曲线轨道钢轨横向振动频域响应特性研究

Study on Lateral Dynamic Response of Curved Track in Frequency Domain

采用离散点支承曲线Euler-Bernoulli梁模拟曲线轨道钢轨,将曲线轨道平面内振动响应力学模型映射至一个具有相同半径的虚拟的圆形环梁中,将圆形环梁视为以支点间距为周期的周期性结构,基于移动谐振荷载作用下周期性结构的频域动力响应特性,可在一个周期基本元内求解曲线轨道钢轨的横向动力响应。利用轨道结构频域动力响应的基本性质,定义钢轨数学模态以及广义波数,进而采用傅里叶级数表示曲线轨道钢轨平面内振动响应。在频域内采用数学模态叠加法表示钢轨的平面内振动响应,最终建立曲线轨道钢轨平面内振动响应频域解析模型。通过对支点横向支承刚度、阻尼系数以及曲线半径、支点间距等因素进行参数分析,得到曲线轨道钢轨横向振动频域响应特性。

Modelling the in-plane dynamic behavior of a curved railway track subjected to fixed harmonic loads is important to understand its dynamic characteristics.Periodic discrete supported curved Euler beam was used to simulate dynamic response of the curved track as it is part of circular structure with the cyclic length of fastener spacing.The mechanical model of in-plane vibration response of the curved track was mapped to a virtual circular ring beam with the same radius.The circular ring beam was regarded as a periodic structure with fastener support spacing as the period.Based on the frequency-domain dynamic response characteristics of periodic structure under moving resonant load,the lateral dynamic response of the curved track rail can be solved in one periodic basic element.Using the basic properties of the frequency domain dynamic response of the track structure,the mathematical mode of the rail and the generalized wave number were defined,and then the Fourier series was used to express the in-plane vibration response of the curved track.In the frequency domain,the mathematical modes superposition method was used to express the in-plane vibration response of the rail,and finally the frequency-domain analytical model of the in-plane vibration response of the curved track rail was established.Finally,based on the parameter analysis of the effect of lateral support stiffness,lateral support damping coefficient,the fastener support spacing and the curve radius,the frequency domain response characteristics of the lateral vibration of the curved track rail were obtained.