摘要
本文从系统动力学的角度，建立了车-线-桥动力分析理论，并编写了计算程序。通过理论分析与试验对比的方法，对车-线-桥理论进行了验证。围绕轨道不平顺随机激励下的车-桥随机振动问题，提出了一种时变系统随机振动的协方差分析法。最后，考虑桥梁结构参数的随机性，提出了一种考虑桥梁结构参数随机性的车-桥耦合振动的摄动求解方法。分别将车-桥随机振动的协方差分析法和随机摄动法与Monte-Carlo法对比，验证了方法的准确性。本文的主要研究内容如下：
(1)建立了车、线、桥动力分析模型，推导了各分体系动力方程。车辆为多刚体系统，采用D’Alembert原理建立其动力方程；轨道结构采用考虑钢轨、轨枕、道碴自由度的三层点支承模型；采用有限元法建立桥梁动力分析模型。
(2)研究车-线-桥动力分析中的轮轨接触几何、轮轨滚动接触理论。引入新型轮轨关系假设，利用迹线法求解轮轨空间几何，并考虑了左右轮轨不均匀压缩以及轮轨脱离情况。采用Hertz理论分析轮轨法向力。推导了轮轨接触蠕滑率的计算公式。对几种重要的蠕滑率／蠕滑力模型进行了总结和比较。
(3)给出了车-线-桥系统动力分析的显式-隐式混合积分法，并编制了车-线-桥耦合振动计算程序。车辆、轨道系统与桥梁系统的动力特征存在较大的差异，采用显式-隐式混合积分方法求解车-线-桥系统动力方程，可在保证精度的前提下提高计算效率。基于车辆、线路和桥梁各分体系的动力方程、轮轨关系和显式隐式混合积分法，在Visual C++平台上开发了车-线-桥耦合振动的分析程序。
(4)通过空重混编列车作用下混凝土连续梁桥的车-线-桥动力响应分析结果与现场实测结果的比较、秦沈客运专线连续梁桥的车-线-桥动力分析与现场试验结果的比较，初步验证了车-线-桥动力分析理论和计算程序的正确性。
(5)提出了车辆-桥梁随机振动的协方差分析法。由白噪声通过成型滤波器得到满足特定谱函数的轨道不平顺输入；成型滤波器系数由宽频带参数识别得出；给出了滤波器参数的速度变换公式。引入时滞系统频响函数的Pade逼近来反应各车轮下轨道不平顺输入间的时间滞后关系。推导了时变系统随机振动的协方差递推求解方法。将车辆-桥梁耦合随机振动的协方差分析法与Monte Carlo模拟法比较验证了协方差递推法的精度。
(6)提出了列车-桥梁垂向随机振动的协方差分析法。针对列车前后轮对下轨道不平顺激励滞后时间过长的问题，提出了反映列车轮对下激励滞后的累次时滞滤波器。建立了列车-桥梁垂向随机振动状态方程模型。除系统位移方差响应外，还给出了加速度方差响应的递推求解格式，并通过与MC模拟法的比较验证了方法的正确性。
(7)将对均值展开的随机摄动法推广到车-桥时变系统，给出了列车-桥梁随机参数结构瞬态随机响应的求解方法。导出了车-桥随机参数时变系统均值摄动法的数值计算格式。通过与Monte Carlo法的比较验证了方法的正确性。最后，研究了桥梁结构参数的随机性对车-桥系统瞬态随机响应的影响。
From the point of view of system dynamics, the train-track-bridge dynamics analysis theory and computing programs are established. Computing results and in site testing results are compared to validate the train-track-bridge analysis theory. A covariance method for time-variant system is proposed to analyze the vehicle-bridge random vibration excited by random rail irregularities. Finally, a perturbation method is derived to analyze the train-bridge transient stochastic responses due to the randomness of bridge parameters. The proposed covariance method and the perturbation method are validated by comparing with Monte Carlo simulation method. The main research work is as follows:
1. Dynamic analysis models for the train, bridge and track are established. And their dynamic equilibrium equations are derived. The train is treated as multi-body system, and its dynamic equations are derived using the D'Alembert principle. The rail structure is modeled as discrete-supported three-layer system considering the degrees of rail, sleeper and ballast. The bridge dynamic model is derived using the finite element method.
2. The wheel/rail contact geometry and rolling contact theories are discussed. A new type wheel/rail relationship is applied, which takes the difference of wheel/rail compression between right and left rail and wheel/rail separation into accounts. The trace line method is introduced to solve the wheel/rail space contact geometry. The Hertz non-linear contact theory is used to calculate the wheel/rail normal forces. Wheel/rail creepage formulas are derived, and several important creep theory are discussed.
3. An explicit-implicit hybrid dynamic integration method is introduced to calculate the train-track-bridge responses; and a computing program based on this method is developed. Great difference exists between the dynamic characteristics of the train-track and bridge systems; and this hybrid integration method can improve the calculation efficiency while retaining considerable accuracy. Base on the train-track-bridge dynamic equations, wheel/rail relationship and hybrid integration method, analysis program to calculate the train-track-bridge dynamic responses is developed on the Visual C++ platform.
4. Dynamic responses of a continuous beam bridge passed by loaded-empty mixed arranged train and a continuous beam bridge on QinShen Passenger Line passed by high speed train are calculated. The calculation results of train-track-bridge system are compared with in site testing results separately, and the correctness of the train-track-bridge analysis theory is partially validated.
5. A time domain method is proposed for analyzing the vehicle-bridge stochastic vibration. The rail irregularity under a single wheelset is produced by the white noise filtration method. The parameters of the shape filter are identified in a wide frequency range; and train speed transformation formula of the shape filter is derived. The Pade approximation of time-delay system is introduced to reflect time-delays among irregularities under different wheelsets. Then, a covariance recursive method for the stochastic vibration analysis of time-variant system is proposed. Results of the covariance method are compared with the Monte Carlo method, which indicates the high accuracy of the proposed method
6. A time domain method is proposed for analyzing the train-bridge stochastic vibration. A stepwise time-delay system based on the high order Pade approximation is proposed to simulate large time-delay excitations under all wheelsets. The train-bridge vertical stochastic vibration model is established. Covariance method to calculate both the displacement and acceleration stochastic responses of train-bridge system is given. Numerical results of the recursive covariance method are compared with those of Monte Carlo simulation to examine the correctness of the proposed method.
7. Extending the improved perturbation method to train-bridge time-variant system, a method to calculate the transient stochastic responses of train-bridge system with uncertain parameters is proposed. An improved perturbation algorithm is derived to evaluate the transient stochastic response of the train-bridge time-variant system. The correctness of the method is verified by comparing with Monte Carlo method. Finally, the effects of randomness of bridge parameters on the stochastic dynamic responses of train and bridge are discussed.
引文
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