多轴车辆——桥梁耦合振动响应的数值解法

针对复杂的车桥耦合振动问题,基于D’Alembert原理导出了3轴5自由度车辆的运动方程,考虑了桥面不平度和车辆与桥梁之间的协调条件,推导了车辆与桥梁的相互作用力,基于模态综合理论建立了3轴移动车辆—桥梁耦合振动的微分方程组,编制分析程序并运用HHT方法进行了数值求解。通过算例和某3跨刚架桥的动载试验研究结果验证了该方法的正确性和有效性。对于复杂的多跨桥梁的振型函数可以通过有限元方法求解然后通过插值函数得到,该方法不仅适用于单跨简支梁,也适用于多跨连续梁桥车桥耦合振动问题的求解,具有过程简单,编程方便,计算速度快,且精度很高,特别适合于工程实际问题的计算。     

槽型宽翼梁剪滞效应分析的有限段法

针对槽型宽翼梁剪滞效应分析已有方法通常忽略横向剪切变形的影响、计算工作量大、不便于工程应用的局限性,提出一种能准确分析变截面槽型宽翼梁剪滞、剪切双重效应的有限段法。基于最小势能原理,建立了槽型宽翼梁考虑剪滞效应和剪切变形双重影响的平衡控制微分方程及自然边界条件。在由方程得出均布荷载作用下的内力和位移初参数解的基础上,导出了槽型宽翼梁的有限段单元刚度矩阵和等效节点荷载列阵。应用有限段法,结合有机玻璃模型梁试验,分析了槽型宽翼梁竖向位移和应力的横向分布规律。数值算例表明,有限段法计算结果与有机玻璃模型试验实测结果以及ANSYS解符合良好;槽型宽翼梁的剪力滞效应明显;在槽型宽翼梁桥的设计与施工控制中,必须充分考虑剪力滞效应和剪切变形对结构应力和位移的影响。     

一种自锚式悬索桥主缆线形的解析法

在传统的地锚式悬索桥主缆线形方程的基础上，引入了自锚式悬索桥主缆、加劲梁和索塔的变形协调方程，得到一种自锚式悬索桥主缆线形的解析方法：该方法可以在不进行有限元分析的情况下，仅给出自锚式悬索桥的跨度、矢跨比以及主缆、加劲梁和索塔的截面属性，通过求解主缆线形方程和变形协调方程所组成的方程组，就能够求出主缆的初始线形和成桥线形、主缆的无应力长度、索鞍偏移量。该方法简单、准确、高效，已经成功地应用在金华康济桥的施工监控中，建成后主缆的成桥线形与设计线形非常接近，最大误差只有27mm，由于该方法能方便而快速地计算出索鞍的偏移量和主缆线形，对优化自锚式悬索桥边跨与主跨的比例提供了一种高效的算法。     

Dynamic tyre friction models for combined longitudinal and lateral vehicle motion

An extension to the LuGre dynamic friction model from longitudinal to longitudinal/lateral motion is developed in this paper. Application of this model to a tyre yields a pair of partial differential equations that model the tyre-road contact forces and aligning moment. A comparison of the steady-state behaviour of the dynamic model with existing static tyre friction models is presented. This comparison allows one to determine realistic values of the parameters for the new dynamic model. Via the introduction of a set of mean states we reduce the partial differential equations to a lumped model governed by a set of three ordinary differential equations. Such a lumped form describes the aggregate effect of the friction forces and moments and it can be useful for control design and online estimation. A method to incorporate wheel rim rotation is also proposed. The proposed model is evaluated by comparing both its steady-state as well as its dynamic characteristics via numerical simulations. The results of the simulations corroborate steady-state and dynamic/transient tyre characteristics found in the literature.     

缺陷尺寸对纤维布混杂加固界面性能影响的数值分析

针对CFS-GFS混杂加固钢筋混凝土梁的一种新型加固方法,通过建立不同材料本构方程,对界面端部附近胶层存在空鼓及混凝土存在裂缝进行了界面非线性有限元数值分析,分别考虑了3种大小的空鼓及5种高度的裂缝对界面性能的影响。研究结果表明胶层空鼓及混凝土裂缝是引起界面端部处粘胶层剥离及混凝土保护层剥离破坏的主要原因。     

横坡段桥梁双桩结构内力和位移计算

针对横坡段桥梁双桩基础,引入陡坡效应,并对桩侧边坡下滑推力和桩侧岩土体抗力进行合理简化,建立基于前后桩各特征桩段结构和受荷特点的挠曲微分方程。采用幂级数法对方程求解,考虑桩顶和桩端的边界条件及各特征桩段之间内力和位移的连续性条件。通过对某双桩工程实例进行理论和有限元计算和分析,得出该理论方法具有一定的可靠性及设计的合理性。分析结果表明:理论计算和有限元计算的最大相对误差为3.32%,且理论计算的前后桩桩顶水平位移为8.573 mm,有限元计算的前后桩桩顶水平位移为8.867 mm,二者均满足规范要求。     

混凝土斜拉桥主梁的非稳态温度场与应力场分析

按非稳态温度场问题的热平衡控制微分方程和弹性力学平面应变问题的计算理论,应用变分原理给出了温度场和应力场的有限元计算列式。根据结构热分析和热应力分析的单向耦合特点提出了在同一有限元模型上按时间差分顺序耦合求解斜拉桥主梁温度场和应力场问题的方法,编写了计算机程序;并计算分析了一混凝土斜拉桥的主梁截面内温度分布和应力分布,对比了温度实测值,得出了几个重要的结论,对同类桥梁的设计具有实际参考价值。     

Automatic generation of the non-holonomic equations of motion for vehicle stability analysis

The mathematical analysis of vehicle stability has been utilised as an important tool in the design, development, and evaluation of vehicle architectures and stability controls. This paper presents a novel method for automatic generation of the linearised equations of motion for mechanical systems that is well suited to vehicle stability analysis. Unlike conventional methods for generating linearised equations of motion in standard linear second order form, the proposed method allows for the analysis of systems with non-holonomic constraints. In the proposed method, the algebraic constraint equations are eliminated after linearisation and reduction to first order. The described method has been successfully applied to an assortment of classic dynamic problems of varying complexity including the classic rolling coin, the planar truck–trailer, and the bicycle, as well as in more recent problems such as a rotor–stator and a benchmark road vehicle with suspension. This method has also been applied in the design and analysis of a novel three-wheeled narrow tilting vehicle with zero roll-stiffness. An application for determining passively stable configurations using the proposed method together with a genetic search algorithm is detailed. The proposed method and software implementation has been shown to be robust and provides invaluable conceptual insight into the stability of vehicles and mechanical systems.     

Damping Performance of Power Transmission System with Hydraulic Torque Converter

In this work three first-order nonlinear, nonstationary differential equations describing a hydraulic torque converter in a power transmission system are used.

A linear model is obtained on the basis of these equations. This model is verified both theoretically and by an experimental test. On the basis of the calculations the torsional damping was determined. This permitted the damping performance of a power transmission system with a hydraulic torque converter to be defined and established.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

基于模型修正的公路简支板梁桥荷载横向分布系数计算方法

为了使得理论计算的桥梁荷载横向分布系数与试验结果更加吻合，并且降低静载试验成本，在铰接板法基础上，提出一种基于模型修正技术的公路简支板梁桥荷载横向分布系数简化分析方法。该方法建立了一种可以考虑板间接缝剪切变形的简化分析模型，并推导了相应的静力和动力方程。针对简化模型的结构特点，提出了以待测桥梁动力试验测得的自振频率和桥梁跨中振型构造目标函数，以竖向弹簧刚度k、扭转弹簧刚度Ψ以及剪切弹簧刚度k_q为待识别参数的模型修正方法。通过提出的模型修正方法，得到实际状态下桥梁的主要参数，以简化模型的荷载横向分布系数影响线为基础，可计算各板梁的横向分布系数；验证了不考虑板梁间接缝剪切变形时，基于简化模型的横向分布系数分析结果与铰接板梁法相同，从而证明了所提简化模型和分析方法的可靠性。最后以一座桥梁为对象，进行了动力测试，识别了简化模型的物理参数。模型修正之后的模态频率和实测值吻合良好，同时振型之间的MAC（模态保证准则）系数也接近于1，从而表明利用所提的模型修正方法可以有效识别简化模型的物理参数，使理论模型和实际桥梁吻合。     

Derivation and validation of nonlinear governing equations for an analysis of vehicle handling

Nonlinear governing equations used to analyze the handling of a ground vehicle are derived from the Lagrange equations of motion. The derived equations are coded using VBA (Visual Basic for Applications) embedded in Microsoft’s Excel Software and simulated in the time domain using the 4th-order Runge-Kutta method. A total of six degrees of freedom are used in the equations; three of these are the directional translation, lateral translation, and yaw of a platform (unsprung) on the base of an inertial ground coordinate, and the other three are the roll, pitch, and yaw of a body (sprung) by a platform-fixed coordinate. Four driving torques and four wheel angles of all tires are used as input control parameters. A simplified Calspan tire model is adopted for the generalized forces of the equations. This is a combined model that can be used to obtain tractional (or braking) and side forces using the inputs of the directional and side-slip ratios and the vertical force. The VBA code realized in this study is validated by comparisons with trimmed equilibrium results and the test data cited in published papers. The major characteristics of this study are: (1) the coordinate systems of the equations are mixed with the inertial frame and the platform-fixed frame, and, as a result, almost all types of driving conditions with long mileages can be simulated; (2) vertical movement is eliminated due the focus on the handling analysis; (3) the body-yaw degree of freedom is separated from the platform-yaw degree of freedom; and (4) the programming is performed by VBA, which is rarely used in the vehicle dynamics field.     

斜拉桥在列车通过时横向动力响应的分析方法

以横摆和摇头为2个独立的自由度,建立列车轮对的振动微分方程。利用结构分析有限元法,推导非对称箱形截面梁单元的横向弯扭耦合刚度矩阵。讨论车桥系统横向振动微分方程及其求解方法。实例分析结果揭示了桥梁横向动力响应的规律,所讨论的分析方法可以有效地处理约束扭转及偏载问题。     

滚动轮胎瞬态和稳态强迫响应分析

采用移动载荷的概念,分别推导了点力激励的响应及分布力激励的响应列式,计算了胎体上点在点载荷作用下的时间历程。为轮胎滚动模型提供基础。     

步行车辆运动弹性动力学分析

步行车辆在快速运动中,既有大刚体运动又有小弹性位移,且还有不连续的边界约束条件,是一个很复杂的动力学问题。本文用有限元方法建立了该系统的动力学模型,采用分段的直接积分法求解其弹性动力响应。     

特长公路隧道洞口污染物扩散的有限元法模拟

建立了公路隧道洞口处排放污染物输送与扩散所遵循的方程组。针对秦岭终南山特长公路隧道洞口环境特点对方程组进行了简化。采用有限元法,考虑洞口排放源、洞口边界与东线洞口排放及隧道西线洞口进风的影响,对该特长隧道洞口排放形成的垂直和水平二维CO质量浓度分布及通量场进行了数值计算。结果表明:以隧道排口为中心形成了随距离明显递减的CO质量浓度场;隧道西线洞口排放CO对东线洞口的进风空气质量产生明显影响;进一步数值分析发现,在隧道外两洞口之间增加一墙体可有效减小两洞口之间的污染影响。     

异形截面钢筋混凝土偏心拉压构件承载能力分析的电算方法

寻求异形截面钢筋混凝土偏心拉压构件承载能力分析的通用方法是一个难点。该文应用基本假定下统一的几何方程、物理方程和不同形式的平衡方程,采用受压区高度判别大小偏心,并通过数值方法解非线性方程,采取一定方法避免正确解的遗漏和对满足弯矩平衡不满足轴力平衡的假解的过滤,用求解得到的涵盖完整的四个象限的Nu-Mu承载能力相关曲线图,直观地对上下翼缘在偏心拉压等各种工况下的承载能力进行校核,借鉴校核求解过程并按合理途径增加两侧配筋一并解决设计问题,编制的程序为解决异形截面偏心受力钢筋混凝土构件配筋的设计和验算提供了方便实用的工具。     

Modeling and Analysis of Nonlinear Multibody Systems

SUMMARY

The method of multibody systems is introduced for the modeling of nonlinear vehicle systems. The equations of motion and the equations of reaction are found. For the dynamical analysis a classification of nonlinear phenomena is presented using objective and subjective criteria. As an illustrative example the dynamical behaviour of a four-body pendulum is investigated.     

曲线弯梁桥振动理论分析

利用广义坐标法和能量原理推导曲线梁桥的振动控制微分方程,解释曲线梁桥振动理论与直线梁振动理论的异同点,在推导质量矩阵的显式表达式过程中考虑截面扭转中心与截面形心的不一致。随后给出了曲线梁动力分析的有限元方法,并完成了相应电算程序的编制。最后通过实例分析并验证本文所提计算理论和计算方法的正确性。     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.