常微分方程通解、特解、所有解的区别与联系

通过具体实例分析、讨论了高等数学中常微分方程的通解、特解和微分方程的所有解之间的区别与联系,并对高等数学教材中二阶线性微分方程的降阶法与二阶常系数非齐次线性微分方程特解求解过程中的作法进行了说明.     

南疆铁路沿线区域人口发展和城镇化水平预测

根据南疆铁路沿线四地州人口发展过程和人口现状与城镇化水平现状,采用联合国人口基金提供的People人口预测软件和大型统计软件SPSS,以及联合国人品司推荐持用于预测世界各国城市人口的方法,简称URGD法,以1998年的统计数据为基础对区域的人口发展和城镇化水平进行了预测到2015年南疆铁路沿线地州人口将达到887万人,城镇化水平将达到37％,随后又对预测的意义进行了探讨,提出了人口发展规划和城镇化水平目标规划,并为规划的实现提出了几点主要的保障措施。     

广义狄氏型的符号光滑测度扰动及其结合的马氏过程

该文研究一类符号光滑测度对广义狄氏型的扰动及其结合的马氏过程.证明了扰动后的二次型是广义狄氏型,并且在给定条件下,得到扰动型结合一好的特殊标准马氏过程.     

细粒土K_(30)试验分级加载变形稳定标准探讨

分级加载的变形稳定标准是影响K_(30)试验准确性和效率的关键因素。对粉质黏土在最佳含水率下,开展了三组压实系数K分别为0.90、0.95和1.00的小型平板载荷试验,得到不同荷载作用下填土变形时程曲线,分析了分级加载下填土变形的时间效应程度,讨论了不同变形稳定标准对K_(30)值的准确性和试验效率的影响。研究表明:根据最后1min变形比(1%)和变形速率Δs(mm/min)两种变形稳定标准,K_(30)试验的分级加载时间随时间效应程度分别呈先增长后缩短和加速增长的变化趋势,后者更符合土变形稳定时间与时间效应程度的正相关变化规律;Δs取0.01能降低51%~58%的试验时间,试验误差在6%以内,Δs增大会使试验误差大幅提高,Δs减小则会使试验时间大幅增加;据此,提出了适用于细粒土压实质量检测的级数-时间分级加载控制法。所得成果可为提高细粒土压实质量检测效率提供试验依据。     

基于实测荷载的铁路钢桁梁桥疲劳可靠性评估

为了对钢桁梁桥疲劳进行评估,引入可靠性理论,提出了基于实测荷载的桥梁疲劳可靠性评估方法。根据某铁路钢桁梁桥实测车辆荷载数据,建立了随机车辆荷载模型。并在考虑车辆荷载随机性的基础上,结合Monte-Carlo法与有限元,分析了钢桁梁桥构件疲劳应力谱,计算了构件疲劳可靠性随时间的变化,并探讨了车辆荷载及荷载效应变异性对构件疲劳可靠性的影响,最后采用β约界法与静力分析法对钢桁梁桥系统疲劳可靠性进行了研究。结果表明,基于随机车辆荷载的构件疲劳应力谱呈现单峰分布;构件疲劳可靠性随运营时间的增加而减小;车辆荷载的增长及荷载效应变异性的增加对构件疲劳可靠性影响较大,当车辆荷载增长率和等效应力变异系数分别增加到5%时,构件疲劳寿命大幅减小;β约界法结合静力分析法可快速确定钢桁梁桥失效模式,桥梁系统疲劳寿命小于构件疲劳寿命。总的来看,基于实测荷载的钢桁梁桥疲劳可靠性评估方法能有效地利用监测数据,对桥梁疲劳评估具有良好的适用性。     

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。     

Effect of wheelset flexibility on wheel–rail contact behavior and a specific coupling of wheel–rail contact to flexible wheelset

The fexibility of a train's wheelset can have a large effect on vehicle–track dynamic responses in the medium to high frequency range.To investigate the effects of wheelset bending and axial deformation of the wheel web,a specifi coupling of wheel–rail contact with a fexible wheelset is presented and integrated into a conventional vehicle–track dynamic system model.Both conventional and the proposed dynamic system models are used to carry out numerical analyses on the effects of wheelset bending and axial deformation of the wheel web on wheel–rail rolling contact behaviors.Excitations with various irregularities and speeds were considered.The irregularities included measured track irregularity and harmonic irregularities with two different wavelengths.The speeds ranged from 200 to400km/h.The results show that the proposed model can characterize the effects of fexible wheelset deformation on the wheel–rail rolling contact behavior very well.     

高速铁路连续箱型梁桥的动力响应与减振分析

根据列车具体的轴距和轴重,建立了和谐号动车组CRH380AL型列车简化模型;对高速铁路两跨连续梁桥采用多自由度欧拉伯努利梁单元进行主梁的模拟,并将液体黏滞阻尼器模拟为有限元阻尼单元;采用Newmark直接积分方法求解了高速列车作用下的连续梁桥运动方程,数值分析了列车车速以及液体黏滞阻尼器的阻尼系数对于高速铁路连续梁桥振动响应的影响。结果表明:黏滞阻尼器对于桥梁具有明显的减振效果,阻尼力不仅与阻尼系数有关还与列车时速有关;同一黏滞阻尼器条件下,桥梁的最大加速度并不随列车速度的增加而单调增加,而是在某些特定列车车速下桥梁的最大加速度出现了峰值,且随着黏滞阻尼器的阻尼系数增大,桥梁振动响应峰值处的最大加速度减幅不同;同一列车时速的条件下,桥梁的减振效果并不是随着阻尼系数的递增呈正比递增,而是随着阻尼系数的增大,阻尼器的减振效果增幅在减小。     

轨下支承失效对直线轨道动态响应的影响

建立了基于Timoshenko梁模型的车辆/轨道耦合动力学模型,分析轨下支承失效对直线轨道动态响应的影响. 钢轨被视为连续弹性离散点支承上的无限长Timoshenko梁,通过假设轨道系统刚度沿纵向分布发生突变来模拟轨下支承失效状态. 推导了考虑钢轨横向、垂向和扭转运动的轮轨滚动接触蠕滑率计算公式. 利用Hertz法向接触理论和沈氏蠕滑理论计算轮轨法向力及轮轨滚动接触蠕滑力. 采用移动轨下支承模型的车辆/轨道耦合系统激振模式,考虑轨枕离散支承对系统动力响应的影响. 通过新型显式积分法求解车辆/轨道耦合动力学系统运动方程,由数值分析计算得到不同轨下支承失效状态下直线轨道的动态响应. 结果表明,轨下支承失效对直线轨道变形及加速度有显著的影响,随着失效轨下支承个数的增加,轮轨相互作用力和轨道部件的位移、加速度将会急剧增大,将加速失效区段线路状况的恶化.      

On a New Route to Chaos in Railway Dynamics

Cooperrider's mathematical model of a railway bogie running on a straight track has been thoroughly investigated due to its interesting nonlinear dynamics (see True [1] for a survey). In this article a detailed numerical investigation is made of the dynamics in a speed range, where many solutions exist, but only a couple of which are stable. One of them is a chaotic attractor.Cooperrider's bogie model is described in Section 2, and in Section 3 we explain the method of numerical investigation. In Section 4 the results are shown. The main result is that the chaotic attractor is created through a period-doubling cascade of the secondary period in an asymptotically stable quasiperiodic oscillation at decreasing speed. Several quasiperiodic windows were found in the chaotic motion.This route to chaos was first described by Franceschini [9], who discovered it in a seven-mode truncation of the plane incompressible Navier–Stokes equations. The problem investigated by Franceschini is a smooth dynamical system in contrast to the dynamics of the Cooperrider truck model. The forcing in the Cooperrider model includes a component, which has the form of a very stiff linear spring with a dead band simulating an elastic impact. The dynamics of the Cooperrider truck is therefore non-smooth.The quasiperiodic oscillation is created in a supercritical Neimark bifurcation at higher speeds from an asymmetric unstable periodic oscillation, which gains stability in the bifurcation. The bifurcating quasiperiodic solution is initially unstable, but it gains stability in a saddle-node bifurcation when the branch turns back toward lower speeds.The chaotic attractor disappears abruptly in what is conjectured to be a blue sky catastrophe, when the speed decreases further.