The propagation law of ultrasonic guided waves in waveguide structures is determined by their dispersion characteristics, and the number of guided waves in symmetric and antisymmetric modes in rails is significant, so the dispersion characteristics are very complex. In order to study the dispersion characteristics of symmetric and antisymmetric modes in rails, this paper derives the wave equation based on the SAFE method with higher order elements, and the correctness of the wavestructure calculation in the SAFE model is verified using the FE method. This paper focuses on the wavestructure state at 0 kHz and the wavestructure changes during mode crossing through and repulsive deflections, and for the first time experimentally verifies the phenomenon of wave structure exchange in rails. The main conclusions are that the dispersion curves between modes with the same symmetry show repulsive deflection, and the dispersion curves between modes with opposite symmetry show crossover; the wavestructure of the rail is mainly rigid body translation and rigid body rotation at frequencies close to 0 kHz; the guided wave at the intersection of symmetric and antisymmetric modes transforms into a fading wave that cannot be continuously propagated in rails; when the dispersion curves are close, the wavestructures between the two modes are linearly superimposed, and when the dispersion curves are deflected by repulsion, the wavestructures of the two modes are exchanged.

中文翻译：

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研究轨道中对称和非对称模式的色散特性：理论和实验研究

超声导波在波导结构中的传播规律是由其色散特性决定的，而导轨中对称模式和反对称模式的导波数量很大，因此色散特性非常复杂。为了研究钢轨中对称模态和反对称模态的色散特性，本文基于SAFE方法推导了高阶单元的波动方程，并利用有限元方法验证了SAFE模型中波结构计算的正确性。本文重点研究了0 kHz时的波结构状态以及模态穿越和排斥偏转过程中的波结构变化，并首次通过实验验证了钢轨中波结构交换的现象。主要结论是，同对称模间的色散曲线呈现排斥偏转，相反对称模间的色散曲线呈现交叉；频率接近0 kHz时，钢轨的波结构主要是刚体平移和刚体旋转；对称模式和反对称模式相交处的导波转变为衰落波，无法在轨道中连续传播；当色散曲线接近时，两种模式之间的波结构线性叠加，当色散曲线因斥力而偏转时，两种模式的波结构交换。