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Mathematical Modeling for Longitudinal Displacement of a Straight Continuously Welded Railway Track and its Numerical Implementation

机译：直线连续焊接轨道纵向位移的数学模型及其数值实现

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摘要

A mathematical model of the longitudinal flexibility of a continuously welded railway track and the methodology for the analysis of the longitudinal displacement of rails under the effects of passing trains is developed to investigate the longitudinal behavior of rails. The purpose of this analysis is to explore the changes of longitudinal stress distribution in the rails due to mechanical loading applied by a travelling train. A half track system is used to derive the equations required to obtain the magnitude of deflection and force of rails and these values are scaled to produce the displacement pattern using the method of superposition. The mathematical model is translated into MATLAB and validation of the program is verified through comparisons of displacement patterns generated by a computer software LONGIN. Analysis of a straight track due to train braking was performed over a track length of 1000 m. The longitudinal displacement obtained showed that maximum longitudinal displacement occur in the middle of the track at the distance of 570 m which is in direct agreement with the published result.
机译：建立了连续焊接铁路轨道纵向挠性的数学模型，并分析了在经过的列车作用下铁路纵向位移的分析方法，以研究铁路的纵向行为。该分析的目的是探讨由于行进的火车施加的机械载荷导致的纵向应力分布的变化。半轨系统用于导出获得钢轨的挠度和力的大小所需的方程式，并使用叠加方法对这些值进行缩放以生成位移模式。将数学模型转换为MATLAB，并通过比较计算机软件LONGIN生成的位移模式来验证程序的有效性。在1000 m的轨道长度上对由于列车制动而产生的直线轨道进行了分析。获得的纵向位移表明最大的纵向位移发生在距离570 m的轨道中间，这与已公开的结果直接一致。

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