基于格林函数法的车辆-轨道垂向耦合动力学分析

ANALYSIS OF THE VEHICLE-TRACK VERTICAL COUPLED DYNAMICS BASED ON THE GREEN'S FUNCTION METHOD

通过直接求解脉冲激励下线性系统的动力学方程得到车辆系统和轨道系统格林函数的显式表达,基于格林函数和轮轨Hertz非线性接触理论,提出了求解车辆-轨道垂向耦合动力学的新方法。利用该方法分析了车辆系统和轨道系统格林函数的特征,计算了轨道随机不平顺和单一谐波两种不平顺激励下的轮轨垂向力以及轮对和钢轨垂向位移响应,并与传统的车辆-轨道耦合动力学计算结果进行对比。研究结果表明:车辆系统的格林函数主要由随时间线性增加的线性项和随时间逐渐衰减的衰减项组成;轨道系统的格林函数随时间波动衰减,0.15 s后初始脉冲激励引起的钢轨振动基本衰减至0;格林函数法与传统方法的计算结果几乎完全吻合,说明了该方法在车辆-轨道耦合动力学计算中的可靠性。

Abstract： This paper presents a new method to analyze the vehicle-track coupled dynamics based on the Green＇s function method and the Non-linear Hertz＇s theory. By numerically solving the dynamic equations of linear systems of the vehicle and the track under pulsed excitations, the explicit expressions of the Green＇s functions of the vehicle and track systems were obtained. Subsequently, the characteristics of the Green＇s functions of the vehicle system and the track system were investigated, and the wheel-rail vertical forces as well as the vertical displacements of the wheelset and the rail were calculated under the excitations of track random irregularity and one single harmonic wave, respectively. The analyzed results of the new method were compared with those calculated from traditional methods. Results showed that the Green＇s function of the vehicle mainly consisted of two parts, describing the linear term and the attenuation term. The Green＇s function of the track attenuated as time increased. The initial pulsed excitation-induced rail vibration attenuated to 0 after 0.15 s. The calculated results using the Green＇s function method coincided well with those calculated from tradition methods, supporting the reliability of the new method.