基于概率密度演化理论的磁浮列车−轨道梁耦合系统随机动力分析

Stochastic vibration analysis of maglev vehicle-guideway coupling system based on PDEM

为研究磁浮列车引起的轨道梁随机振动问题,建立磁浮车辆-控制器-轨道梁耦合系统时变随机动力分析模型,运用数论选点法(NTM)选取N-维代表性点集和随机谐和函数法(SHF)生成随机轨道不平顺时域样本,进而将概率密度演化理论(PDEM)引入磁浮动力分析系统,采用Newmark-β时程积分法和带TVD(total variation diminishing)格式的双边差分法求解概率密度函数、均值和标准差。以常导(EMS)磁浮列车通过三跨连续型轨道梁为例,基于MATLAB平台自主开发程序,计算车辆子系统和轨道梁子系统的随机动力响应及概率密度函数,采用Monte Carlo法(MCM)和文献计算结果验证本文模型的计算效率和精度,并对行车速度和支座刚度对系统随机动力响应的影响规律进行分析。研究结果表明:基于概率密度演化理论的磁浮系统随机动力分析模型具有很高的计算效率和精度,与Monte Carlo法相比,求解效率提高了1~2个数量级;在相同随机轨道不平顺激励下,轨道梁中跨跨中加速度、首车车体加速度、轨道梁中跨跨中挠度的概率密度曲线规则程度依次减小;系统随机响应随车速增大而增大,但并非呈线性增大;车辆和轨道梁动力响应均值随支座刚度增加而减小并逐渐趋于稳定;当采用较柔的支座时,响应将被放大。

To study the random vibration of guideway caused by high-speed maglev vehicle,a stochastic vibration model of maglev vehicle-controller-guideway coupled system was proposed.The number theory method(NTM)was employed to select the N-dimension representative point sets and the stochastic harmonic functions(SHF)was utilized to generate the random track irregularity samples,and the general probability density evolution method(PDEM)was adopted to analyze the dynamic responses of the maglev system.The Newmark-βintegral method and the double-side finite deference method with TVD(total variation diminishing)scheme were adopted to calculate the probability density function,mean value and standard deviation.Taking the electromagnetic suspension vehicle passing through a continuous guideway as an example,firstly,the random dynamic responses and probability density function of vehicles and guideway were calculated.Meanwhile,the Monte Carlo method(MCM)and the results in literature were used to verify the calculation efficiency and accuracy of the proposed method.Finally,the influence of the vehicle running speed and the bearing support stiffness on random dynamic responses was analyzed and discussed.The results show that the model based on PDEM is more accurate and efficient than MCM with calculation efficiency increasing by 1-2 order of magnitudes.With the excitation of random irregularity,the regularity degree of the contour of probability density function from small to large is midspan acceleration of guideway,the first car acceleration and the mid-span deflection,respectively.The stochastic dynamic response of vehicle-bridge system tends to increase with the increase of the vehicle speed,but does not increase in linear.The mean value of dynamic responses of vehicle and guideway decreases with the increase of bearing stiffness and tends to be stable gradually,and the vibration will be amplified when the flexible supports are used.