Premium
Floating ladder track response to a steadily moving load
Author(s) -
Hosking Roger J.,
Milinazzo Fausto
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.871
Subject(s) - moving load , critical speed , vibration , beam (structure) , euler's formula , mathematics , wavenumber , elasticity (physics) , track (disk drive) , structural engineering , mathematical analysis , physics , acoustics , engineering , optics , mechanical engineering , thermodynamics
Floating ladder rail tracks, which can significantly reduce traffic vibration and noise, have already been installed at several railway sites in and around Tokyo. The steel rails are fixed onto successive ladder‐like sections with two parallel longitudinal reinforced concrete sleepers, which are then mounted upon discrete resilient supports on a concrete bed. A simple mathematical model in which a continuous horizontal Bernoulli–Euler beam on periodic discrete elastic supports represents each floating ‘combined rail’ (i.e. rail and longitudinal sleeper), used earlier to discuss the low‐frequency free vibrations in the system, is again adopted to investigate the response due to a steadily moving load. We demonstrate that Fourier transforms can be invoked to obtain the forced deflexion, which depends upon the load speed. A contribution from the periodic supportsdetermines the steady component of the deflexion moving with the load, and the other contributions from the supports produce oscillations. As is the case for a load moving over a beam or plate with continuous support, the response may be characterized using the free flexural wave dispersion relation—although there is now a countably infinite number of dispersion curves, corresponding to the existence of propagation bands in the periodic structure. The lowest wavenumber local minimum in the phase speed (coincident with the group speed) defines the primary critical load speed of most interest, at which the magnitude of the steady component accompanying the moving load becomes large. This primary critical load speed depends upon the relative elasticity of the discrete supports, which must not be too low if the floating ladder track is to be safe for fast rail systems. Copyright © 2007 John Wiley & Sons, Ltd.