基于梁格林函数的有砟轨道高频振动响应特性分析

Analysis of high-frequency vibration response characteristics of ballasted track based on Green’s functions of beam

建立具有周期性离散支撑的有砟轨道模型,以无限长Timoshenko梁的格林函数为基础求解轨道运动方程,得到轨道的频域格林函数和时域格林函数。将频域响应和时域响应相关联,并分别与2.5D有限元法的频域计算结果和有限元法的时域计算结果进行对比。利用梁格林函数研究不同道砟模型对轨道振动响应的影响,以及在移动载荷作用下钢轨高频响应的多普勒效应。研究结果表明:采用梁格林函数可以在避免模态截断限制的条件下实现对轨道响应的快速计算;考虑道砟质量不会影响钢轨的高频响应,而在300 Hz以下的低频响应会有明显变化,且时域响应的衰减速度会减缓;在移动载荷作用下,轨枕跨中钢轨的pinned-pinned共振频率处会出现多普勒效应,其与载荷的移动速度密切相关。

The periodic model of the discretely supported ballasted track was established.The track dynamic equation was solved based on Green's functions of the infinite Timoshenko beam,the frequency-domain and time domain Green's functions of the track were obtained,which associated the frequency-domain response with the time-domain response,and compared the response with the frequency-domain results of the 2.5D finite element method and the time-domain results of the finite element method respectively.Subsequently,the effect of different ballast models on the rail vibration response as well as the Doppler effect of the rail high-frequency response under the moving load were studied through Green's functions of the beam.The results show that using Green's functions of the beam can realize the fast calculation of the rail response at the condition of avoiding any limitation due to the modal truncation.Considering the quality of ballast will not affect the high-frequency response of the rail,but the low-frequency response below 300 Hz would change significantly,and the decay rate of the response in the time domain will slow down.Under the action of the moving load,the Doppler effect appears in the pinned pinned resonance frequency range of the rail at mid span,and the effect is closely related to the moving speed of the load.