半车车辆-道路耦合动力分析模型的研究与应用

在不平整路面上行驶的车辆会产生道路与车辆的耦合振动.为简化分析,先将车辆和道路视为两个子系统,然后再耦合为一个整体系统.车辆采用1/2车辆4自由度模型,道路采用弹性多层体系有限元模型,通过轮胎与路面的位移相容条件,建立车辆-道路整体耦合动力分析模型,推导出了系统的动力平衡方程组,并探讨了方程组的解耦方法,提出了反映车辆运行品质和道路设计参数的理论计算指标,为车-路耦合动力分析的深入研究,以及系统研究道路结构设计参数与车辆运行品质的相互关系提供理论基础和求解依据.此外,通过解耦和编程分析,还对沥青路面和水泥混凝土路面两种典型路面结构的运行品质指标进行了分析和评判,以期为不同路面结构设计和分析提供参考.     

路面平整度的时间序列模型

介绍非标准道路的路面平整度的时间序列模型,研究道路实测数据的时间序列模型.通过对实际路段的数据采集,进行道路平整度实例分析和道路平整模型的平稳性检验、模型的识别和估计,确定了模型参数,检验模型的适用性.实例表明了模型的置性度和合理性.     

路面平整度的时间序列模型

介绍非标准道路的路面平整度的时间序列模型,研究道路实测数据的时间序列模型.通过对实际路段的数据采集,进行道路平整度实例分析和道路平整模型的平稳性检验、模型的识别和估计,确定了模型参数,检验模型的适用性.实例表明了模型的置性度和合理性.     

变温条件下考虑车辆-路面相互作用的车辙分析

研究沥青路面结构的车辙问题,首先基于车辆与路面的相互耦合作用,建立路面不平整度引起的车辆荷载简化模型;然后根据沥青混合料蠕变试验数据,拟合出基于修正Burgers模型的沥青路面车辙的计算参数;最后结合气温观测数据,借助ABAQUS有限元软件,引入路面温度场,建立了考虑连续变温的日车辙预估计算模型.模拟了考虑车辆 路面相互作用的沥青路面在连续变温条件下的车辙变化规律,并分析研究了温度、车辆荷载以及车速对车辙的影响.结果表明,考虑车辆 路面相互作用得到的日累积车辙深度增大了6.5%,说明这一因素对沥青路面车辙的预测是不可忽略的;轴载及路面不平整度均与车辙量线性相关;而相同轴载作用下,温度越高,车辙增长越快,得到的车辙量越大;随着车速增大,车辙深度呈减小趋势,并且在车辆与路面发生共振的车速下,该文模型得到的结果增大了32%.     

轨道结构随机场模型与车辆-轨道耦合随机动力分析

将轨道结构视为一个参数随机系统,提出并建立了轨道结构的随机场模型.利用车辆-轨道耦合动力学的基本方法,将轨道系统有限单元模型与多刚体车辆模型相结合,建立了考虑铁路线路参数空-时随机变化的车辆-轨道动力计算模型.算例表明:所提出的方法较为可靠且高效;线路参数随机性对车辆-轨道系统的动力响应有明显的影响,随线路参数离散程度的增加,可能造成行车不安全、轨道损伤加剧等一些问题.     

灰色Verhulst模型优化的新方法

通过分析传统灰色Verhulst模型利用倒数变换求解白化方程发现了灰色微分方程与白化方程不匹配而导致误差的根源,提出了直接对原始序列的一次累加序列作倒数变换后建立与倒数替换后的白化方程相匹配的灰色微分方程来估计参数a和b,并在此基础上将优化灰导数以改造灰色方程与利用平均相对误差最小为指标确定响应系数的方法相结合对模型进行了优化.结果表明,该优化模型对其本身的时间响应函数所表达的曲线进行模拟和预测具有重合性.通过实例分析说明了优化模型使得传统模型的模拟预测精度得到明显的提高.     

Helbing流体力学交通流模型的守恒形式

得到了Helbing交通流流体力学模型的标准守恒形式,并证明了模型的双曲性,这对研究模型的解析性质和数值格式至关重要.基于给出的守恒形式,设计了高效求解模型方程的LDG(lo-cal discontinuous Galerkin)格式,并模拟了由不稳定平衡态到稳定的时停时走波的演化.数值模拟也表明,通过扩散系数校正确实使模型得到改进,避免了车辆碰撞和出现极端高密度.     

两个新的减肥差分方程模型和解法

根据能量守恒和热量变化规律,建立了跑步减重的两个新的差分方程模型.首先,引入计算基础代谢的Liu公式,对基本模型做进一步的细化,得到一个改进的一阶线性差分方程模型;然后,基于BMI指数与跑步速度关系建立了另一个改进的一阶非线性差分方程模型,对两个改进的模型进行稳定性分析,得到模型存在稳定解的条件,并进行了解析和数值的求解计算;最后,分析了运动时间、热量消耗对体重变化的影响,结果表明改进后的模型更贴合实际情况.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

债券定价及利率风险的市场价格的重构方法

假设利率变化的模型是由随机微分方程给出,则可以用推导Black-Scholes方程的方法来推出债券价格满足的偏微分方程,得到一个抛物型的偏微分方程.但是,在债券定价的方程中隐含有一个参数λ称为利率风险的市场价格.所谓债券定价的反问题,就是由不同到期时间的债券的现在价格来得到利率风险的市场价格.对随机利率模型下债券定价的正问题先给予介绍和差分数值求解方法,并介绍了反问题,且对反问题给出了数值方法.     

Numerical and experimental investigation on stochastic dynamic load of a heavy duty vehicle

Numerical simulation and field test are used to investigate tire dynamic load. Based on multi-body dynamics theory, a nonlinear virtual prototype model of heavy duty vehicle (DFL1250A9) is modeled. The geometric structural parameters of the vehicle system, the nonlinear characteristics of shock absorber and leaf springs are precisely described. The dynamic model is validated by testing the data, including vertical acceleration of driver seat, front wheel, intermediate wheel and rear wheel axle head. The agreement between the response of the virtual vehicle model and the measurements on the test vehicle is satisfactory. Using the reliable model, the effects of vehicle speed, load, road surface roughness and tire stiffness on tire dynamic load and dynamic load coefficient (DLC) are discussed. The results demonstrate that the proposed model can offer efficient and realistic simulation for stochastic dynamic loads, so as to investigate vehicle road-friendliness.     

车桥系统的耦合振动

通过用正弦波形模拟桥面的不平和考虑移动车辆-桥梁间的相互作用,在Euler-Bernoulli梁理论的基础上建立了一种车桥系统的耦合振动模型．利用模态分析法和Runge-Kutta法对模型进行数值求解,获得了车桥系统耦合振动的动态响应和共振曲线．发现车桥耦合振动的共振曲线中存在两个共振区域,一个反映主共振而另一个反映次共振．讨论了桥面不平、桥梁振型和车辆间的相互作用对系统振动的影响．数值结果表明,这些参数对系统振动的影响很大,桥面不平和振型对车桥系统耦合振动的影响不能忽略,设计车速应该远离临界车速．     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

柔性头颅模型撞击弹性板的动态响应分析

将柔性接触撞击过程处理为一个振动系统响应,采用机械网络图和求机械阻抗的方法解决了这一动态响应问题。柔性接触撞击模型考虑了头部的实际结构,把头部简化成撞击部位的头皮和头骨的质量、头部其它部分的头骨和脑液的质量、头部的刚度、头皮和脑液的阻尼系数组成的振动模型,弹性板也同样简化成由质量、刚度和阻尼构成的振动模型。采用求激振点速度阻抗的方法,得到了系统的动态撞击力、头部所受到的撞击加速度值,以及板的弹性变形、系统的固有频率等动态响应。实验数据与计算数据符合较好,证明方法是计算撞击作用下系统动态响应的实用方法,从而为头部撞击保护设计提供参考。     

The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters

This paper investigates the variability of dynamic responses of a beam resting on an elastic foundation, which is subjected to a vehicle with uncertain parameters, such as random mass, stiffness, damping of the vehicle and random fields of mass density, and the elastic modulus of the beam and stiffness of elastic foundation. The vehicle is modeled as a two-degree-of-freedom spring-damper-mass system. The equations of motion of the beam was constructed using a finite element method. The mass and elastic properties of the beam, and the stiffness of foundation are assumed to be Gaussian random fields and were simulated by the spectral represent method. Masses, stiffness of the spring, and the damping coefficient of the vehicle are assumed as Gaussian random variables. The numerical analyses were performed using the finite element method (FEM) in conjunction with the Monte Carlo simulation (MCS). The variability of dynamic responses of the beam were investigated with various cases of random parameters. For each sample, the equations of motions were solved with the Wilson-q integral method to find dynamic responses. The influence of random system parameters and their correlation on the response variability is discussed in detail.     

Analytical study on dynamic responses of a curved beam subjected to three-directional moving loads

Considering the warping resistance, inertia force and moving three-directional loads, a more comprehensive set of governing equations for vertical, torsional, radial and axial motions of the curved beam are derived. The analytical solutions for vertical, torsional, radial and axial responses of the curved beam subjected to three-directional moving loads are obtained, using the Galerkin method to discretize the partial differential equations and the modal superposition method to decouple the ordinary differential equations. The analytical results are compared with the numerical integration and a published work to verify the validity of the proposed solutions. Effects of Galerkin truncation terms and damping ratio on solution convergence are also discussed. Considering first-mode and higher-mode truncation respectively, the conditions of resonance and cancellation are analyzed for vertical, torsional, radial and axial motions of the curved beam. Taking a curved bridge under passage of a vehicle as an example, the influences of system parameters, such as vehicle speed, braking acceleration, bridge curve radius, bridge span and bridge deck elastic modulus, on bridge midpoint vibration are explored. The proposed approach and results may be beneficial to enhance understanding the three-directional vehicle-induced dynamic responses of curved bridges. It is shown that when the axial motion, or the multiple moving loads are involved, the first-order truncation are not accurate enough and one should use higher-mode truncation to study the responses of curved beams. In addition, it is necessary to consider damping in the vibration study of curved beams.     

三维横向流体诱发直管振动的数值模拟

基于有限体积法和有限元法,结合动网格控制技术,建立了横向流体作用下三维弹性直管流致振动计算的数值模型,实现了计算结构动力学与计算流体力学之间的联合仿真．首先,通过对刚性管的静止绕流计算,研究了网格离散方式和不同湍流模型对圆柱类结构静止绕流流场特征的影响和预测能力,得到了适用于双向耦合分析的CFD模型;其次,利用基于双向流固耦合方法的流致振动模型,计算并分析了流体力与结构位移间的相位关系,指出流体力与位移间的相位差是由流体力引起的,同时对双向耦合和单向耦合进行了比较分析;最后通过对直管流致振动的数值计算,联合管表面压力、尾流区时均速度、分离角等时均量,分析了尾流区的流场特征.     

Nonlinear vibration of buckled nanowires on a compliant substrate

Buckling of thin nanowires on a pre-strained compliant substrate has been widely used to make nanowire-based stretchable electronics. On nanometer scale, surface effect plays an important role on a buckled nanowire structure. In addition, as the amplitude of the deflection of the buckled nanowire is larger than its thickness, geometrical nonlinearity should be taken into account. Taking the kinetic energy caused by the out-of-plane motion into account, and on the basis of Euler beam theory, a theoretical model for a nanowire-substrate structure is established, combined with the influences of the nano-scale surface effect and geometrical nonlinearity. By means of Lagrange's equation, the equation of motion is derived and then solved by the Symplectic (Partitioned) Runge–Kutta method (PRK). Several numerical examples are analysed to study the nonlinear vibration of the structure. The analytical expressions of stable and unstable equilibrium points, and the relationship between the vibration amplitude and the natural frequency are obtained. The influences of surface effect and pre-strain on the dynamic behaviour are analysed. Through these numerical results, one can find that when the surface elastic modulus and surface residual stress are considered, the number of unstable equilibrium points would increase to three. The frequency obtained with positive surface elastic modulus is greater than that obtained with negative surface elastic modulus, implying that the positive surface elastic modulus can make the nanowire-substrate structure stiffer. Furthermore, when the pre-strain increases, the locations of stable and unstable equilibrium points move further away from the initial displacement, and the homoclinic orbits become expanded. The results presented in this paper should be useful to guide the design of nanowire-based stretchable electronics.     

大挠度圆柱壳在温度场中的热弹耦合振动分析

对温度场与与应力场耦合时的圆柱壳的非线性热弹耦合的振动问题,推导得到了基本的振动方程,热传导方程和协调方程,对短圆柱壳运用伽辽金(Galerkin)法求解,得出振幅随时间变化的数值解,得到一些有价值的结论．即随着温度幅值和耦合系数的增大,振动衰减的速度变缓,热弹耦合效应减弱．随着长径比、长厚比的增大,振幅衰减的速度变快,同时热振动频率也随之增大,即热弹耦合效应增强．耦合系数越大,轴向应力、轴向力以及轴向弯矩越小．