轨道结构中高频振动特性分析

Mid-and high-frequency vibration characteristics of track structures

通过建立数学模型,分别将钢轨、轨道板和混凝土支承层简化为Euler梁和Timoshenko梁,基于谱单元法推导了板式无砟轨道结构单层梁和三层梁模型的谱单元刚度矩阵和谱元法求解方程。基于该模型,运用Matlab编制了计算程序,仿真分析了无砟轨道结构参数对轨道结构中高频振动和1阶垂向pinned-pinned频率的影响。计算验证了谱单元法在轨道结构的高频振动分析中的有效性和适用性。算例分析结果表明:扣件刚度在200-1000Hz范围对轨道结构振动有显著影响,减小扣件刚度有利于轨道下部结构减振降噪,增加扣件刚度有利于轨道上部结构减振;路基刚度在0-60Hz范围对轨道结构低频振动影响显著,增加路基刚度可降低轨道结构的低频振动;Euler梁模型与Timoshenko梁模型计算结果的差异主要在中高频范围,Timoshenko梁模型在中高频范围适应性更好。

By establishing a mathematical model,and simplifying the rail,slab track and concrete supporting layer to Euler-Bernoulli beam and Timoshenko beam respectively,the spectral element stiffness matrix and spectral element governing equation for the single-layer beam and three-layer beam models of slab track structures are derived based on the spectral element method.Based on the model,the calculation program is compiled by using Matlab,and the influence of the ballastless track structure parameters on mid-and high-frequency vibration and first order vertical pinned-pinned frequency of the track structure is analyzed.The validity and applicability of the spectral element method in mid-and high-frequency vibration analysis of track structures are verified by calculation.The results of example analysis show that the stiffness of the fastener has a significant effect on the vibration of the track structure in frequency range of 200-1000 Hz.Reducing the stiffness of the fastener is good for reducing vibration and noise of the track substructure,whereas increase of fastener stiffness is beneficial to vibration reduction of the track superstructure.The influence of the subgrade stiffness on the vibration of track structure is significant in frequency range of 0-60 Hz.Increasing subgrade stiffness can reduce the low frequency vibration of the track structure.The difference between the Euler-Bernoulli beam model and the Timoshenko beam model is mainly in the middle and high frequency range,and the Timoshenko model has better adaptability in the middle and high frequency range.