An effective technique is proposed for identifying the track modulus, i.e., the foundation stiffness of the rails, using the contact-point response of the moving test vehicle. First, for a simple beam resting on an elastic foundation under a moving sprung mass, closed-form solutions are derived for the responses of the vehicle and its contact point with the rail. It is shown that the track modulus can be well identified via the first rail frequency (RF) extracted from the contact-point response, in that (1) the first RF is most outstanding compared with the other RFs in the vehicle-generated responses; and (2) the contact-point response outperforms the vehicle response as it is free of the disturbing effects of the vehicle and driving frequencies. The proposed technique is then verified numerically along with the key parameters assessed. The main conclusions are: (1) the first RF can be easily recognized as the “cliff” of the RF “plateau” in the contact-point spectrum; (2) the track irregularity has a little effect on the identification of track modulus; (3) a moderate speed is recommended for the test vehicle for a balance between efficiency and accuracy; and (4) the efficacy of the proposed technique remains good even with the presence of track damping and irregularity. Moreover, the application of the proposed technique to detecting the damage modeled by variation in foundation stiffness is demonstrated.

中文翻译：

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车辆扫描法轨道模数检测

提出了一种有效的技术来识别轨道模量，即轨道的基础刚度，使用移动测试车辆的接触点响应。首先，对于在移动的簧载质量下放置在弹性基础上的简单梁，推导出车辆及其与轨道接触点的响应的封闭形式解。结果表明，通过从接触点响应中提取的第一个轨道频率 (RF) 可以很好地识别轨道模量，因为 (1) 在车辆生成的响应中，第一个 RF 与其他 RF 相比最为突出；(2) 接触点响应优于车辆响应，因为它不受车辆和驾驶频率的干扰影响。然后对所提出的技术以及评估的关键参数进行数值验证。主要结论是：（1）第一次RF可以很容易地识别为接触点频谱中RF“高原”的“悬崖”；(2)轨道不平度对轨道模数的识别影响不大；(3) 为了平衡效率和准确度，建议测试车辆采用适中的速度；(4) 即使存在轨道阻尼和不规则，所提出的技术的效果仍然很好。此外，还展示了所提出的技术在检测由基础刚度变化建模的损坏中的应用。(3) 为了平衡效率和准确度，建议测试车辆采用适中的速度；(4) 即使存在轨道阻尼和不规则，所提出的技术的效果仍然很好。此外，还展示了所提出的技术在检测由基础刚度变化建模的损坏中的应用。(3) 为了平衡效率和准确度，建议测试车辆采用适中的速度；(4) 即使存在轨道阻尼和不规则，所提出的技术的效果仍然很好。此外，还展示了所提出的技术在检测由基础刚度变化建模的损坏中的应用。