曲线轨道空间振动响应特性研究

曲线轨道空间振动存在平面内振动、平面外弯扭耦合振动，通过建立曲线轨道空间振动频域解析模型，对曲线轨道动力响应特性进行研究。将曲线轨道视为圆形结构的一部分，利用圆形结构周期性的特性，在一个基本元之内求解曲线轨道的动力响应。通过引入移动谐振荷载作用下轨梁动力响应的频域数学模态，得出曲线轨道轨梁频域响应的级数表达。在频域内采用数学模态叠加法表示曲线轨梁的纵向、横向、垂向及扭转振动，进而求解得到基本元内轨梁的频域动力响应。经计算表明，文中提出的频域解析模型能够得到精确的曲线轨道频域响应。通过分析速度、半径、超高等因素，得到以下结论：准静态激励下单个移动轴荷载对曲线轨梁的垂向、横向及扭转振动的影响范围在作用点两侧±5m左右；轴荷载移动速度对曲线轨梁横向位移、扭转变形具有显著的影响，随着速度的增加，曲线轨道由过超高状态逐渐过渡到理想超高状态，最终进入欠超高状态，轨梁横向位移、扭转变形方向发生改变，响应幅值先减小后增加；半径、超高和速度对曲线轨梁垂向位移、横向位移及扭转变形影响较大；随着半径的增加，速度对位移响应的影响程度降低；准静态移动轴荷载列作用下曲线轨梁垂向、横向及扭转频域响应主要集中在40Hz以内的频段；横向振动、扭转振动频谱分布范围较宽。

Study on dynamic characteristics of a curved track in 3 dimensions

Dynamic characteristics of the curved track are very complex due to the in-plane and out-of-plane vibrations. Modelling the curved track in theoretical method is important to understand its physical properties. The curved track with a certain length can be regarded as one part of a circular structure with the cyclic length of fastener spacing. Dynamic response of the curved track can be solved within one basic cell of track in the frequency domain according to the properties of the periodic structure. A periodic discretely supported curved Euler beam is used to simulate the curved track. Mathematical modes of rail in the frequency domain are proposed and dynamic response of the curved track in 3 dimensions are expressed by series superposition of the mathematical modes. It is shown that the accurate frequency response of the curved track can be obtained by the curved track model proposed in this paper. Several conclusions can be obtained according to the model. The influence range of a single moving axle on the vertical, lateral and torsional vibrations of the curved track is about 5m on both sides of the load point. The velocity has a significant effect on lateral and torsional vibrations of the curved track. The directions of the lateral and torsional vibrations will change when the velocity increases. As the speed increases, the curved track transfers from the surplus superelevation state to the inadequate superelevation state gradually and the response amplitude decreases first and then increases. The radius, elevation of curve and velocity have great influence on the vertical, lateral and torsional vibrations of the curved track. As the radius increases, the effect of velocity on dynamic response is reduced. The dynamic response of the vertical, lateral and torsional vibrations of the curved track under a sequence of moving axles in the frequency domain is mainly within 0~40Hz. The spectrum distribution of horizontal, torsional vibrations is wider than vertical vibrations.