In this study, the possibility of using the rail vibration frequency to assess the longitudinal temperature force on the rail of ballasted track was investigated experimentally. An empirical formula was subsequently derived to link the frequency index to multiple factors, including the longitudinal temperature force, under-rail stiffness, and fastener spacing. Further tests were conducted to analyse the applicability and accuracy of the frequency index in continuous longitudinal force measurements under different line conditions (i.e. in the non-expansion zone and expansion zone). A technique for using the frequency index to assess the longitudinal temperature force was finally developed. The main results are as follows. (1) The first-order pinned–pinned modal frequency and peak frequency of the mid-span response are very close, and they both change linearly with the longitudinal temperature force on the rail. The rate of change in the vertical direction is larger than that in the horizontal direction. (2) Even if influenced by multiple factors, the peak frequency of the rail mid-span response is suitable for continuous longitudinal temperature force assessment under appropriate measures, and longitudinal temperature force detection could be realized with proper preparation. (3) Using the mid-span response frequency to detect the temperature force of rail located in the expansion zone causes deviation of the results, and under-rail materials whose stiffnesses are insensitive to temperature help reduce this deviation.

在这项研究中，实验研究了使用轨道振动频率评估压载轨道在轨道上的纵向温度力的可能性。随后导出了一个经验公式，将频率指数与多个因素相关联，包括纵向温度力，轨道下刚度和紧固件间距。进行了进一步的测试，以分析频率指数在不同线路条件下（即在非扩展区和扩展区）在连续纵向力测量中的适用性和准确性。最终开发了一种使用频率指数评估纵向温度力的技术。主要结果如下。（1）一阶固定模式的频率和中跨响应的峰值频率非常接近，它们都随着导轨上的纵向温度力线性变化。垂直方向的变化率大于水平方向的变化率。（2）即使受到多种因素的影响，中跨响应的峰值频率也适合在适当的措施下进行连续的纵向温度力评估，并且通过适当的准备就可以实现纵向温度力的检测。（3）使用中跨响应频率检测位于扩展区中的钢轨的温度力会导致结果偏差，而刚度对温度不敏感的钢轨下材料会减小该偏差。（2）即使受到多种因素的影响，中跨响应的峰值频率也适合在适当的措施下进行连续的纵向温度力评估，并且通过适当的准备就可以实现纵向温度力的检测。（3）使用中跨响应频率检测位于扩展区中的钢轨的温度力会导致结果偏差，而刚度对温度不敏感的钢轨下材料会减小该偏差。（2）即使受到多种因素的影响，中跨响应的峰值频率也适合在适当的措施下进行连续的纵向温度力评估，并且通过适当的准备就可以实现纵向温度力的检测。（3）使用中跨响应频率检测位于扩展区中的钢轨的温度力会导致结果偏差，而刚度对温度不敏感的钢轨下材料会减小该偏差。