Analytical model of the dynamics of railway sleeper (original) (raw)

A Fast Analytic Method to Calculate the Dynamic Response of Railways Sleepers

Journal of Vibration and Acoustics, 2018

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 inst...

Influence of Sleepers Shape and Configuration on Track-Train Dynamics

The paper is devoted to the study of dynamical behaviour of railway tracks as continuous systems (rails) supported by periodically spaced sleepers and subjected to moving concentrated loads. Several cases of dynamical problems, where elastically supported beams are excited by a moving concentrated force, are considered. In particular, the study is focused on interactions with structure periodic in the space. Results on one-dimensional structures are extended to the case of a two-dimensional system. The problems of stopping bands, passing bands, and mistuning are also mentioned.

Influences of Lateral Wheel Loads on the Sleeper Responses of a Railway Track

2019

Recently, the instrumented sleeper has been developed to measure the sleeper response in-situ. An analytical model of the dynamics of railway sleepers has been developed to calculate rapidly the sleeper response under vertical wheel loads. However, lateral wheel loads are not taken into account in this model but would influence the sleeper response. This paper presents a new analytical model of the dynamics of railway sleepers under lateral wheel loads. In this model, the sleeper is considered as a Euler-Bernoulli’s beam resting on a visco-elastic foundation. Thereafter, by combining the relation between the reaction forces and displacements of the periodically supported beam, the sleeper response can be calculated with help of the Green’s function. Finally, the numerical application shows the influence of the laterals wheel load on the sleeper response.

Influence of Non-Homogeneous Foundations on the Dynamic Responses of Railway Sleepers

International Journal of Structural Stability and Dynamics, 2020

In a railway track, the sleeper’s responses on a non-homogeneous foundation have been investigated by researchers focusing on the foundation behavior along the rails. However, the foundation can also vary along the sleeper length, particularly when the track is newly tamped. The foundation at the sleeper center is often weaker than those under the rails and this non-homogeneity directly affects the sleeper responses. This paper presents a new model to calculate the influence of such foundations on the dynamic responses of the railway sleepers. This model is developed by combining a finite element model for the sleepers and foundation and a model of periodically supported beams subjected to moving loads for the rails. In this paper, the foundation contains three parts with different mechanical behaviors. The sleeper’s responses can be calculated by transforming the finite-element dynamic stiffness matrix to the one considering the boundary conditions and the relation between the rail...

Dynamic Response of Railway track using two parameter model

International Journal of Science and Engineering Applications, 2013

In the present analysis, an infinite Euler-Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using two parameters with damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solution of the governing differential equation analytically. It gives beam deflection under moving load in closed form for damped case. At subcritical speed the absolute value of the deflection of the beam increases with increase of the load velocity. Peak maximum deflection appears when the load travels at the critical speed.

On Vertical Analysis of Railway Track Vibrations

The paper herein presents a vertical vibration analysis of the ballasted track using a new model of the periodic support of the rail that improves the prediction of the rail response for both low and high frequencies. The model of the periodic support consists of two three-directional Kelvin-Voigt systems for the rail pad and the ballast, and a mixed Kelvin-Voigt/Maxwell system for the subgrade. Also, the inertia of the sleeper and the ballast block are introduced. The rail response due to a stationary and moving harmonic load is analyzed by applying the Green's functions method. The influence of the rail pad stiffness and of the Doppler effect on railkway track vibrations are presented.

Identification of train loads from the dynamic responses of an integrated sleeper in situ

Journal of Intelligent Material Systems and Structures, 2020

The monitoring of railway tracks can be performed through several measurement techniques. Recently, a method of diagnosing the railway track has been proposed using fiber Bragg gratings integrated inside the railway sleeper. An analytical model for the dynamics of railway sleepers has been developed allowing calculation of the sleeper responses. In this model, using the relation between the rail forces and displacements of a periodically supported beam, the sleeper’s dynamic equation is written with the help of the Euler–Bernoulli beam and Dirac’s delta distribution. Subsequently, the sleeper dynamic responses are calculated using the Green’s function. This article presents an application of this model to identify the train loads from the strains measured in situ. Based on this model, we can obtain a matrix which presents the link between the loads and the sleeper responses. Then, by substituting the Fourier transform of measured strains at the middle and at the two rail seats of th...

Numerical Analysis of Railway Track Vibrations

The numerical prediction models are used both for evaluation of the track-soil interaction forces as well as for prediction of the ground-borne vibrations. The dynamic track-soil interaction forces are calculated using a detailed train model and the dynamic behaviour of the layered spring-damper system and the through-soil coupling of the sleepers for the soil model [1,2,3,6,7]. The calculation of the groundborne vibration level at the distance is based on the viscous-elastics soil model, too. In the frequency domain free-field response numerical results are presented using the response spectra and the frequency response function (FRF) of the viscoelastic soil medium at the distance, [6,8,9,10,11]. In the next step these functions can be applied to the structure (e.g. engineering and building) dynamic response calculation arising railway traffic using the relevant computational building structure model.

Nonlinear Train-Track-Bridge Interaction with Unsupported Sleeper Group

2020

Article history: Received: 23.02.2020 Accepted: 1.04.2020 Published: 26.06.2020 One of the main characteristics of the ballasted track compared to the slab track is the ability to reduce the level of vibration on the bridge surface. However, due to factors such as the asymmetric or permanent settlement of the ballast layer (compaction), crushing, or moving of ballast particles, a gap between sleeper and ballast appears. This problem intensifies vibrations in the track and, as a result, can affect the dynamic response of the bridge. So far, the lack of scientific attention to this issue on the railway bridge is noticeable. Hence, in this article, by examining a nonlinear dynamic model of Train-Track-Bridge interaction, the effect of the unsupported sleeper on the dynamic behavior of a concrete railway bridge is studied. For this purpose, the influence of a suspended sleeper-group at the different positions along the bridge span, in a range of train speed and gap size, are investigate...

Simulation of structural vibrations induced by a moving load on railway tracks

A numerical approach for a simulation of the effect of moving loads on the vibration of a railway track and the vibration of a structure in the surrounding of the track is presented. Comparative analyses are performed. The rails, sleepers, elastic pads as well as the structure in the surrounding are described by finite elements, and the ballast and subsoil by boundary elements. The simulation is performed in the frequency domain. The investigation indicates that the speed of a moving load has a significant influence on the track and ground vibrations. The results show that in order to obtain a more realistic characteristic of the structural response to the ground motions it is not enough just to consider the vertical component of the ground motions.