Gilles Forêt

Dynamic analytic model of pre-stressed concrete mono-block railways sleepers

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 Greens 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.

ANALYTICAL MODEL OF THE DYNAMICS OF RAILWAY SLEEPER

The periodically supported beam is an analytical model of the dynamics of a railway track, where each rail together with its supports (sleepers) is independent of the other one. However , the sleepers connect the two rails and their behaviour could influence the response. This study develops an analytical model for this type of track by considering the sleepers as Euler-Bernoulli beams resting on a visco-elastic foundation. By using a relation between the reaction forces and displacement of the periodically supported beam [1], we can obtain a dynamic equation of a sleeper based on Dirac delta distribution. Then, the response of the sleepers can be obtained by using the Green function. This model is a fast method to calculate the dynamic responses of railway sleepers and track.

A fast semi-analytical method for computing the response of railway tracks on nonlinear foundations

The nonlinear vibration of railway tracks is a subject of some recent investigations. A main source of non-linearity comes from the railway foundations. For example, ballast and its lower layers or support systems of non-ballasted railway could have nonlinear behaviors. Models of beam under moving forces are often used for this dynamic system, and then the models are solved by numerical method or perturbation technique for some special nonlinear cases. This communication present a new method for calculating the response of railway tracks under moving trains loads. Based an analytical model of periodically supported beam, this model holds for all kinds of nonlinear foundations. Then, by using harmonic balance techniques and iteration procedures, a new method is developed to calculate the response of the model provided that the loading forces form a periodic impulse series. This kind of loading force represents charges of moving trains with equal mass wagons. This method is demonstrated to converge to the analytic solution of the model in case of linear foundation. Then, it is applied to bilinear and nonlinear foundation as examples. The results show that the nonlinear parameters of foundation have a strong influence on the railways track responses. This semi-analytical method is simple and could be efficient to compute the nonlinear vibrations of railway tracks.