Abstract
Abstract The article presents an original approach to the analysis of railway track dynamics. The “beam-inside-beam” concept is introduced as a dynamic generalisation of the static head-on-web effect, based on the two-layer model of rail. Rail head is a distinguished element of the rail. The system of distributed moving loads excites rail head as a beam supported by the rail web being considered as a viscoelastic layer. Rail head vibration is a kinematic excitation of the whole rail profile, including the rail head. The whole rail is also considered as a beam on viscoelastic foundation with parameters used in typical analyses of railway track dynamics. Vibrations of the whole rail obtained from the analysis of the two-layer “beam-inside-beam” model are compared with vibrations of typical one-layer track model. It is known that the static head-on-web effect is very limited. The range of significant rail head displacements covers nearly 0.6 m of area centred around the wheel position. This observation is also valid in the case of moving constant load. In other words, the dynamic effect of rail head vibrations in the case without imperfections type of track-vehicle is practically the same as in the static head-on-web case. Nevertheless, the analysis of track imperfections impact with various factors influencing the system behaviour, like the axles load and configuration, the track elastic parameters, the length of imperfection, or the train speed, show that the head-on-web effect is significant and should be analysed in more detail. For this purpose, a new model “beam-inside-beam” is proposed. The Fourier series are used to solve the two considered models. The load and unknown functions in the models’ solutions are expanded in the arbitrarily assumed interval which practically covers non-zero track response for the analysed system of parameters (group of wheels). This solving method for equation of motion was experimentally validated in the paper by Czyczula et al. (2017). Validation of the “beam-inside-beam” model is considered as future work and the current article should be recognised as a preliminary study of the analysed effects under assumption of being purely theoretical investigation so far, although forming hierarchically organised building of more complex rail models is possible to partially verify in further steps of modelling process.
Highlights
The problem of dynamic response of the track under a moving load is the subject of many theoretical and experimental studies.Under some assumptions, the beam on elastic foundation can be considered as a typical track model
The beam on elastic foundation can be considered as a typical track model
One should underline that the dynamic “head-on-web” effect becomes stronger with increasing train speed and changes with rail foundation stiffness variation
Summary
The problem of dynamic response of the track under a moving load is the subject of many theoretical and experimental studies. Analysis of a set of distributed moving forces, described with Heaviside functions Analysis of a set of forces varying harmonically and associated with track imperfections – including phase of sine function for particular axles In all the above described generalisations of classical approach, the track response model is composed of rail (as the beam) and viscoelastic or elastic foundation. The rail head effect in a static load case was studied analytically by Orringer et al [20]. The effects of rail head vibrations on track response are studied in a steady state case. In the model, both the rail head and the whole rail profile are described as the Bernoulli–Euler beams. The moving load is modelled by a set of distributed forces moving with constant velocity
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