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Modelling of floating-slab tracks with continuous slabs under oscillating moving loads
No full textThis paper discusses modelling of floating-slab tracks on rigid foundations. The model consists of an upper Euler–Bernoulli beam to account for both the rails and a lower Euler–Bernoulli beam to account for the slab. There are two continuous resilient layers in the model: one to account for railpads between the rails and the slab and one to account for slab-bearings underneath the slab. The Fourier transformation method is used to calculate displacements of such a track under an oscillating moving load. These results are used to calculate the cut-on frequencies and critical velocity of the track. The work in this paper also demonstrates some basic concepts in the context of vibration of infinite systems including dispersion curves, critical velocities, load-velocity lines and coupling of systems in the wavenumber-frequency domain. The paper offers a complete treatment of the issues important to the analysis of a double-beam system not elsewhere available in the published literature
A numerical model for calculating vibration from a railway tunnel embedded in a full-space
No full textVibration generated by underground railways transmits to nearby buildings causing annoyance to inhabitants and malfunctioning to sensitive equipment. Vibration can be isolated through countermeasures by reducing the stiffness of railpads, using floating-slab tracks and/or supporting buildings on springs. Modelling of vibration from underground railways has recently gained more importance on account of the need to evaluate accurately the performance of vibration countermeasures before these are implemented.This paper develops an existing model, reported by Forrest and Hunt, for calculating vibration from underground railways. The model, known as the Pipe-in-Pipe model, has been developed in this paper to account for anti-symmetrical inputs and therefore to model tangential forces at the tunnel wall. Moreover, three different arrangements of supports are considered for floating-slab tracks, one which can be used to model directly-fixed slabs. The paper also investigates the wave-guided solution of the track, the tunnel, the surrounding soil and the coupled system. It is shown that the dynamics of the track have significant effect on the results calculated in the wavenumber–frequency domain and therefore an important role on controlling vibration from underground railways
Modelling of floating-slab track with discontinuous slab part 2: response to moving trains
No full textA floating-slab track with discontinuous slab provides a spatially-varying stiffness under a constant moving load. When a train moves on such a track, even with the absence of rail roughness, a parametric excitation develops as wheels move up and down applying dynamic forces at the wheel-rail interface. The dynamic force is magnified if one of its principal frequencies matches with any of the train or the track resonance frequencies. In this paper, a new method based on a Fourier series representation is developed to couple a moving train to a track with discontinuous slab. A two-degree-of-freedom system is used to model a quarter of a train with four axles and two bogies moving on a track with constant velocity. The purpose of this work is to investigate the dynamic effect of slab discontinuity on trains running in underground railway tunnels, where the velocity is less than 100km/hr. For typical parameters of a train and a track, it is found that the force at the wheel-rail interface is only increased by 1% of its static value due to slab discontinuity. However, the dynamic effect may be more important in circumstances where high-speed or heavy-axled trains are used in underground tunnels.<br/
Modelling of floating-slab tracks with discontinuous slabs in underground railway tunnels
No full textA computationally efficient software application for calculating vibration from underground railways
No full textThe PiP model is a software application with a user-friendly interface for calculating vibration from underground railways. This paper reports about the software with a focus on its latest version and the plans for future developments. The software calculates the Power Spectral Density of vibration due to a moving train on floating-slab track with track irregularity described by typical values of spectra for tracks with good, average and bad conditions. The latest version accounts for a tunnel embedded in a half space by employing a toolbox developed at K.U. Leuven which calculates Green's functions for a multi-layered half-space.<br/
A software application for calculating vibration due to moving trains in underground railway tunnels
No full textModelling of floating-slab track with discontinuous slab part 1: response to oscillating moving loads
No full textThis paper presents three different methods for modelling a track with discontinuous slab under oscillating moving loads. These are the Fourier–Repeating-unit method, the Periodic-Fourier method and the Modified-phase method. The first two methods, borrowed from the literature of periodic infinite structures, are accurate if careful consideration is taken when performing numerical integrations. The third method, not presented elsewhere before, is faster and simpler; it is only valid for velocities of moving loads lower than the critical velocity of the track, but this “velocity effect” is of no consequence for underground railways. Discontinuity of slab provides a parametric excitation for moving loads over floating-slab tracks. It is shown that in the frequency range of ground-borne vibration, more vibration propagates from such tracks at resonance frequencies of the slabs, compared with tracks with continuous slabs. It is found that the velocity effect is insignificant when calculating displacements of a typical floating-slab track under oscillating moving loads with velocities less than 100km/hr. However, a correction has to be made to account for the right phase between the input force and the output displacement. <br/
An insertion loss model for evaluating the performance of floating-slab track for underground railway tunnels
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