For a train moving along a curved path, centrifugal forces are induced in addition to gravitational loads. In this paper, the 2.5D approach for loads moving along a straight path is extended to treating both the vertical and horizontal loads moving along a curved path. Firstly, closed-form solutions for the problem are derived for the cases of vertical and horizontal loads. Then, the 2.5D approach with finite/infinite elements in the Cartesian coordinates are summarized. By approximating a curved path by a number of small chordwise segments and by using the 2.5D approach to simulate each segment, the displacements in the global polar coordinates are obtained by summing up those of each segment in the local Cartesian coordinates, considering the time lags and direction changes. For linear systems, the responses due to vertical and radial loads can be computed separately. In the numerical simulation, the theory presented will be verified by two typical cases. The frequency-splitting phenomenon is found to exist for the horizontal loads, as well as for the vertical loads, moving over a curved path. The radial response induced by the centrifugal force cannot be ignored, and the displacement outside the railway track is larger than that inside. Such an effect should be considered in the design of curved paths for highspeed railways. The method presented herein can be adopted to solve problems with varying radius of curvature.

对于沿弯曲路径行驶的火车，除了重力载荷外，还会感应离心力。在本文中，沿直线路径移动的2.5D方法已扩展为处理沿曲线路径移动的垂直和水平负载。首先，针对垂直和水平载荷的情况，得出了该问题的封闭形式的解决方案。然后，总结了在笛卡尔坐标系中具有有限/无限元素的2.5D方法。通过用多个较小的弦线段近似弯曲路径，并使用2.5D方法模拟每个段，考虑时滞，通过将局部笛卡尔坐标系中每个段的位移相加得出全局极坐标的位移和方向变化。对于线性系统，垂直和径向载荷引起的响应可以分别计算。在数值模拟中，将通过两种典型情况来验证所提出的理论。发现在弯曲路径上移动的水平负载和垂直负载都存在分频现象。离心力引起的径向响应不容忽视，铁轨外部的位移大于内部的位移。在高速铁路弯道的设计中应考虑这种影响。可以采用本文提出的方法来解决曲率半径变化的问题。以及垂直载荷，都在弯曲的路径上移动。离心力引起的径向响应不容忽视，铁轨外部的位移大于内部的位移。在高速铁路弯道的设计中应考虑这种影响。可以采用本文提出的方法来解决曲率半径变化的问题。以及垂直载荷，都在弯曲的路径上移动。离心力引起的径向响应不容忽视，铁轨外部的位移大于内部的位移。在高速铁路弯道的设计中应考虑这种影响。可以采用本文提出的方法来解决曲率半径变化的问题。