中文摘要：

导波传播模式分析是钢轨长距离导波检测和振动噪声控制的基础。钢轨中的导波传播模式可以通过波数频率关系和对应的结构形变来有效识别。应用半解析有限元法（Semi-analytical finite element method,SAFE）,基于虚功原理构建导波在任意截面弹性波导中传播的控制方程,求解弹性波导中导波传播的频散曲线和结构形变。应用该方法求解0~8 k Hz频率范围自由状态CHN60型钢轨中导波传播的波数频散关系和结构形变,并讨论8个基本传播模式的特点。采用模态力锤及多传感器测量钢轨截面形变的模态分析试验方法得到钢轨横向和垂直振动模态导波的波数-频率系数,数值分析与试验结果相符合。

英文摘要：

Acoustical guided waves modal analysis in rail is the basis of long distance guided wave inspection and rail vibration and noises control. In particular the various propagating guided waves in the rail are identified in terms of their propagation wavenumber coefficients and their corresponding deformed shapes. The semi-analytical finite element method is used to formulate the governing equation for guided waves propagating in elastic waveguides of arbitrary cross-section on the basis of the virtual work principle, wavenumber dispersion curves and deformed shapes are extracted by solving governing equation, which provide the basis for selecting mode and frequency during application. The propagating guided waves wavenumber dispersion curves and deformed shaped under 0-8 kHz frequency range for CHN60 type free rail are obtained using semi-analytical finite element method, and the characteristics of the eight based guided waves mode in rail are discussed. Instrumented hammer experimental study and modal analysis using sever vibration accelerometers mounted on rail are carried out to verify the vertically vibrating mode and horizontally vibrating mode guided waves wavenumber dispersion coefficient. Modeling and experimental investigations of lateral and vertical excitation in railhead shows that good agreement between numerical calculation and experiment.