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

Abstract

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

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

“…An impact hammer printed circuit board (PCB) Piezotronic 086D50 is used to excite a vertical force on a Table 1. Parameters of the railway track (Azoh et al, 2014;Tran et al, 2018). sleeper at different positions (see Figure 5).…”

“…In this article, an ''inverse problem'' has been developed to determine the vertical train loads based on the analytical model of the railway sleeper which has been presented by Tran et al (2018). By considering a beam resting on a Kelvin-Voigt foundation and by assuming a vertical periodic load, the sleeper strain can be calculated rapidly with the help of Green's function.…”

“…Some research focuses on the pre-stressed concrete sleeper using finite element method (FEM) in two dimensions (2D) and in three dimensions (3D) (see Arab et al, 2011; Kumaran et al, 2003). Tran et al (2018) have developed an analytical model of the railway sleeper which allows us to calculate the sleeper response posed on a homogeneous foundation in a shorter time than numerical models.…”

Matching Boundary Conditions for the Euler–Bernoulli Beam

“…e Euler-Bernoulli beam is one of the most important models in the study of one-dimensional solid structures, which is widely applied in engineering, such as railway and bridge engineering [1,2]. e beam always has a finite length in most real practical applications.…”

Development of innovative methodologies to reduce railway rolling noise through Genetic Algorithm-based shape optimization techniques

“…As a down side, they require a great number of steps during the problem solution computation if an appropriate precision if wanted, with the associated high computational cost. Examples of track modelling in the time domain can be found in [63][64][65], the latter case applied to the particular case of a sleeper. Due to the fact that the calculation time required would not be viable for the optimization procedures developed in the present Thesis, this section will focus on the several existing frequency domain-based models.…”