扣件胶垫刚度频变的车辆-轨道耦合时变随机振动扩展辛分析

运用扩展辛数学方法、周期拟稳态求解法与随机振动虚拟激励法，建立了车辆-轨道垂向耦合时变系统的随机振动扩展辛分析模型，高效计算了扣件胶垫频变刚度影响下车辆-轨道耦合时变系统的随机振动频域特征，并与车辆-轨道耦合时不变系统的随机振动频域特征进行了对比。研究发现:1）对于低速地铁线路而言，在现有扣件胶垫低频初始刚度及其刚度频变幅度的变化范围内，时变与时不变系统中车轮及轮下结构垂向随机振动加速度频谱的差异很小，因此地铁线路上应用定点激励模型可满足工程要求；2）在高铁线路上，扣件胶垫刚度的频变幅度越大，车轮及轮下结构垂向随机振动加速度的最高功率峰及其对应主频在时变与时不变系统内的差距也越大，因此在扣件胶垫刚度频变幅度较大的高速线路上采用动点激励模型才能保证较高的运算精度。

THE GENERAL SYMPLECTIC ANALYSIS OF TIME-VARIANT RANDOM VIBRATION OF VEHICLE-TRACK COUPLED SYSTEM WITH FREQUENCY-DEPENDENT STIFFNESS OF RAIL PADS

Combined with a generalized Symplectic method and a periodical pseudo-steady method and a pseudo-excitation method for random vibration, a general Symplectic model for the random vibration of a time-variant vehicle-track coupled system was established. This model was used to calculate the influence of the frequency-dependent stiffness of rail pads on the frequency-domain random vibration of a time-variant vehicle-track coupled system, which was further compared with the frequency-domain random vibration of a time-invariant vehicle-track coupled system. The conclusions show that:as for the low-speed subway, the difference of the vertical frequency-domain random vibrations of both vehicle wheels and the structures under vehicle wheels between in time-variant vehicle-track coupled model and in time-invariant one is small within the variable range of the low-frequency initial stiffness and the frequency-dependent stiffness of existing rail pads. Therefore, the time-invariant vehicle-track coupled model can meet the engineering requirement in subway. In high-speed railway, the greater is the frequency-dependent extent of the stiffness of rail pads, the bigger is the disparity of the highest power peaks and the corresponding dominant frequencies of both vehicle wheels and the structures under vehicle wheels between in time-variant model and in time-invariant one; thus, the time-variant vehicle-track coupled model other than the time-invariant one should be applied for the accurate calculation of the random vibrations of high-speed railway with the highly frequency-dependent stiffness of rail pads.