【作者】 徐文涛；

【导师】 林家浩； 张亚辉；

【作者基本信息】 大连理工大学 ， 计算力学， 2010， 博士

【摘要】 随着国民经济的迅速发展,铁路和公路交通日渐繁忙；而行车速度不断提高,车辆负荷逐渐增大,使得交通车辆与支承(道路或桥梁)结构动力相互作用越来越受到重视。由于移动车辆对道路／桥梁结构的动力冲击作用使结构工作状态和使用寿命发生改变；而且运行车辆的平顺性和安全性又是评价结构设计参数合理与否的重要考虑因素。因此车辆-道路／桥梁相互作用系统的综合研究对于车、路和桥的设计和制造至关重要。由于路面的不平度,车辆与结构相互作用具有很强的随机性。然而传统随机振动分析方法的低效率限制了人们对该工具的应用。迄今为止,关于车辆与结构随机振动分析的研究成果还不多。本文在随机振动理论框架下,采用虚拟激励法,精细积分法等高效、精确的计算力学方法,研究车辆随机振动、车辆与道路／桥梁耦合随机振动,以及各种动力响应的统计特性。并且根据车辆与道路／桥梁相互作用的特点对上述方法进行扩展,提出了一系列快捷精确的车辆随机振动灵敏度分析方法,高效地针对车辆结构的随机振动特性进行优化设计,提高车辆平顺性、降低对结构物的不良影响。主要工作包括以下几方面。1.车辆与道路结构垂向耦合随机振动分析对于车辆-公路垂向耦合振动系统,通过建立随车辆同步移动的坐标系,推导出了适用于车辆与路面相互作用动力分析的二维移动单元形式。在移动坐标系下,路面模型单元被看作沿道路随车辆“流动”的概念单元,在这些单元上车辆是相对静止的,作用点的力和位移向量不用随着车辆位置的变化而更新。因此,运动微分方程的右端时间积分项消失,而行驶速度、地基参数等耦合因素对系统的影响被累加进振动方程的质量、阻尼、刚度矩阵中,使固定坐标系下的时变耦合振动问题转化为移动坐标系下的拟静力问题分析。该方法构造简单,将耦合非平稳随机振动问题方便地转化为拟静力问题进行分析,具有较高的精度和效率。2.车辆平稳随机振动灵敏度分析及优化基于传统随机振动分析方法的结构动力优化一直存在着分析过程复杂,计算量庞大,动力灵敏度分析难于实施等困难。本文将虚拟激励法在结构随机响应优化领域进行推广,针对车辆平顺性优化的灵敏度分析,提出了一种求解灵敏度信息的快速、精确方法。此方法在采用虚拟激励法对结构进行动力分析的基础上,根据响应信息对结构振动方程关于设计变量进行求导,可得到与原振动方程结构一致的灵敏度方程。通过对灵敏度方程激励项的虚拟模拟,将平稳随机荷载作用下具有阻尼系统的动力响应灵敏度计算问题转化为虚拟荷载作用下的动力响应问题进行求解,从而避免了求解特征向量的繁重计算量。同时该方法在一阶灵敏度分析的基础上可以方便快速地进行二阶灵敏度(Hessian矩阵)的分析。3.基于模拟技术的车辆随机振动多目标优化结构随机响应优化问题因不可避免地要对随机振动分析过程进行反复迭代而致计算量异常繁重,很难得到工程应用。尤其在多目标优化领域,迄今为止,目标函数的统一、有效的灵敏度分析还没有找到现实可行的高效方法,使得基于灵敏度的优化方法不易实现。本文基于模拟技术,寻求反映设计变量和响应之间关系的“替代函数”,将Kriging模型引入车辆随机振动领域,经过对样本的改造,在优化迭代过程中用替代函数代替目标函数进行优化,同时对替代函数进行必要的修正,以保证更好的精度。这样避免了过多的重分析过程,显著提高了计算效率。多目标函数通过中心法来处理,亦即对每一个目标函数自适应地引入一个上界,形成目标函数的水平截集,并重复地计算由原约束集和目标函数水平截集组成的交集的中心来达到求解多目标优化问题的目的。4.车辆与道路／桥梁耦合随机振动分析及优化设计对于车桥耦合时变系统,采用虚拟激励法将路面随机不平度转化为一系列简谐不平度的叠加,根据荷载形式使用相应的精细积分格式进行时域积分。这种虚拟激励-精细积分方法(PEM-PIM)较之传统的逐步积分方法解决了载荷“突变”和积分步过小的问题,极大地提高了耦合振动分析效率,使得耦合振动动力优化灵敏度分析的高效计算得以实现。本文基于这种方法,通过对耦合振动方程的一阶、二阶求导,得到一阶、二阶灵敏度方程的状态空间表达形式,将多点部分相干非平稳阻尼系统动力响应灵敏度分析问题转化为一系列虚拟荷载作用下的普通动力响应问题求解。应用本文方法可以高效地给出计算机意义下的敏度和Hessian矩阵精确解。5.基于有限元方法的车辆-道路／桥梁耦合动力系统随机振动力学行为研究该耦合系统随机振动力学行为的研究涉及随机振动分析、优化设计、疲劳寿命估计等多项力学难题,而且需要对大型有限元模型进行耦合随机振动分析,动辄成千上万的自由度,传统方法庞大的计算量成为这类问题的瓶颈。其随机分析若采用传统方法是不堪忍受的,甚至有些问题不能进行求解。为此,本文将虚拟激励法,耦合振动分析的PEM-PIM方法,高效的灵敏度分析方法等先进的计算手段相结合,并应用到实际车辆中。最终通过对客车车辆、车桥耦合系统等有限元模型的数值计算,研究了其随机疲劳寿命、冲击系数等力学行为,并验证了以上方法在工程应用中的高效性。更多还原

【Abstract】 With the rapid development of national economy, railway and highway transportations are getting increasingly busy. Higher speeds and heavier loads of the vehicles have caused the dynamic interactions between vehicles and road/bridge structures received much attention. As the dynamic impacts applying on the supporting (road or bridge) structures by moving vehicles affect the working status and service lives of these structures significantly; and the running smoothness and safety of vehicles have become the main factors in evaluating the reasonability of structural design parameters, therefore a comprehensive research of the interactions between vehicles and road/bridges are of great importance for their design and construction. The vibrations of vehicles and road/bridge coupled systems induced by road irregularity are essentially random, but the research work associated with such random vibration has not been well developed because of the high complexity and cost of conventional methods for random vibration analysis. Up to date, not much research work on vehicle-road/bridge system random vibration can be found in the literature. In the present thesis, some advanced computational mechanics methodology, including the pseudo excitation method (PEM) for random vibration, the precise integration method (PIM) for time history integration, etc, are introduced into the present research on dynamic analyses and optimum of various coupled vehicle and supporting structure systems based on the theoretical framework of random vibration. Furthermore some innovative schemes based on the above methodologies have been developed, which can be summarized as follows:1. Vertical random vibration analysis of vehicle-pavement coupled systemsFor vertical random vibration analysis of vehicle-pavement (or road) coupled system, the two-dimensional moving element method (MEM) is derived by using a coordinate system which moves with the vehicle. The pavement elements are regarded as conceptual elements that’flow’with the moving vehicle along the pavement in this coordinate system, and vehicle is static. It is never necessary to cross from one element into another, which avoids the updating of force or displacement vectors due to change of the contact point with the elements. It can be found that the element stiffness and damping matrices thus easily obtained are simply a revision of the corresponding static element stiffness and damping matrices by superposing the terms with the velocity, foundation parameter and other coupled effects. So the non-stationary random vibration can be transformed conveniently into a stationary one, and it is accurate and efficient.2. The sensitivity analysis and optimum for vehicle stationary random vibration The complicated analysis process and costly computation efforts are always the mainly difficulties for the random vibration optimum design based on conventional methods, which lead to the difficulty of the random vibration sensitivity analysis. In this thesis, an accurate and efficient sensitivity analysis formula for optimizing the ride comfort of vehicle suspension system is derived. Based on the dynamic responses analysis using PEM, the random equations of motion with the right-hand side random acceleration is replaced by a pseudo acceleration excitation, thus various first and second orders of sensitivity formulas are calculated conveniently by differentiating these equations. Using the method the random dynamic sensitivity analysis is transformed into a deterministic one, and the optimal solutions when vehicle ride comfort is the objective function are derived by means of these flexibilities. The optimization efficiency and the computational accuracy are numerically justified.3. Multi-objective stochastic dynamic optimum design for vehicles based on simulation technologyIt is particularly unacceptable for stochastic dynamic optimum of structures in practical engineering field, which requires usually many re-analyses and complicated analyses process. Especially to multi-objective optimum, the unified and efficient sensitivity analysis method applied to the objective functions has not been well developed. In this thesis, the Kriging model is extended to vehicle multi-objective optimum problems, a method of filled function is set up to build the approximate mapping relationship between the design variables and the responses, and the random responses analysis is performed using the filled function instead of the objective function, with necessary modification for the filled function in every step to keep the precision. The optimization efficiency is thus enhanced remarkably by avoiding too many re-analyses. The multi-objective function is processed by means of the method of centers, i.e. by self-adaptively introducing an upper bound on each objective function that forms the level sets of the objective functions, and repeatedly calculating the center of the intersection sets consisting of the original constraint sets and the level sets of the objective functions.4. The random vibration analysis and optimum design for vehicle-bridge coupled random vibrationFor dynamic analysis of vehicle-bridge coupled system, the PEM has been applied to transform the random surface roughness into the superposition of a series of deterministic pseudo-harmonic surface unevenness. The PIM has also been extended to simulate the continuous variation of the contact forces, both in their magnitudes and positions, within each time step. As a result, the solution of the uniformly modulated, multi-point, different-phase, non-stationary random vibration can be obtained efficiently by means of PEM-PIM. An innovative method (PEM-PIM Based Sensitivity) for first and second order sensitivity analyses of structural random responses is developed based on PEM-PIM. For the random equations of motion, by replacing the right-hand side random excitation by the pseudo-excitation, various first and second order sensitivity formulae can be derived conveniently and accurately.5. FEM-based random vibration analysis and associated mechanical behaviors study of vehicle-road/bridge coupled systemsThis subject is concerned with many problems, including random vibration analysis, stochastic dynamic optimum and fatigue life estimation, and so on. Analysis of such random vibration mechanical behaviors has long been regarded as very difficult, particularly if finite element models with many degrees of freedom are used. Optimum design is even more difficult although it is of great concern and significance. To overcome these difficulties, some advanced computational mechanics methodology, such as PEM for random vibration, PIM for the numerical integration in the time domain or space domain and some efficient sensitivity analysis methods are used in this paper to study the random vibration mechanical behaviors in the vehicle engineering field. Some useful results about structure random fatigue life, vehicle dynamic impact influence and structure random dynamic optimum are obtained, and the efficiency and computational accuracy of the proposed methods are justified.更多还原