轨道结构动力分析的傅里叶变换法

将傅里叶变换法应用于轨道结构动力分析，首先对轨道结构振动方程进行傅里叶变换，求解傅里叶变换域中的振动位移，再通过快速离散傅里叶逆变换得到轨道结构的振动响应。该方法适用于任何复杂的轨道结构动力学问题。文中针对轨道结构连续弹性单层梁模型和双层梁模型，用傅里叶变换法求得了单轮通过时的轨道临界速度，分析不同的轨下橡胶垫板和弹性扣件、荷载速度及激振频率对轨道结构振动的影响。研究表明，轨道结构有多个临界速度，特别需要关注的是最小的轨道临界速度，这一速度容易被中、高速列车超过，从而引起轨道结构的强烈振动。另外，用连续弹性单层梁模型得到的最小轨道临界速度与理论计算结果一致；对双层梁模型，则很难用解析的方法求得轨道临界速度。

Dynamic Analyses of Track Structure with Fourier Transform Technique

The Fourier transform technique is applied to analyze the track structure dynamics. First, the vibration equations of the track structure are transformed by the Fourier Transform. The vibration displacements in the Fourier Transform domain are solved then with this transformed equation. Finally, the vibration responses of the track structure are obtained by performing the inverse fast Fourier transform. This technique is applica- ble to any complicated dynamic problem of the track structure. On the basis of the single layer and the double layer continuous elastic beam models for the track structure the track critical velocities when a single wheel passes by are calculated with the Fourier Transform technique. Influences of different rail pads and fastening rigidities and the load velocities as well as the load exciting frequencies on the track structure vibration are investigated. The studies show that there are several critical velocities in the track structure and what we should pay great attention to is the minimum track critical velocity which may be easily exceeded by moderate and high speed trains and may induce the track structure to vibrate strongly. In addition, the simulated minimum track critical velocity with the single layer continuous elastic beam model well agrees with the theoretical computation result. However, it is difficult to obtain the track critical velocity by the analytic method for the double layer beam model.