高速列车-轨道-路基耦合垂向振动特性分析

随着高速铁路的发展,列车运行速度和列车载重的不断提高,轨道结构承受的动载荷不断增大,其反复作用的结果必将导致轨道结构部件疲劳破坏更加突出,可靠性下降,并加速残余累积变形;反过来轨道结构部件的破坏,影响列车行驶的安全性和舒适性.因此,列车-轨道-路基耦合系统动力学问题越来越受到学术界的关注.采用统一模型法,建立车辆、钢轨、轨枕、道床和路基为一体的二系垂向耦合动力分析模型,利用新型显式积分法对耦合系统运动方程进行数值积分计算,分析列车速度、轨枕间距、轨道不平顺及列车重量对列车运行的品质、动位移以及轨道结构振动的影响规律.对车辆运行速度的控制以及对轨道结构设计、施工和养护提供有用的参考.     

钢轨横向不均匀支撑刚度对钢轨波磨的影响

建立了钢轨波浪形磨损计算模型，模型中考虑车辆轨道垂向横向耦合动力学行为、轮轨三 维滚动接触力学行为和轮轨材料摩擦磨损的循环相互作用关系. 发展了相应的计算程序，并 用1: 1试验装置验证了理论模型. 详细分析了实际线路上由轨枕离散支撑导致的钢轨横向不均匀刚度和不同行车速度对曲线钢轨接触表面不均匀磨损的影响. 通过数值分析可知： (1)列车通过曲线钢轨时，轨枕离散支撑导致的钢轨横向不均匀刚度易引发曲线钢轨波磨的形 成和发展；(2)这类钢轨波磨具有与轨枕间距几乎相等的波长和28~35mm的短波长，这个短波长不均匀磨损主要是由轮轨高频接触振动引起；(3)同一个转向 架4个车轮作用下形成的钢轨波磨最大深度波谷的分布是不同的；(4) 改变过车速度不能有效地抑制轨枕离散支撑导致的钢轨波磨形成和发展速度.     

车-轨-桥耦合动力系统影响参数分析

为了考虑高速列车、板式无砟轨道和桥梁相互作用的特点,需将列车模拟为质量-弹簧-阻尼多刚体相互约束的系统,通过列车车轮与钢轨的接触关系,建立车-轨-桥耦合系统的运动方程。重点分析了双线列车以不同工况通过高速铁路桥梁时,列车行驶状态(速度和加速度)、列车悬挂系数和钢轨-轨道-桥梁连接参数分别对车-轨-桥耦合系统的动力学性能影响。结果表明,(1)列车的加速度和速度的变化对耦合系统有不同程度的影响,随着列车行驶速度与加速度在一定范围内增加,车体自身结构的位移振动响应逐渐减小,而钢轨和桥梁结构的位移振动响应则不断增加;(2)列车悬挂参数的改变对列车自身结构影响较大,而对钢轨和桥梁结构影响很小;(3)车体一系刚度系数增大会引起列车系统结构振动响应变大,但车体二系刚度系数的增加却抑制了车体结构的振动响应;(4)除了钢轨的最大加速度随着连续刚度系数增加呈线性递减外,列车、钢轨和桥梁的振动响应不易受钢轨与桥梁间连接参数的影响。     

高速移动荷载下黏弹性半空间体的动力响应

分别以移动荷载和黏弹性半空间体模拟运动列车荷载和地基,分析了地基在运动列车作用下的动力响应.首先采用Green函数法求解黏弹性半空间体在各种移动荷载模式作用下的动力响应的解析解,包括恒常和简谐移动点源、线源和面源荷载.然后采用IFFT算法和自适应数值积分算法计算解析解中的二维积分,得到了包括低音速、跨音速和超音速移动荷载作用下位移的数值结果.最后分析了速度对位移的分布和最大值的影响,发现当速度大于Rayleigh波速时,位移发生显著变化.     

移动简谐力作用下三维多孔饱和半空间的动力问题

研究了移动荷载作用下多孔饱和地基的动力问题.应用Fourier变换求解该问题的控制偏微分方程,考虑了荷载的移动速度及振动频率对多孔饱和地基动力响应的影响,重点研究了移动速度达地基表面波速时多孔饱和半空间的振动问题(马赫效应),并与相应的弹性介质的解答进行了比较.结果显示当移动速度与多孔饱和半空间的表面波速相近时,地基会产生很大的振动;当移动速度大于表面波速时,多孔饱和半空间的动力响应与弹性半空间的动力响应有较大的差别.     

纵向力作用下无缝线路动态特性有限元分析

本文通过建立无缝线路有限元动力分析模型,研究了钢轨自振频率和温度力之间的关系.该动力模型包括钢轨模型,钢轨扣件模型,轨枕模型,考虑了钢轨断面特性,钢轨磨耗,轨下刚度以及扣件的弹性刚度和扭转刚度等因素对动力模型计算的影响.分别分析了钢轨磨耗,轨枕支承间距,扣件刚度,钢轨类型以及轨下刚度等参数改变的情况下,钢轨纵向力变化对钢轨振动特性的影响.对部分的计算数据与实际试验测得的数据进行比较分析后,发现通过有限元方法所建立分析模型的计算结果与现场测试结果对比有较好的吻合,采用所建立的计算模型可以更准确地分析无缝线路轨道结构中钢轨纵向力与振动特性的内在联系.     

移动简谐荷载作用下轨道结构动态响应研究

研究了移动简谐荷载作用下轨道结构的动态响应特性,首先,将轨道结构简化为连续离散点支撑的弹性Euler梁模型,并建立了移动荷载作用下轨道系统动力学微分方程,基于无限周期结构在频域内的性质和叠加原理,推导出了移动简谐荷载作用下轨道结构上任意点的动态响应解析表达式;然后,数值分析了激励频率、扣件刚度、扣件阻尼对轨道结构动态响应的影响。研究结果表明:钢轨动态响应共振峰出现在荷载激励频率附近;随着激励频率的增大,钢轨动态响应峰值向高频方向移动;在高频段内,钢轨动态响应随着扣件刚度的增大而增大;扣件阻尼对系统的共振峰值及峰值带宽无显著影响,但在高频段内扣件阻尼具有明显抑制振动的作用,通过增大阻尼可以有效控制轨道的高频振动。     

矩形移动荷载作用下饱和-非饱和土双层地基的动力响应分析

考虑地基为饱和-非饱和土双层半空间,利用连续介质力学和多相孔隙介质理论,构建双层地基的统一动力控制方程并进行耦合求解。利用Dirac-delta函数和Heaviside阶跃函数将矩形移动荷载作用描述为时间和空间坐标的解析函数,将荷载函数代入地基动力控制方程,采用三重Fourier变换以及降阶法进行求解,并对推导结果进行退化验证及对饱和-非饱和土双层地基的动力响应进行分析。研究表明,当荷载移动速度小于瑞利波速时,竖向振动峰值很小,振幅随速度的增大发生小幅增涨,但当荷载速度达到瑞利波速时,竖向振动发生激增;随着速度进一步增大,竖向位移多次出现峰点。非饱和土的饱和度及土层厚度也对地基振幅存在显著影响。     

高速铁路碎石道砟振动的离散元模拟

道砟振动对其磨损、破碎和道床累积变形有显著影响,为揭示高速车辆移动荷载作用下道砟动态响应特性,建立有砟道床离散元模型,开展车辆-轨道耦合动力学计算得到离散元模型输入荷载,模拟分析高速车辆以不同速度通过时有砟道床的振动响应,并与车辆-轨道耦合动力学计算结果进行对比分析。结果表明,轨枕、道砟和道床块振动位移波形相似,位移幅值沿道床深度方向减小,道床块振动位移与轨枕底面以下0.3m处道砟的振动位移相当;轨枕、道床块振动速度与加速度随行车速度提高而增大;受道砟颗粒间复杂相互作用的影响,道砟振动加速度会出现突变。道床离散元模型能合理反映道砟颗粒的振动响应特性,道床块模型体现了道床层在有砟轨道结构中的动力传递与减振特性,两种道床模型的计算结果具有一定的相似性。     

带支撑黏弹性阻尼器框架减震性能分析

对带有支撑黏弹性阻尼器耗能框架结构振动方程进行傅里叶变换,求解该振动方程的频域解,再通过傅里叶逆变换得出该方程的时域解,由此研究了阻尼器的支撑系数ψ、松弛时间系数η对结构地震响应的影响,分析了带支撑黏弹性阻尼器在结构各楼层均匀布置时结构的地震作用及结构各振型的底部剪力。结果表明:支撑系数ψ超过一定数值时,阻尼器支撑对结构的地震反应影响很小;框架结构中带支撑的黏弹性阻尼器宜合理控制松弛时间系数η,使其不大于0.5。     

Response of railway track system on poroelastic half-space soil medium subjected to a moving train load

Based on the dynamic poroelastic theory of Biot, dynamic responses of a track system and poroelastic half-space soil medium subjected to moving train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.     

Effects of the dynamic wheel–rail interaction on the ground vibration generated by a moving train

Based on Biot’s fully dynamic poroelastic theory, the dynamic responses of the poroelastic half-space soil medium due to quasi-static and dynamic loads from a moving train are investigated semi-analytically. The dynamic loads are assumed to be generated from the rail surface irregularities. The vehicle dynamics model is used to simulate the axle loads (quasi-static loads) and the dynamic loads from a moving train. The compatibility of the displacements at wheel–rail contact points couple the vehicle and the track–ground subsystem, and yield equations for the dynamic wheel–rail loads. A linearized Hertzian contact spring between the wheel and rail is introduced to calculate the dynamic loads. Using the Fourier transform, the governing equations for the poroelastic half-space are then solved in the frequency–wavenumber domain. The time domain responses are evaluated by the fast inverse Fourier transform. Numerical results show that the dynamic loads can make important contribution to dynamic response of the poroelastic half-space for different train speed, and the dynamically induced responses lie in a higher frequency range. The ground vibrations caused by the moving train can be intensified as the primary suspension stiffness of the vehicle increases.     

Periodically supported beam on a visco-elastic layer as a model for dynamic analysis of a high-speed railway track

This paper presents a theoretical study of the steady state dynamic response of a railway track to a moving train. The model for the railway track consists of two beams on periodically positioned supports that are mounted on a visco-elastic 3D layer. The beams, supports, and layer are employed to model the rails, sleepers and soil, respectively. The axle loading of the train is modeled by point loads that move on the beams. A method is presented that allows to obtain an expression for the steady-state deflection of the rails in a closed form. On the basis of this expression, the vertical deflection of the rails and its dependence on the velocity of the train is analyzed. Critical velocities of the train are determined and the effect of the material damping in the sub-soil and in the pads on the track response at these critical velocities is studied. The effect of the periodic inhomogeneity of the track introduced by the sleepers is studied by comparing the dynamic response of the model at hand to that of a homogenized model, in which the supports are assumed to be not discrete but uniformly distributed along the track. It is shown that the vertical deflection of the rails predicted by these models resemble almost perfectly. The elastic drag experienced by a high-speed train due to excitation of track vibrations is studied. Considering a French TGV as an example, this drag is calculated using both the inhomogeneous and homogenized models of the track and then compared to the rolling and aerodynamic drag.     

高速列车引起的地基振动半解析解

随着列车速度的提高,地基振动的反应越来越大。根据有限元理论、轨道动力学及地基土振动Green函数,建立了轨道-无限地基土相互作用理论分析模型。为了组装系统的动力方程,通过引入静态自由度凝聚模式来消除梁存在转动自由度。借助文献[12]的柔度矩阵定义并通过Hankel变换获得了系统的刚度矩阵,进而采用Newmark法求出了系统动力反应。最后,以瑞典X2000高速旅客列车为对象进行仿真,通过与试验结果的比较来说明本文方法的可行性。     

Interaction of railway vehicles with track in cross-winds

This paper presents a framework for simulating railway vehicle and track interaction in cross-wind. Each 4-axle vehicle in a train is modeled by a 27-degree-of-freedom dynamic system. Two parallel rails of a track are modeled as two continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The vehicle subsystem and the track subsystem are coupled through contacts between wheels and rails based on contact theory. Vertical and lateral rail irregularities simulated using an inverse Fourier transform are also taken into consideration. The simulation of steady and unsteady aerodynamic forces on a moving railway vehicle in cross-wind is then discussed in the time domain. The Hilber–Hughes–Taylor α-method is employed to solve the nonlinear equations of motion of coupled vehicle and track systems in cross-wind. The proposed framework is finally applied to a railway vehicle running on a straight track substructure in cross-wind. The safety and comfort performance of the moving vehicle in cross-wind are discussed. The results demonstrate that the proposed framework and the associated computer program can be used to investigate interaction problems of railway vehicles with track in cross-wind.     

Frequency– and Time-domain BEM Analysis of Rigid Track on a Half-Space with Vibration Barriers

The rapid development of high-speed trains like the TGV or the ICE in recent years results in high dynamic loads causing vibrations which propagate from the train-track structure into the ground and further into nearby buildings. In this context it is important to develop rigid tracks with improved dynamic behaviour and to investigate possible means of vibration reduction. The boundary element method in frequency and time domain is used to simulate train-track structures subjected to dynamic loading and the reduction of vibrations which for instance can be achieved via a trench running parallel to the rigid track. In this context the non-causality error, which arises when the time-domain BEM algorithm is applied to mathematically concave domains, is discussed and the substructure method is proposed as a solution to this problem. A two-layered cylindrical elastic structure on a half-space with a trench is added as an example of a possible application.     

考虑地面效应的高速列车远场气动噪声计算方法研究

为研究高速列车远场气动噪声的计算方法,根据高速列车近地面运行的实际情况,利用半自由空间的Green函数求解FW-H方程;建立考虑地面效应时的远场声学积分公式,并研究地面效应对高速列车远场气动噪声的影响.研究表明,由于存在地面效应,原来的自由声场变成了相当于真实列车声场与镜像列车声场的叠加,并且作用在镜像列车上的力源和法向运动速度与真实列车上的相同.当列车运动速度为350 km/h时,不考虑地面效应时,远场测点的等效连续A计权声压级的最大值为90.76 dB;考虑地面效应之后,远场测点的等效连续A计权声压级的最大值为94.72 dB.     

Propagation of perturbances generated in classic track, and track with Y-type sleepers

Railway track with classic and Y-shaped sleepers or slab track is composed of two rails that are assumed to be infinitely long and joined with sleepers by viscoelastic pads. Numerous assumptions are used in railway-track modelling, leading to different simplifications. The two-dimensional periodic model of track consists of two parallel infinite Timoshenko beams (rails) coupled with equally spaced sleepers on a viscoelastic foundation. Nowadays the interest of engineers is focused on slab track and track with Y-shaped sleepers. The fundamental qualitative difference between the track with classic and Y-shaped sleepers is related to local longitudinal symmetric or antisymmetric features of the railway track. The sleeper spacing influences the periodicity of the foundation elasticity coefficient, mass density (rotational inertia) and the effective shear rigidity. Track with classic concrete sleepers is affected much more by rotational inertia and shear deflections than track with Y-shaped sleepers. The increase of the elastic-wave velocity in track with Y-shaped sleepers and more uniform load distribution will be proved by analysis and simulation. The analytical and numerical analyses allows us to evaluate the track properties in a range of moderate and high train speeds. However, the correct approach is not simple, since the structure of the track interacts with the wheels, wheelsets and vehicles, which constitute complex inertial loads. We note that the growth of amplitude in selected velocity ranges depends strongly on the track type.     

高速列车服役模拟建模与计算方法研究

高速铁路的出现, 使得轮轨交通技术达到更高的层次.速度提升不仅对列车的牵引动力与动力学性能提出更高要求. 而且,列车与线路、气流等运行环境的耦合作用加剧,并直接影响到了列车的运行品质和安全性. 在高速列车发展初期,研究关注的是如何保证高速列车能高速、平稳和安全运行. 随着运行速度的提高,系统间耦合加强, 服役模拟也越来越受到重视. 而今天,高速列车的服役模拟、健康管理与故障预警成为研究热点,掌握系统全局动态行为、了解微观局部振动是车辆系统动力学研究的方向.本文以高速列车服役模拟为需求, 提出基于循环变量法的长编组列车建模与计算方法,实现任意列车编组的仿真, 得到不同编组位置车辆的服役状态;提出滑移窗口的轨道建模与车线耦合计算方法,得到列车在任意长线路上运行的服役状态; 提出基于时变参数的长期服役计算方法,实现列车在不同服役状态与服役时间的服役模拟. 因此, 基于本文提出的模拟方法,能够实现列车在不同寿命阶段的服役模拟, 而且还可以应用于高速磁浮列车,甚至未来超高速真空管道磁浮列车.