Numerical and Experimental Study on Measuring Method of Rail Axial Stress of Continuous Welded Rails Based on Use of Resonant Frequency

Abstract

This paper proposes a newly developed method, which measures absolute axial stress of continuous welded rails (CWR), based on the change of resonant frequency of standing wave mode of rails in the periodic infinite railway track structure. First, the authors theoretically derived dominant simultaneous equations regarding the vibration motions of a three-dimensional Timoshenko-beam under compressive or tensional axial-loadings. By applying the Floquet's theorem to dominant equations of the unit cell, which is an irreducible sub-structure with periodicity of the infinite track structure, the equations are simplified into Eigen-value problems in the frequency domain. Numerical dispersion analyses of wave modes propagating in a track made clear the relation among axial-loadings, wavenumber and natural frequency and provided an evaluation of the feasibility of the proposed method for the measurement of the absolute axial stress. Furthermore, in-situ measurements in the existing CWR track experimentally confirmed the linearity between the axial stress and the resonant frequency.

<b>Improvement of Accuracy of Method for Measuring Axial Force of Rail Based on Natural Frequency</b>

“…In order to measure the axial force of a CWR, a simple method was proposed based on changing vibration mode characteristics of the rail with the axial force [12][13][14]. This method has many advantages; for example, the absolute value of the axial force is measurable, it is neither labor intensive nor does it require large-scale measuring equipment, and measuring time is short.…”

Estimation of Rail Axial Force in High‐Speed Railway Ballastless Track Based on Wave Modes

“…To measure the rail axial force in an actual track structure, Aikawa et al [16] studied the resonance frequencies of ballast track, presenting that the pinned-pinned frequency could be used as the index for measuring rail axial force in ballast track. However, the sensitivity of the experimental result is higher than the numerical one.…”

Analysis of vertical vibration band gap characteristics of periodic discrete support rail

“…3.1 无限周期轨道结构的能带 钢轨采用CHN60轨, 轨道结构相关参数取值见 表1, 其中扣件刚度取值参考Aikawa等人 [17] 图 6 (网络版彩图)一阶"pinned-pinned"振型 表 3 不同钢轨阻尼损耗因子对应带隙频率 表 5 不同扣件阻尼损耗因子对应带隙频率…”

“…陆建飞等人 [13,14] 将轨道简化为桥梁 间的连接弹簧, 利用传递矩阵法研究了移动荷载下周 期性高架铁路桥的动力响应, 得到了周期性高架桥的 能带结构. Abe等人 [15] 在Thompson研究基础上, 考虑 Aikawa [17] 建立了有砟轨道的三维梁单元模型, 通过周 期结构理论以及Floquet变换方法分析了轨道结构频 散特性与温度力之间的关系, 但该方法建模及分析过 程比较复杂. 冯青松等人 [18] x A x…”