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Modelling the Floating Ladder Track Response to a Moving Load by an Infinite Bernoulli-Euler Beam on Periodic Flexible Supports

Published online by Cambridge University Press:  28 May 2015

Roger J. Hosking  and
Fausto Milinazzo
Roger J. Hosking
Affiliation:
School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
Fausto Milinazzo*
Affiliation:
Department of Mathematics, University of Victoria, Canada
*
Corresponding author. Email: [email protected]
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Abstract.

An infinite Bernoulli-Euler beam (representing the “combined rail” consisting of the rail and longitudinal sleeper) mounted on periodic flexible point supports (representing the railpads) has already proven to be a suitable mathematical model for the floating ladder track (FLT), to define its natural vibrations and its forced response due to a moving load. Adopting deliberately conservative parameters for the existing FLT design, we present further results for the response to a steadily (uniformly) moving load when the periodic supports are assumed to be elastic, and then introduce the mass and viscous damping of the periodic supports. Typical support damping significantly moderates the resulting steady deflexion at any load speed, and in particular substantially reduces the magnitude of the resonant response at the critical speed. The linear mathematical analysis is then extended to include the inertia of the load that otherwise moves uniformly along the beam, generating overstability at supercritical speeds – i.e. at load speeds notably above the critical speed predicted for the resonant response when the load inertia is neglected. Neither the resonance nor the overstability should prevent the safe implementation of the FLT design in modern high speed rail systems.

Keywords

93A3074H1074H1574H5544A30Bernoulli-Euler beamperiodic flexible supportsmoving loadsupport dampingload inertiafloating ladder trackFourier-Laplace transform solution
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 4 , November 2012 , pp. 285 - 308
Copyright
Copyright © Global-Science Press 2012

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References

[1]Wakui, H., Ladder sleepers perform well in tests, Railway Gazette International 159, 589–592 (1997).Google Scholar
[2]Wakui, H. and Matsumoto, N., Performance test of ballasted ladder track at TTCI and floating ladder track in Japan, Proceedings of the National Research Council 18th Transportation Research Board Annual Meeting (Washington, USA), pp. 110 (2002).Google Scholar
[3]Xia, H., Chen, J. G., Xia, C. Y., Inoue, H., Zenda, Y. and Qi, L., An experimental study of train-induced structural and environmental vibrations of a rail transit elevated bridge with ladder tracks, Proceedings of the Institution of Mechanical Engineers, Part F: J. Rail and Rapid Transit 224, 115–124 (2010).Google Scholar
[4]Ding, De-yun, Gupta, Shashank, Liu, Wei-ning, Lombaert, Geert and Degrande, Geert, Prediction of vibrations induced by trains on line 8 of Beijing metro, J. Zhejiang University (Science A) 11, 280–293 (2010).Google Scholar
[5]Ding, De-yun, Liu, Wei-ning, Gupta, S., Lombaert, G. and Degrande, G., Prediction of vibrations from underground trains on Beijing metro line 15, J. Central South University of Technology 17, 1109–1118 (2010).CrossRefGoogle Scholar
[6]Hosking, R. J., Husain, Saiful Azmi and Milinazzo, F., Natural flexural vibrations of a continuous beam on discrete elastic supports, J. Sound and Vibration 272 169–185 (2004).Google Scholar
[7]Hosking, R. J. and Milinazzo, F., Floating ladder track response to a steadily moving load, Math. Meth. Applied Sc. 30, 1823–1841 (2007).Google Scholar
[8]Metrikine, A.V. and Dieterman, H. A., Instability of vibrations of a mass moving along an axially compressed beam on a viscoelastic foundation, J. Sound and Vibration 201, 567–576 (1997).Google Scholar
[9]Verichev, S. N. and Metrikine, A.V., Instability of a mass that moves uniformly along a beam on a periodically inhomogeneous foundation, J. Sound and Vibration 260, 901–925 (2003).Google Scholar
[10]Timoshenko, S., Method of analysis of static and dynamical stresses in rail, Proc. of the Second International Congress of Applied Mathematics, Zurich, 1–12 (1927). See also Collected Papers, 422–435.Google Scholar
[11]Fryba, L., Vibrations of Solids and Structures under Moving Loads, Noordhoff International Publishing (1972).CrossRefGoogle Scholar
[12]Davys, J. W., Hosking, R. J. and Sneyd, A. D., Waves due to a steadily moving source on a floating ice plate, J. Fluid Mech. 158, 269–287 (1985).Google Scholar
[13]Squire, V. A., Hosking, R. J., Kerr, A. D. and Langhorne, P. J., Moving Loads on Ice Plates, Kluwer Academic Publishers (1996).CrossRefGoogle Scholar
[14]Schulkes, R. M. S. M. and Sneyd, A. D., Time-dependent response of a floating ice sheet to a steadily moving load, J. Fluid Mech. 186, 25–46 (1988).Google Scholar
[15]Nugroho, W. S., Wang, K., Hosking, R.J. and Milinazzo, F., Time-dependent response of a floating flexible plate to an impulsively-started steadily moving load, J. Fluid Mech. 381, 337–355 (1999).CrossRefGoogle Scholar
[16]Bonnefoy, F., Meylan, M.H. and Ferrant, P., Nonlinear higher-order spectral solution for a two-dimensional moving load on ice, J. Fluid Mech. 621, 215–242 (1999).CrossRefGoogle Scholar
[17]Milewski, P. A., Vanden-Broeck, J-M and Wang, Z., Hydroelastic solitarywaves in deep water, J. Fluid Mech. 679, 628–640 (2011).CrossRefGoogle Scholar
[18]Vanden-Broeck, J-M. and Parau, E., Two-dimensional generalized solitarywaves and periodic waves under an ice sheet, Phil. Trans. R. Soc. A 369, 2957–2972 (2011).CrossRefGoogle Scholar
[19]Parau, E. and Vanden-Broeck, J-M, Three-dimensional waves beneath an ice sheet due to a steadily moving pressure, Phil. Trans. R. Soc. A 369, 2973–2988 (2011).Google Scholar
[20]Hosking, R.J., Sneyd, A.D. and Waugh, D.W., Viscoelastic response of a floating ice plate to a moving load, J. Fluid Mech. 196, 409–430 (1988).Google Scholar
[21]Wang, K., Hosking, R. J. and Milinazzo, F., Time-dependent response of a floating viscoelastic plate to an impulsively started moving load, J. Fluid Mech. 521, 295–317 (2004).CrossRefGoogle Scholar