随机变分方程解的存在,唯一性问题

研究了随机有限元方法的理论基础－随机变分方程解的合理性问题，证明了一般形式的随机变分方程解的存在与唯一性定性，明确了在随机扰动算子不足以破坏均值微分算子的强制性条件－不会导致方程类型变异的前提下，Ｆｒｅｄｈｏｌｍ择一定理的第二个结果成立，此时在概率１的意义上变分解存在而且唯一。     

肋骨非均匀排列的圆柱壳振动特性研究

研究了肋骨非均匀排列对加肋圆柱壳振动特性的影响。首先,以安德森定域效应的原理为基础,肋骨间距为随机分布,分析了肋骨非均匀排列时圆柱壳的振动特性,然后,采用两种肋骨间距,交替排列,构造整个圆柱壳的肋骨不等间距排列形式,两种肋骨间距的确定方法是:保持两种肋骨间距的总和不变,逐步增大两者的间距差,从而增加相邻的肋骨间的两个圆环结构的固有频率差,直至固有频率差趋于不变,最终确定了两种肋骨间距。分别计算并对比分析了肋骨等间距和不等间距排列的圆柱壳的均方振速,结果表明:肋骨不等间距排列具有一定的减振效果。     

基于随机Melnikov方法的甲板上浪船舶混沌运动研究

应用随机Melnikov方法和庞加莱截面研究甲板上浪时船舶的混沌运动。考虑甲板上浪对船舶静稳性的影响,建立随机横浪中船舶横摇运动方程。由随机Melnikov过程结合均方准则确定船舶产生混沌运动的参数域,计算不同参数域中船舶横摇响应的庞加莱截面和时间历程。结果表明,增加船舶阻尼将抑制混沌运动的发生。甲板上浪时船舶横摇响应的庞加莱截面上有两个吸引域,船舶运动过程有两个横摇中心。在非混沌参数域中,船舶只围绕其中的一个横摇中心运动;在混沌参数域中,发生由一个横摇中心到另一个横摇中心的随机跳跃。     

随机风浪中舰船横摇倾覆概率分析

以路径积分法为基础,采用Gauss-Legendre公式探讨了随机风浪作用下舰船的运动及其倾覆概率计算。考虑阻尼力矩、复原力矩的非线性及风浪的随机性,建立了随机风浪中舰船运动的非线性微分方程,应用路径积分法给出白噪声随机扰动和定常风倾力矩作用时横摇角概率密度函数随时间的演变,按照现有的倾覆准则给出舰船倾覆概率的表达式。通过算例,验证了路径积分法的准确性,分析了各个参数对横摇角概率密度的影响,计算得出了不同风速、不同航速下的倾覆概率,以及倾覆概率随时间的变化。研究表明,此方法简便可行,并能在数量上预报舰船在随机风浪下的倾覆概率。     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

Speed variation during peak and off-peak hours on urban arterials in Shanghai

Increased speed variation on urban arterials is associated with reductions in both operational performance and safety. Traffic flow, mean speed, traffic control parameters and geometric design features are known to affect speed variation. An exploratory study of the relationships among these variables could provide a foundation for improving the operational and safety performance of urban arterials, however, such a study has been hampered by problems in measuring speeds. The measurement of speed has traditionally been accomplished using spot speed collection methods such as radar, laser and loop detectors. These methods can cover only limited locations, and consequently are not able to capture speed distributions along an entire network, or even throughout any single road segment. In Shanghai, it is possible to acquire the speed distribution of any roadway segment, over any period of interest, by capturing data from Shanghai’s 50,000+ taxis equipped with Global Positional Systems (GPS). These data, hereafter called Floating Car Data, were used to calculate mean speed and speed variation on 234 road segments from eight urban arterials in downtown Shanghai. Hierarchical models with random variables were developed to account for spatial correlations among segments within each arterial and heterogeneities among arterials. Considering that traffic demand changes throughout the day, AM peak, Noon off-peak, and PM peak hours were studied separately. Results showed that increases in number of lanes and number of access points, the presence of bus stops and increases in mean speed were all associated with increased speed variation, and that increases in traffic volume and traffic signal green times were associated with reduced speed variation. These findings can be used by engineers to minimize speed differences during the road network planning stage and continuing through the traffic management phase.     

Incorporating Driver Behaviors in Network Design Problems: Challenges and Opportunities

The goal of a network design problem (NDP) is to make optimal decisions to achieve a certain objective such as minimizing total travel time or maximizing tolls collected in the network. A critical component to NDP is how travelers make their route choices. Researchers in transportation have adopted human decision theories to describe more accurate route choice behaviors. In this paper, we review the NDP with various route choice models: the random utility model (RUM), random regret-minimization (RRM) model, bounded rationality (BR), cumulative prospect theory (CPT), the fuzzy logic model (FLM) and dynamic learning models. Moreover, we identify challenges in applying behavioral route choice models to NDP and opportunities for future research.     

地铁车站结构随机振动响应分析

基于地震反应的随机非确定性,运用基于概率统计方法的随机振动理论进行结构抗震分析,考察结构的动力可靠度,是一种合理的设计方法。运用虚拟激励法对青岛地铁五四广场站进行随机振动分析,避免了传统方法计算的冗繁,得到了具有统计意义的结构动力响应。考虑x向功率谱输入时,弯矩分布较为均匀;地铁结构体型变化较大的部位剪力明显增大;柱底剪力较小,边跨柱剪力小于中跨柱底剪力。考虑y向功率谱函数输入时,沿梁轴向剪力值逐渐增大,柱底剪力明显大于x向输入时的柱底剪力,边跨柱柱底剪力大于中跨柱底剪力。所得结论为地铁站这一复杂结构形式进行基于可靠度理论的设计提供了依据,可以作为同类设计的参考指导。     

双线铁路下承式连续梁拱组合桥列车一桥梁时变系统空间振动随机分析

在列车一桥梁时变系统横向振动能量随机分析理论的基础上，采用26个自由度的列车空间振动模型，以空间梁单元模拟桥梁结构，以普通空间梁元即12自由度的空间梁元来模拟拱及吊杆结构，建立了双线铁路下承式连续梁拱组合式桥列车一桥梁时变系统空间振动分析模型，分别以构架人工蛇行波及前苏联规律性的竖向不平顺函数为横向及竖向激振源，进行双线铁路下承式连续梁拱组合式桥列车一桥梁时变系统空间振动响应分析。计算了列车以不同车速通过桥梁的空间振动响应，所得结果可供设计参考。     

随机响应约束下的桁架结构拓扑优化

研究随机响应约束下的桁架结构拓扑优化问题具有重要的工程应用前景.文章采用自适应遗传算法(AGA)求解了随机响应约束下的桁架结构拓扑优化问题.通过引入海明距离生成高质量的初始种群、采用自适应的交叉和变异算子以及对适应度函数进行线性标定这三个步骤改进了遗传算法的搜索效率以及收敛性.在拓扑优化列式中考虑杆件以及各自由度的拓扑变量以精确地模拟优化过程中杆件和结点的删除.建立了随机载荷作用下结构均方响应的表达式,并以此作为拓扑优化问题的约束条件.另外,提出了一些启发式算法来引导杆件和结点的删除.最后,通过对随机激励下的二维桁架以及三维桁架进行拓扑优化计算,证明了本文方法的实用性和有效性.