This paper proposes a three-dimensional dynamic model for high-speed railway trains moving over curved bridges considering the transition curves, circular curves, and superelevation. Key features of this study are to consider the nonlinear geometrical relationships and creep relationships between the wheels and rail, for which the interactive iterative numerical algorithms are developed based on the equations of vertical displacement and rolling of wheelset, and the torsional resonance conditions of the vehicle–bridge system are verified. The results show that the torsional vibration will cause amplification on vertical dynamic response of the beam on the outside edge of the curve. The deficient/surplus superelevation plays an important role in the lateral and torsional angular displacements of the bridge, and the peak of the torsional resonance response can be reduced by adjusting the practical superelevation of the curve. The variations of wheel–load reduction rate and derailment coefficient in the curve section are positively correlated to the deficient/surplus superelevation. The curve radius is the key factor affecting the wear and fatigue of wheel–rail, and when the curve radius is greater than 7000 m, the wear and fatigue can be significantly reduced. Running at a deficient superelevation level can also reduce the wear and fatigue.

中文翻译：

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高速列车在超高不足或超高曲线桥上行驶的相互作用动力响应

本文提出了一种考虑过渡曲线、圆曲线和超高的高速铁路列车在曲线桥上行驶的三维动力学模型。本研究的主要特点是考虑轮轨之间的非线性几何关系和蠕变关系，基于轮对的垂直位移和滚动方程以及车辆的扭转共振条件，开发了交互式迭代数值算法。 ——桥系统得到验证。结果表明，扭转振动会放大曲线外缘梁的垂直动力响应。不足/剩余超高在桥梁的横向和扭转角位移中起着重要作用，并且可以通过调整曲线的实际超高来降低扭转共振响应的峰值。曲线段轮载减载率和脱轨系数的变化与不足/剩余超高呈正相关。曲线半径是影响轮轨磨损和疲劳的关键因素，当曲线半径大于7000 m时，磨损和疲劳可以显着降低。在不足的超高水平上跑步也可以减少磨损和疲劳。当曲线半径大于7000m时，磨损和疲劳可以显着降低。在不足的超高水平上跑步也可以减少磨损和疲劳。当曲线半径大于7000m时，磨损和疲劳可以显着降低。在不足的超高水平上跑步也可以减少磨损和疲劳。