轨道结构随机场模型与车辆-轨道耦合随机动力分析

将轨道结构视为一个参数随机系统,提出并建立了轨道结构的随机场模型.利用车辆-轨道耦合动力学的基本方法,将轨道系统有限单元模型与多刚体车辆模型相结合,建立了考虑铁路线路参数空-时随机变化的车辆-轨道动力计算模型.算例表明:所提出的方法较为可靠且高效;线路参数随机性对车辆-轨道系统的动力响应有明显的影响,随线路参数离散程度的增加,可能造成行车不安全、轨道损伤加剧等一些问题.     

半车车辆-道路耦合动力分析模型的研究与应用

在不平整路面上行驶的车辆会产生道路与车辆的耦合振动.为简化分析,先将车辆和道路视为两个子系统,然后再耦合为一个整体系统.车辆采用1/2车辆4自由度模型,道路采用弹性多层体系有限元模型,通过轮胎与路面的位移相容条件,建立车辆-道路整体耦合动力分析模型,推导出了系统的动力平衡方程组,并探讨了方程组的解耦方法,提出了反映车辆运行品质和道路设计参数的理论计算指标,为车-路耦合动力分析的深入研究,以及系统研究道路结构设计参数与车辆运行品质的相互关系提供理论基础和求解依据.此外,通过解耦和编程分析,还对沥青路面和水泥混凝土路面两种典型路面结构的运行品质指标进行了分析和评判,以期为不同路面结构设计和分析提供参考.     

随机激励下四自由度车辆-道路耦合系统动力分析

采用四自由度车辆模型,以 Gauss平稳随机过程模拟路面的不平整度,编制程序得到不同路面等级下的不平整度序列;并将车辆和道路看作一个相互作用的整体系统,建立了车辆 道路耦合系统的动力平衡方程.在对车辆施加随机激励时,为了简化分析过程,避开以往研究中使用随机振动理论求解动轮胎力的复杂性,将得到的路面不平整度序列,直接以向量的形式输入到所建立的动力平衡方程中.基于增量形式的Newmark-β法开发了一个MATLAB程序对该方程进行求解.并对所提出的理论模型进行了试验验证,证明了模型的可靠性.随后,通过一个实例,分析了车速变化、路面等级变化对车辆动荷载系数和车体垂向加速度的影响.最后,对不同路基刚度对车辆振动特性的影响规律进行了探讨.     

高维同宿环扭曲分支与稳定性

利用沿同宿环的线性变分方程的线性独立解作为在同宿环的小管状邻域内的局部坐标系来建立Poincaré映射,研究了高维系统扭曲同宿环的分支问题．在非共振条件和共振条件下,获得了1-同宿环、 1-周期轨道、 2-同宿环、 2-周期轨道和两重2-同期轨道的存在性、 存在个数和存在区域．给出了相关的分支曲面的近似表示．同时,研究了高维系统同宿环和平面系统非扭曲同宿环的稳定性．     

地基-结构相互作用系统的时域参数识别

提出地基-结构相互作用系统的时域参数识别方法．在建立地基-结构相互作用的计算模式和运动方程的基础上,运用扩展的卡尔曼滤波技术,将相互作用系统中的参数作为增加的状态变量,建立了该系统的时域参数识别方法．并依据大型振动台条件下的层状地基-贮仓结构相互作用系统的模型试验数据,实施了地基-结构相互作用系统时域参数识别的全过程．计算结果表明,该方法产生良好的参数估计．     

饱和地基上弹性基础的竖向振动特性研究

采用解析的方法研究了饱和地基上受一简谐竖向荷载作用下弹性基础的动力响应．在分析中,首先利用积分变换技术获得了饱和介质基本控制方程的变换解,然后基于基础-半空间完全放松接触、半空间表面完全透水或不透水的假设,建立了该动力混合边值问题的对偶积分方程,并把该对偶积分方程进一步化为易于数值求解的第二类Fredholm积分方程A·D2文末数值算例给出了动力柔度系数、位移和孔隙水压力随振动频域和土-基础体系物理力学参数特性的变化曲线．结果表明:饱和地基上弹性基础的动力响应完全不同于饱和地基上刚性圆板的动力响应．所用方法可用于研究波的传播、土-结构动力相互作用等许多问题．     

车辆-轨道垂向耦合系统求解过程的改进算法

考虑到轨道结构长度随系统响应持时的增加而增长，提出了一种改进的车辆 轨道垂向耦合系统的动力响应求解算法.该算法事先选定某一定长度的轨道结构，并获得该轨道结构的质量矩阵、阻尼矩阵和刚度矩阵；通过在求解过程中不断地对车辆子系统定位，判断是否需要对车辆子系统的位置和轨道结构的响应矩阵进行调整，以此来达到仅增加系统响应持时而不增加轨道结构长度的目的.算例表明:该改进加快算法是精确、高效的，不仅可以真实地模拟车辆在轨道上的前进运行状态，而且可以保证轨道子系统的轨道单元数量不随系统响应持时的增加而增长，这为快速求解车辆 轨道垂向耦合系统提供了一种有效的计算方法.     

整函数空间A_(H-Ω)中的可除性问题

本文给出了一个解决整函数空ＡＨ-Ω中可除性问题的系统方法．利用次调和函数和加权函数系以及ＡH-Ω空间中函数的Ｐｈｒａｇｍｅｎ－Ｌｉｎｄｅ１ｏｆ性质，刻划了可除空间中函数和加权系的特性，并给出了若干等价的判别条件．     

车桥系统的耦合振动

通过用正弦波形模拟桥面的不平和考虑移动车辆-桥梁间的相互作用,在Euler-Bernoulli梁理论的基础上建立了一种车桥系统的耦合振动模型．利用模态分析法和Runge-Kutta法对模型进行数值求解,获得了车桥系统耦合振动的动态响应和共振曲线．发现车桥耦合振动的共振曲线中存在两个共振区域,一个反映主共振而另一个反映次共振．讨论了桥面不平、桥梁振型和车辆间的相互作用对系统振动的影响．数值结果表明,这些参数对系统振动的影响很大,桥面不平和振型对车桥系统耦合振动的影响不能忽略,设计车速应该远离临界车速．     

一类含有参数和有理奇性哈密顿系统的同宿与异宿轨道

研究一类含有两个参数和有理奇性平面哈密顿系统的同宿与异宿轨道,该问题来源于一个关于聚合物流体剪切流动特性的研究．借助常微定性理论和不变流形分析的方法,文中给出了系统存在同宿与异宿轨道的条件,并通过数值计算检验了所得理论结果。     

A stochastic dynamic model of train-track-bridge coupled system based on probability density evolution method

An innovative stochastic dynamic model of a 3D train-track-bridge coupled system (TTBS) with refined wheel/rail interaction is established for a high-speed railway based on the random theory of probability density evolution method (PDEM). The multi-coupling effect of excitations can be simultaneously input into the new model, e.g. random track irregularity, random vehicle loads, stochastic system parameters, et al. Moreover, a new approach, named “Number theoretic method of multi-target probability functions” (NTM-mp), is developed to obtain the discrete point sets of multidimensional random parameters in hypercube space, aims to solve the point design of system uncertainty. The stochastic harmonic function (SHF) is applied to generate representative random track irregularity samples. The results of TTBS got by PDEM are verified with several typical case studies for its efficiency and reliability, which are the deterministic results in the representative publication, the Monte Carlo method (MCM) results, and the field testing results on the high-speed railway. At last, a typical case study of TTBS on a high-speed railway is presented for numerical analysis. Discussions and significant conclusions on the random dynamic responses are presented.     

A novel dynamics model for railway ballastless track with medium-thick slabs

Motivated by the requirements for elaborated slab ballastless track dynamics analysis in practical engineering application, a novel dynamic model for the railway ballastless tracks with medium-thick slabs is proposed in this work based on the Reissner–Mindlin plate theory, and it is implemented into the coupled dynamics analysis of a vehicle and the ballastless track. First, an efficient and easily programmable computational algorithm is adopted to solve the transverse deflection of the Reissner–Mindlin plate, in which the displacements and shear strains are chosen as the independent variables and subsequently constructed by spline functions, resulting in no shear-locking effect. The involved partial differential equations are transformed into ordinary ones by using the energy variation principle. Further, a mathematical model for the ballastless track dynamics analysis is established, which can consider the effects of the shear deformation and moment of inertia involved in the medium-thick track slab. Experimental verification and comparative analysis with other models demonstrate the accuracy and efficiency of the proposed model. Finally, a spatially coupled dynamics model of a vehicle and the ballastless track is developed, and it is efficiently solved by using the hybrid explicit-implicit time integration method. Compared with the widely used modelling the track slab by elastic thin plate, the reliability and advantages of the proposed vehicle-slab track coupled dynamics model are demonstrated.     

Design of a coordinated adaptive backstepping tracking control for nonlinear uncertain active suspension system

This paper presents a novel adaptive backstepping tracking control for nonlinear uncertain active suspension system, which can achieve the coordinated control over the sprung-mass acceleration and suspension dynamic displacement for nonlinear uncertain active suspension system based on a developing model-reference system. First, according to adaptive backstepping control principle, this model-reference system is designed with purpose of providing the ideal reference trajectories for the sprung-mass displacement and vertical velocity, respectively. Then, the design of a coordinated adaptive backstepping tracking controller is conducted to make the control plant accurately track the prescribed performances of the model-reference system by virtue of the backstepping technique and Lyapunov stability theory, in which a virtual controller with online parameter regulation rules is designed and implemented to guarantee the stability of vehicle body. Finally, a numerical example is provided to verify the effectiveness of our designed adaptive backstepping tracking controller under various operating scenarios.     

A probabilistic model for track random irregularities in vehicle/track coupled dynamics

Track irregularities generally viewed as weak stationary random processes are perhaps the most important excitations to the vehicle/track coupled system. To better clarify the random vibration characteristics and probabilistic relationships between track random irregularities and dynamic behaviors of vehicle/track systems, it is a necessity to consider the full properties of track irregularities on amplitude, frequency and probability in vehicle/track interactions. The purpose of this paper is to develop a probabilistic model to select representative and realistic track irregularity sets from numerous data with higher efficiency and accuracy. To establish the vehicle/track interaction model, the finite element method and vehicle/track coupled dynamics are adopted and effectively combined, which can be used to reveal the interaction mechanisms between the moving vehicles and the guiding tracks. Moreover, the probabilistic transmission relationships between track irregularities and system responses are addressed by introducing a probability density evolution method. Through detailed comparisons with the experimental measurements and other advanced models, this proposed model is proved to be fairly effective and highly efficient.     

Study on numerical simulation methods of the railway vehicle-track dynamic interaction

A very efficient numerical simulation method of the railway vehicle–track dynamic interaction is described. When a vehicle runs at high speed on the railway track, contact forces between a wheel and a rail vary dynamically due to the profile irregularities existing on the surface of the rail. A large variation of contact forces causes undesired deteriorations of a track and its substructures. Therefore these dynamic contact forces are of main concern of the railway engineers. However it is very difficult to measure such dynamic contact forces directly. So it is important to develop an appropriate numerical simulation model and identify structural factors having a large influence on the variation of contact forces. When a contact force is expressed by the linearized Hertzian contact spring model, the equation of motions of the system is expressed as a second–order linear time–variant differential equation which has a time–dependent stiffness coefficient. Applying a well–known Newmark direct integration method, a numerical simulation is reduced to solving iteratively a time–variant, large–scale sparse, symmetric positive–definite linear system. In this study, by defining a special vector named a contact point one, it is shown that this time–variant stiffness coefficient can be expressed simply as a product of the contact point vector and its transpose and so the Sherman–Morrison–Woodbury formula applied for updating the inverse of the coefficient matrix. As a result, the execution of numerical simulation can be carried out very efficiently. A comparison of the computational time is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The steady vibrations and resistance of a railway track to the uniform motion of an unbalanced wheel

A model of a railway track, in the form of an infinite Timoshenko beam resting on equally spaced massive visco-elastic supports, is considered. Steady vertical vibrations of the track due to a harmonic force moving along it at a constant velocity are investigated. The vertical displacement of the track is represented in a moving system of coordinates by a generalized Fourier series. The steady vertical vibrations of a massive rigid wheel rolling along the track at a constant velocity and loaded by a vertical harmonic force are investigated. The track-wheel interaction force is expressed as a generalized Fourier series whose coefficients are determined using an equality relating the vertical displacements of the wheel and the track. Vibrations of the wheel due to centrifugal force and periodic changes in the track parameters are considered. Parametric vibrations of a wheel moving at a constant velocity under a static load due to periodic variation in the stiffness of the track are investigated. The force with which the track resists the uniform motion of an unbalanced wheel is computed.     

Fuzzy multi-objective optimization of passive suspension parameters

The paper proposed a systematic and effective optimization process to optimize a 3-D vehicle suspension dynamic model with eight DOF, including seat vertical motion, suspension vertical, pitching and rolling motions and wheels vertical motions using fuzzy optimization, to attain the best compromise between ride comfort and vehicle-generated road damage. The results show a substantial improvement in the vertical ride quality is obtained while keeping the suspension deflections within their allowable clearance when the vehicle moves at a constant velocity v = 20m/s, and the comfort performance of a suspension seat can be considerably enhanced.     

Track geometry defect rectification based on track deterioration modelling and derailment risk assessment

Analysing track geometry defects is critical for safe and effective railway transportation. Rectifying the appropriate number, types and combinations of geo-defects can effectively reduce the probability of derailments. In this paper, we propose an analytical framework to assist geo-defect rectification decision making. Our major contributions lie in formulating and integrating the following three data-driven models: (1) A track deterioration model to capture the degradation process of different types of geo-defects; (2) A survival model to assess the dynamic derailment risk as a function of track defect and traffic conditions; (3) An optimization model to plan track rectification activities with two different objectives: a cost-based formulation (CF) and a risk-based formulation (RF). We apply these approaches to solve the optimal rectification planning problem for a real-world railway application. We show that the proposed formulations are efficient as well as effective, as compared with existing strategies currently in practice.