【摘要】 随着城市轨道交通曲线段线路增多，曲线轨道的环境振动问题逐渐引发社会关注。以曲线整体式轨道为例，利用双重傅里叶变换和围道积分推导移动简谐荷载下曲线轨道的挠度响应解答，研究曲线轨道的频散特性及空间振动特性。研究表明，曲线轨道的自振频率与频散曲线的最小频率接近，约等于单自由度质量-弹簧系统的自振频率计算值。当扣件阻尼为欠阻尼时，轨道挠度随荷载频率升高先增大后减少，最大值在自振频率位置，当扣件阻尼过大时，轨道挠度随频率升高不断减少。在满足曲线轨道最小曲线半径的要求下，列车速度对曲线轨道竖向挠度的影响很小，径向挠度则随列车速度的增加先减小后增大，存在一个理想车速使得径向挠度为零。增加曲线半径对竖向挠度无影响，但会引起原理想车速范围内径向挠度增大和最大扭转角值减少，增加超高角对竖向挠度也无影响但可以有效减少径向挠度。研究对于曲线轨道的减振设计具有一定的参考价值。更多还原

【Abstract】 As the number of curved urban rail transit lines increases, environmental vibration problem induced by curved track is increasingly attracting social attention. Taking a curved fixed track as an example, its deflection response solution to moving harmonic loads was derived based on double Fourier transformations and contour integration technique,the dispersion characteristics and spatial vibration characteristics of the curved track were studied. Research indicates that the natural frequencies of the curved track are close to the minimum frequencies in the dispersion curves, and almost equal to the natural frequencies of single freedom mass-spring system. When the rail pad is underdamped, the track’s deflection increases initially and decreases later with the increase of load frequency, and the peak value remains at the natural frequency. When the damping of the rail pad is overlarge, the track’s deflection reduces continuous with the increase of the load frequency. When the requirement of minimum radius of the curved track is met, the track’s vertical deflection is essentially independent of the train’s speed, but the radial deflection decreases at first and then increases as the train’s speed increases. So, there exists an ideal train speed at which the radial deflection vanishes. Although increasing the radius of curved track has no effect on the vertical deflection, it induces increase of the radial deflection and decrease of the maximum torsional angle below the original ideal train speed. Increasing the super-elevation angle also has no effect on the vertical deflection, but it can effectively reduce the radial deflection. The presented research may provide some reference to the vibration attenuation design of curved tracks.更多还原