摘要
现代车辆—线路—桥梁耦合振动分析研究不但需要精细合理的车辆模型,更需要准确反应桥梁(线路)实际工作状态的动力分析模型。更加精细合理、运算效率高的车—线—桥耦合振动模型,应不仅仅停留在单一的竖向分析、横向分析上,车辆纵向振动应该被更合理地考虑,同时要求更加全面地综合考虑整个体系中的各种因素,更系统地分析车桥相互作用的影响,更合理地考虑轮轨接触力和轮轨关系。
论文以武汉天兴州公铁两用大桥和现场试验为背景,系统地研究了精细的车辆—线路—桥梁耦合振动模型,分别建立了轮轨竖向密贴和轮轨法向密贴的车辆—线路—桥梁耦合振动分析的有限元和模态法方程,抛弃了传统车辆纵向以名义运动平动的基本假定,考虑了桥梁的初始构形和弹性变形的影响,分析了车辆的纵向振动,提出了基于实验验证的桥梁基准有限元模型的车辆—线路—桥梁耦合振动思路,并用武汉天兴州公铁两用大桥实测数据进行了验证。
论文的主要研究工作和取得的成果包括：
1.将车辆—桥梁(线路)作为一个整体系统,轮对的侧滚和浮沉两个自由度由钢轨位移确定,采用弹性系统动力学总势能不变值原理及其形成系统矩阵“对号入座”法则,分别基于模态坐标和物理坐标建立了不考虑和考虑轨道的系统运动方程。车辆模型已不再受左、右对称假设的限制,可考虑车辆偏心、轮对高速自旋角动量等因素的影响。
2.由于钢轨和车轮踏面均为空间曲面形状,轮轨实际应该是在接触点公法线方向密贴约束。论文对轮轨竖向密贴约束的使用范围进行了讨论,将车辆—桥梁(线路)作为一个整体系统,建立了基于轮轨法向密贴的车辆—线路—桥梁耦合运动方程,并与轮轨竖向密贴模型进行了比较。
3.车辆荷载的作用下,桥梁结构将发生下挠变形,特别是大跨度柔性桥梁,而且实际桥梁往往设置了一定的预拱度,车辆整体实际是倾斜地沿着桥面运行。本文将车辆的运动分解成整车倾斜地沿着线路运行和车辆相对自身局部系统微幅振动的叠加,从而基于桥梁初始线形及变形后的构形建立了车—桥(线)竖向及空间耦合模型,结合算例进行了分析研究和验证。
4.车辆—线路—桥梁耦合振动的研究一般规定车辆纵向的名义运动,忽略车辆各构件的纵向振动,不涉及到列车驱动力和制动力。本文放弃了对车辆纵向名义运动的假定,建立了考虑纵向振动的车辆—线路—桥梁的空间耦合模型。它不但可以更精确地分析车辆的空间振动行为,还可以研究分析车辆的纵向振动,对桥上刹车、制动等问题进行更合理地分析。
5.车辆—线路—桥梁耦合振动分析研究一般是依据桥梁设计图纸建立有限元模型,这样的桥梁有限元模型往往与实际结构存在一定的差异。若基于实测数据对模型进行修正,可得到反映桥梁真实动力行为的有限元模型,依据此模型可更合理地对桥梁结构进行分析研究。本文以武汉天兴州公铁两用大桥环境振动实验为基础,基于实测数据对桥梁的有限元模型进行修正,得到反映桥梁真实动力特性的基准有限元模型,进行车辆—线路—桥梁空间耦合振动分析,并于试验结果进行了比较和验证。
6.轨道结构一般采用常规有限元建模,往往需要较多的自由度、计算量较大。本文将车辆—线路—桥梁作为一个整体系统,钢轨和桥梁采用区间B样条小波(BSWI)单元离散,建立了车辆—线路—桥梁耦合运动方程,并进行相应的响应计算。
In the present to analyze and study the train-track-bridge dynamic interaction, in addition to the accurate vehicle models, the dynamic FEM models which can describe the actual operational condition of the bridges/track is more significant and necessary. Vertical and transverse vibration, as well as the longitudinal vibration should all be analyzed, but not just the unilateral vertical or transverse vibration in an accurate and effective model of train-track-bridge coupling vibration. Based on it various components of the whole dynamic system should be analyzed comprehensively; the interaction of the vehicle-bridges should be considered systematically; the wheel-rail contact force and the wheel-rail relationship are taken into account reasonably.
With Wuhan Tianxinzhou Bridge (a highway and railway bi-purposed bridge) and its field test as background, An accurate model of train-track-bridge dynamic interaction was study systematically in the present study. The finite element model and the modal method equations of the train-track-bridge coupling vibration with the wheel track closure in vertical direction and in normal direction were established respectively. The traditional basic assumption of nominal moving in traverse was abandoned. The effects of the original configuration and the elastic deformation of the bridge were considered. By analyzing the longitudinal vibration of the vehicle, the novel thought of vehicle-line-bridge coupling vibration based on the of finite element model was proposed. And then the field test data of the Wuhan Tianxinzhou highway and railway bi-purposed Bridge was used for verification. The main contents and achievements of the thesis include:
1. The train, bridge and track are considered as an entire system, and two degrees of freedom of the wheel set, roll and bouncing, are determined by the displacement of the rail. Respectively, based on the modal coordinate and physical coordinates, motion equations for both of the train-bridge system and the train-track-bridge system are established according to the principle of total potential energy with a stationary value in elastic system dynamics and the rule of "set-in-right-position" Then disengaged assumption of right-and-left symmetry, the vehicle model can involve more actual factors, such as the eccentricity of vehicles, the high-speed spin angular momentum of wheel set and so on.
2. As the profiles of rail and wheel tread are special curve, their interaction should be tight constraints on the direction of common normal at contact points. In this thesis, application of the vertical tight constraint is studied, and coupling motion equations of the train-track-bridge system based on normal tight constraints are established, compared with those based on vertical tight constraints.
3. In fact, the train is moving on oblique deck of bridges, especially on that of long-span flexible ones, because of the deformation under vehicle load as well as pre-camber. The motion of vehicle is divided into two components, oblique movement along the track and micro-amplitude vibration relative to itself. Then vertical and special models of the train-track-bridge system are developed respectively based on the original and deformed decks, and verified by experimentations.
4. In tradition analysis of train-track-bridge interaction, longitudinal nominal motion of vehicle was defined first, and the longitudinal vibration was not considered, involving no driving or braking force of train. In this thesis, a model of train-track-bridge spatial dynamic interaction considering longitudinal vibration is established without the presumption of vehicle longitudinal nominal motion. Not only the spatial vibration of train-track-bridge interaction, but also the longitudinal vibration of train and the special dynamic problem such as braking or driving on the bridge, can be analyzed more comprehensively.
5. In previous study of train-track-bridge interaction, the vibration finite element model of bridge established mainly in term of design drawings is usually different from practical states of bridge. A baseline FEM model reflecting the actual dynamic characteristics of bridge structure can be obtained by updating the initial model based on the field measured data. According to this baseline model, the bridge dynamic characteristics can be researched more reasonably. Taking Wuhan Tianxinzhou Bridge and its field test as background, the baseline FEM model reflecting the actual bridge dynamic characteristics is obtained by model updating on the base of the field measured data. Then the numerical results obtained by the train-track-bridge model proposed in this thesis are validated by comparing with field experimental results.
6. Adopting conventional elements to model track structures often leads to considerable degrees of freedom and large amount of calculation. In this study, the vehicle, rail and bridge are taken as a whole system. The rail and bridge are discredited by B-spline wavelet element, while the rails bed between the rail and bridge is simulated by uniform distribution springs and dampers, thus a model of train-track-bridge spatial dynamic interaction is established, and the corresponding dynamic response calculation is carried out.
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