Nonlinear Structures in Moving Coordinates—Part 1: Infinite Bar Under Moving Axial Loads
,” Comput. Struct.
, 84
(21
), pp. 1368
–1380
.13.
Nguyen
, V.-H.
, and Duhamel
, D.
, 2008
, “Finite Element Procedures for Nonlinear Structures in Moving Coordinates—Part II: Infinite Beam Under Moving Harmonic Loads
,” Comput. Struct.
, 86
(21–22
), pp. 2056
–2063
.14.
Ding
, H.
, Chen
, L.-Q.
, and Yang
, S.-P.
, 2012
, “Convergence of Galerkin Truncation for Dynamic Response of Finite Beams on Nonlinear Foundations Under a Moving Load
,” J. Sound Vib.
, 331
(10
), pp. 2426
–2442
.15.
Gavrić
, L.
, 1995
, “Computation of Propagative Waves in Free Rail Using a Finite Element Technique
,” J. Sound Vib.
, 185
(3
), pp. 531
–543
.16.
Thompson
, D.
, 1997
, “Experimental Analysis of Wave Propagation in Railway Tracks
,” J. Sound Vib.
, 203
(5
), pp. 867
–888
.17.
Kostovasilis
, D.
, Thompson
, D.
, and Hussein
, M.
, 2017
, “A Semi-Analytical Beam Model for the Vibration of Railway Tracks
,” J. Sound Vib.
, 393
, pp. 321
–337
.18.
Kostovasilis
, D.
, 2017
, “Analytical Modelling of the Vibration of Railway Track
,” Ph.D. thesis
, University Southampton, Southampton, UK.https://eprints.soton.ac.uk/id/eprint/41381119.
Di Mino
, G.
, Di Liberto
, M.
, Maggiore
, C.
, and Noto
, S.
, 2012
, “A Dynamic Model of Ballasted Rail Track With Bituminous Sub-Ballast Layer
,” Procedia—Soc. Behav. Sci.
, 53
, pp. 366
–378
.20.
Aikawa
, A.
, 2015
, “Dynamic Characterisation of a Ballast Layer Subject to Traffic Impact Loads Using Three-Dimensional Sensing Stones and a Special Sensing Sleeper
,” Constr. Build. Mater.
, 92
, pp. 23
–30
.21.
Grassie
, S.
, 1995
, “Dynamic Modelling of Concrete Railway Sleepers
,” J. Sound Vib.
, 187
(5
), pp. 799
–813
.22.
Esmaeili
, M.
, Hosseini
, S.
, and Sharavi
, M.
, 2016
, “Experimental Assessment of Dynamic Lateral Resistance of Railway Concrete Sleeper
,” Soil Dyn. Earthquake Eng.
, 82
, pp. 40
–54
.23.
Laryea
, S.
, Safari Baghsorkhi
, M.
, Ferellec
, J.-F.
, McDowell
, G.
, and Chen
, C.
, 2014
, “Comparison of Performance of Concrete and Steel Sleepers Using Experimental and Discrete Element Methods
,” Transp. Geotech.
, 1
(4
), pp. 225
–240
.24.
Kumaran
, G.
, Menon
, D.
, and Krishnan Nair
, K.
, 2003
, “Dynamic Studies of Railtrack Sleepers in a Track Structure System
,” J. Sound Vib.
, 268
(3
), pp. 485
–501
.25.
Arab
, A. A.
, Badie
, S. S.
, and Manzari
, M. T.
, 2011
, “A Methodological Approach for Finite Element Modeling of Pretensioned Concrete Members at the Release of Pretensioning
,” Eng. Struct.
, 33
(6
), pp. 1918
–1929
.26.
Mohamad
, A.
, 1994
, “Tables of Green's Functions for the Theory of Beam Vibrations With General Intermediate Appendages
,” Int. J. Solids Struct.
, 31
(2
), pp. 257
–268
.27.
Foda
, M.
, and Abduljabbar
, Z.
, 1998
, “A Dynamic Green Function Formulation for the Response of a Beam Structure to a Moving Mass
,” J. Sound Vib.
, 210
(3
), pp. 295
–306
.28.
Zauderer
, E.
, 1989
, Partial Differential Equations of Applied Mathematics
, 3rd ed., Wiley
, Hoboken, NJ.29.
Azoh
, T. S.
, Nzie
, W.
, Djeumako
, B.
, and Fotsing
, B. S.
, 2014
, “Modeling of Train Track Vibrations for Maintenance Perspectives: Application
,” Eur. Sci. J.
, 10
(21
), pp. 260
–275
.https://eujournal.org/index.php/esj/article/view/3858/367430.
Roach
, G. F.
, 1992
, Green's Functions
, 2nd ed., Cambridge University Press
, Cambridge, UK
.31.
Stakgold
, I.
, 1979
, Green's Functions and Boundary Value Problems, Pure and Applied Mathematics
, 3rd ed., Wiley
, New York.Copyright © 2019 by ASME
You do not currently have access to this content.
