Vertical Stability of Longitudinal Continuous Ballastless Track Under Temperature Variation
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摘要:为研究纵连式无砟轨道垂向失稳的形态和过程，基于欧拉梁挠曲微分方程推导了温度作用下轨道板上拱波形曲线，得到了上拱矢度与波长的关系；并利用势能驻值原理分析了存在初始上拱时轨道板垂向失稳的平衡路径. 研究表明：与假设变形法相比，解微分方程法精度更高，误差可降低近30%；轨道板的失稳过程包括持稳、胀板和失稳3个阶段，且初始上拱矢度越大，轨道板的持稳极限和胀板极限越小；分析了温度力释放对轨道板上拱平衡路径的影响，表明轨道板失稳的平衡路径会出现强化阶段，且摩擦因数越大，强化阶段出现越早，但变形较小时，温度力释放对轨道板板上拱的影响极小；初始上拱矢度越大，轨道板允许上拱越大，初始上拱小于50 mm时，轨道板难以发生垂向的失稳.Abstract:To study the vertical instability form and process of a longitudinal continuous ballastless track, the arch curve of the slab that is influenced by temperature can be deduced based on the deflection differential equation of the Euler beam. The equation of the arch camber and wavelength of the slab was obtained from the arch curve. The equilibrium path of the slab with the initial arch was analysed based on stationary potential energy. Compared with the method of assuming a deformation, the method of solving differential equations is more accurate, and the error is reduced by nearly 30%. The course can be divided into three stages: steady, expansion, and destabilization. The limit of the steady and expansion stages decreases along with the increase of the initial arch camber. The effect of the release of slab temperature on the equilibrium path shows that the path appears as a stiffening stage, and the larger the friction coefficient, the earlier the stage occurs, whereas it has little effect when the deformation is small. The larger the initial camber, the greater the allowed wavelength is. When the initial arch is smaller than 50 mm, the vertical instability of the slab does not occur.
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Key words:
- continuous track/
- slab/
- temperature effect/
- stability
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图 4上拱矢度与等效温升的关系
Figure 4.Relationship between upper arch and equivalent temperature rise
表 1主要计算参数
Table 1.Main calculation parameters
参数 取值 参数 取值 密度/（kg•m–3） 2 500 横断面面积/m2 0.51 弹性模量/Pa 3.55×1010 宽度/m 2.55 线膨胀系数 1×10–5 厚度/m 0.2 重力荷载/（N•m–1） 12 507.75 惯性矩/m4 1.7×10–3 
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表 2最大上拱位移
Table 2.Maximum camber displacement
f0 1 5 10 20 50 100 150 最大上拱位移 0 0 0 0 2.4 失稳 失稳 下载:
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