Abstract
The paper presents an analysis of linear models track response under longitudinal loads due to braking and accelerating of the train as well as constant traction forces. Longitudinal forces on the wheel-rail contacts are uniformly distributed on the whole length of train. Analysis is carried out under assumption that – in short time – train speed does not change significantly. Therefore stationary response of rail track is considered. The problem of critical speed is presented. Effect of vertical imperfections on the longitudinal rail displacement is considered under assumption that longitudinal forces varying in time are changed proportionally to the vertical forces. These forces are proportional to the amplitude of vertical imperfections. This analysis should be recognised as the main novelty of the paper. In the summary, certain practical conclusions are formulated as well as the further investigations are pointed out.
Highlights
Railway track dynamic response mainly concern vertical plane
Original approach for the analysis of the problem may be shortly formulated as follows: varying in time longitudinal loads are proportional to the varying in time vertical loads and these loads are proportional to the amplitude of vertical track imperfections
Circular frequency ω and amplitude Δθ of varying load are associated with vertical track imperfections, assumed as cosine shape, and train speed v
Summary
Railway track dynamic response mainly concern vertical plane Horizontal plane (lateral and longitudinal directions) were analysed in the papers [47]. Effect of longitudinal forces in rails on the vertical track response was studies in the papers [2,8]. This paper should be considered as a significant improvement of the analyses presented in the previous papers of authors [4, 7]. Mentioned papers concern only constant in time longitudinal forces. In this paper varying in time forces are taken into account. Original approach for the analysis of the problem may be shortly formulated as follows: varying in time longitudinal loads are proportional to the varying in time vertical loads and these loads are proportional to the amplitude of vertical track imperfections. Last assumption is typically used in analyses of track vertical response Last assumption is typically used in analyses of track vertical response (comp. [2, 9])
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