Green函数法解非均匀弹性地基板的自由振动

把板在特定域中的Green函数当作影响函数,根据实际板的边界条件首先求出虚拟域中的Green函数“源”,继而确定板内任意点的挠度及内力。在板的振动问题中及板的分布惯性力的影响后就可得到其自振频率的本征方程,从而计算出其各阶自振频率的值。文中附有算例,并把其计算结果与已有解析解作了比较,表明它们之间具有良好的吻合。     

列车荷载作用下轨道和地基的动响应分析

分析了列车运动荷载引起的应力波在轨道结构和周围地基中的传播,用动力子结构方法求解了铁路轨道和多层地基的相互作用问题,特别是在模型中考虑了轨枕离散支撑的作用.研究的对象结构包括列车运动荷载和受轨枕支撑的钢轨,以及下面的无限分层黏弹性地基.通过傅里叶变换求解微分形式的支配方程,得到了在频域和波数领域中的钢轨以及周围地基的振动准解析解,而响应时程则通过傅里叶逆变换得到.利用结果可以评估高速铁路列车运行时产生的轨道与周围地基的振动强度;同时提出了一种直观的方法来确定轨道与地基中产生共振时列车运行的临界速度.     

长编组高速列车的列车风动模型实验研究

列车风是高速列车运行时诱导产生的气流流动, 是列车空气动力学重要的研究内容和保证列车运行安全的重要方面. 本文利用缩尺比例为1\bh8的八编组高速列车模型进行了列车风的动模型实验,测试了明线运行状态下列车周围的流动参数,突破了短编组列车风动模型测试所带来的局限性.列车风系综平均曲线和标准差曲线说明: 列车头部会引起稳定的列车风,在车身和车尾处的列车风具有非常明显的非定常特征.列车风所反映的车身周围的气流扰动在第二节车厢开始显现, 列车风速振荡上升,在第七节车厢达到局部最大值.转向架舱和车厢间风挡间隙的气流干扰并没有在列车风曲线上表现出来.利用本征正交分解法分析列车风尾迹区的实验结果,发现列车风的扰动能量集中于近尾迹区, 次之是车身发展区.以各次实验结果中列车风的峰值位置距离车尾远近为条件,对列车风实验结果进行条件平均分析,表明列车尾涡生成时与列车风探针间的相对位置关系会影响列车风尾迹区的峰值形态.      

长编组高速列车的列车风动模型实验研究

列车风是高速列车运行时诱导产生的气流流动,是列车空气动力学重要的研究内容和保证列车运行安全的重要方面.本文利用缩尺比例为1:8的八编组高速列车模型进行了列车风的动模型实验,测试了明线运行状态下列车周围的流动参数,突破了短编组列车风动模型测试所带来的局限性.列车风系综平均曲线和标准差曲线说明:列车头部会引起稳定的列车风,...     

高速列车车轮踏面剥离引起的轮轨冲击力学响应有限元模拟

车轮踏面剥离是轨道车辆车轮非圆化损伤的常见形式之一。轮轨滚动接触过程中,车轮踏面剥离会循环冲击钢轨,诱发异常大的轮轨动态相互作用,严重影响高速列车运行平稳性和安全性。基于三维轮轨滚动接触有限元模型,模拟了高速列车车轮踏面剥离引起的轮轨冲击力学响应,分析了轮轨冲击过程中的轮轨接触力/压力、接触斑及黏/滑特性、钢轨表面节点速度分布和应力/应变状态等响应特征,讨论了列车速度、剥离长度和剥离深度等关键参数对轮轨冲击响应的影响。结果发现,车轮踏面剥离引起的轮轨动态垂向接触力随列车速度的提高呈现出先增大后减小的变化趋势,并在列车速度为300 km/h出现最大值,约为轮轨准静态垂向接触力的1.35倍;随着剥离长度的增大,轮轨动态接触力、轮/轨von Mises应力和等效塑性应变均显著增大;随着剥离深度的增大,仅车轮von Mises应力和等效塑性应变显著增大。     

高速列车制动盘温度场的建模及分析

高速列车在制动过程中,制动盘在制动块的摩擦力作用下温度急剧升高,从而产生了热应力。过高的热应力往往会引起制动盘的疲劳破损,因此在设计制动盘时考虑温度场的影响非常重要。对速度为300km/h的列车在紧急制动工况下的制动盘,建立了含有局部内热源的数学模型和瞬态热传导方程。采用微分求积法,对热传导方程中的温度函数进行关于空间坐标的离散,得到了离散节点上仅含时间自变量的温度函数表示的一阶常微分方程组,然后采用龙格-库塔法求解。最后,对Mechanite Cast Iron G.C.40、AISI301、Chromium Copper Casting三种材料制造的制动盘进行分析和计算,得到了制动过程中温度随时间和沿轮轴半径的变化情况。结果表明:导热好的材料的温度沿径向分布的均匀程度好;制动过程中有动压力作用时,导热好的材料在有效摩擦区域沿径向的温度场与热流的分布规律基本一致,并逐渐趋向于稳态值。     

考虑地面效应的高速列车远场气动噪声计算方法研究

为研究高速列车远场气动噪声的计算方法,根据高速列车近地面运行的实际情况,利用半自由空间的Green函数求解FW-H方程;建立考虑地面效应时的远场声学积分公式,并研究地面效应对高速列车远场气动噪声的影响.研究表明,由于存在地面效应,原来的自由声场变成了相当于真实列车声场与镜像列车声场的叠加,并且作用在镜像列车上的力源和法向运动速度与真实列车上的相同.当列车运动速度为350 km/h时,不考虑地面效应时,远场测点的等效连续A计权声压级的最大值为90.76 dB;考虑地面效应之后,远场测点的等效连续A计权声压级的最大值为94.72 dB.     

基于涡旋识别方法的高速列车尾涡结构的讨论

利用改进型延迟分离涡模拟方法对缩尺比例1:30的高速列车简化模型的绕流流场进行数值计算,主要针对近尾流区的涡旋结构展开具体讨论. 通过不同的涡旋识别方法,发现在尾涡结构中,高涡量的强涡旋主要聚集于尾车附近,而涡量较低但处于相对稳定状态的涡旋分布在大部分尾流空间中. 对此,主要基于最新提出的涡旋定义及其物理意义认为,由于边界层在尾部发生的流动分离,剪切变形以及高涡量的扩散对强涡旋的形成发挥着重要的作用,而涡旋会被较强的剪切旋转拉伸,使得局部复杂的流动表现出突出的湍流特性;另一方面,尽管涡强度明显下降,但是在强剪切应变迅速衰减的情况下,流向涡核中的涡旋涡量是主要的,此时,在较接近地面的情况下,流体微团以涡核为中心的旋转运动使得涡旋与地面之间的相互作用成为主导的流动机制. 虽然涡强度会相对缓慢地衰减,但是从湍流能量产生的角度,该机制对涡旋的自维持发挥重要的作用,从而使尾涡结构能够相对稳定地存在于尾流流动中.      

双参数地基上圆（环）板轴对称稳态振动的解析解

本文应用贝塞尔函数理论，根据不同的ω值获得了双参数地基上圆（环）板轴对称稳态振动的解析解。最后，给出了一些计算结果。     

基于Fluent与Simpack的高速列车流固耦合联合仿真

基于列车系统动力学和高速列车空气动力学建立了高速列车流固耦合联合仿真计算方法。利用Fluent和Simpack分别计算高速列车气动特性和气动作用下的高速列车动力学性能,通过实时传递气动参数和姿态参数,实现高速列车流固耦合的联合仿真。利用建立的流固耦合方法研究了横风速度为10．7m／s时高速列车以350km／h速度运行时的流固耦合动力学行为。比较了离线仿真和联合仿真两种方法下列车气动力与姿态、安全性和舒适性指标的差异。研究表明,列车一气流的流固耦合效应对头车气动力和姿态的影响显著,头车安全性指标有所恶化。     

高速列车紊态外流场的数值模拟研究

高速列车是近地运行的细长、庞大物体,它的空气绕流问题有其特殊性,本文以不可压缩粘性流体的Navier-Stokes方程和k-ε两方程紊流模型为基础,采用有限元方法求解了高速列车三维紊态外流场,针对有限元法应用于流场计算时常出现的问题,采用分离式解法,非对称矩阵一维变带宽压缩存储及带宽极小化等方法,最大限度地降低计算存储量;并采用罚函数法,集中质量矩阵,缩减积分法,带参数迭代法以及 引入松弛因子等技术,提出了一套用有限元法计算非线性问题的求解方法,提高了收敛速度的计算严谨,计算方法和计算结果对列车空气动力学的深入研究有一定的帮助。     

An explicit time domain solution for ground stratum response to harmonic moving load

Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi–analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier–Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.The project is partially supported by the National Natural Science Foundation of China (50538010). The English text was polished by Yunming Chen.     

The numerical solutions of Green's functions for transversely isotropic elastic strata

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A Radiation Condition for Layered Elastic Media

This study aims to establish a generalized radiation condition for time-harmonic elastodynamic states in a piecewise-homogeneous, semi-infinite solid wherein the “bottom” homogeneous half-space is overlain by an arbitrary number of bonded parallel layers. To consistently deal with both body and interfacial (e.g. Rayleigh, Love and Stoneley) waves comprising the far-field patterns, the radiation condition is formulated in terms of an integral over a sufficiently large hemisphere involving elastodynamic Green's functions for the featured layered medium. On explicitly proving the reciprocity identity for the latter set of point-load solutions, it is first shown that the layered Green's functions themselves satisfy the generalized radiation condition. By virtue of this result it is further demonstrated that the entire class of layered elastodynamic solutions, admitting a representation in terms of the single-layer, double-layer, and volume potentials (distributed over finite domains), satisfy the generalized radiation condition as well. For a rigorous treatment of the problem, fundamental results such as the uniqueness theorem for radiating elastodynamic states, Graffi's reciprocity theorem for piecewise-homogeneous domains, and the integral representation theorem for semi-infinite layered media are also established.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

The effective permeability of a heterogeneous porous medium

The effective (single-phase) permeability of an (infinite) heterogeneous porous medium is studied using a formalism of Green's functions. We give formal expressions for it in the form of a series expansion involving the microscopic random-permeability field many-body correlation functions of higher and higher order.The particular case of a log-normal medium of infinite extent is studied using field-theoretical methods. Using partial series resummation techniques, we derivea formula up to all orders in the local correlations which was first reckoned by many authors by means of a first-order calculation. The formula — which remains an approximation — works whatever the dimensionality of the space, and gives the following simple estimate for the effective permeability in 3 D:K _eff=k ^1/33. The method is general and the approximations can be systematically improved on when more complex situations are studied.Roman Letters D number of dimensions of the space in which the flow takes place - f(r) body force field,N - f(q) Fourier-transformed body-force field, Nm³ - G ₀(r, r) Green's function of the Laplace operator, m^–1 - g(k,r, r) velocity propagator before averaging, m^–1 - G(r, r) velocity propagator after averaging, m^–1 - j(r) a scalar dimensionless field - k(r) local value of the permeability at point r, m² - K _eff effective permeability - K _g geometric average of the local permeability, m² - l typical size of the averaging volume, m - L characteristic length of the porous medium or of the reservoir, m - L(r, r) projection operator, m^–2 - M(r, r) scattering operator, m^–3 - p(r) local value of the pressure, Nm^–2 - p(k,r, r) pressure propagator before averaging, m^–1 - P(r, r) pressure propagator after averaging, m^–1 - r position vector, m - r modulus of vectorr, m - unit vector pointing in the direction ofr - q Fourier wave vector, m^–1 - q modulus of the Fourier wave-vectorq, m^–1 - unit vector pointing in the direction ofq - projector over vector - 1 unit tensor - X(r) a local random variable - ¯X(r) volume averaged local random variable - X (r) ensemble averaged local random variable - V large-scale averaging volume, m³ - Z(j) generating functional of a random field - Z(r,j) modified generating functional of a random field - Z normalization factor Greek Letters ₀ average value of the logarithm of the permeability - (r) fluctuation of the logarithm of permeability at pointr - viscosity of the fluid, Nt/m² - (r–r) two-point correlation function of the fluctuations of the logarithm of the permeability - _k correlation length of the permeability correlation function, m - _u correlation length of the velocity correlation function, m     

A boundary element solution to scattering of elastic SH wave by arbitrarily shaped inclusions embedded in an infinite anisotropic medium

Scattering problems for inhomogeneous bodies are investigated by the integral equation method. The boundary integral equation (BIE) for the scattered displacement field associated with finite inhomogeneities in an anisotropic medium are derived with the help of the generalized Green's identity. The discretization of BIE is based upon the constant element, linear element and quadratic element. Several numerical examples for calculating the scattering displacement, stress and scattering cross section from a cylinder, an interface crack, and two elliptic cylinders are given. Results show that the present method can be advantageously applied to a wide range of scattering problems of elastic waves.     

An application of non-singularity BEM to plate bending, buckling and natural vibration problems

In this paper the fundamental solution of the singular governing equation of plate static bending is taken as the Green's function, which can satisfy the governing equation precisely in the plate region. Based on the principle of superposition, let the function values on the plate boundary, induced by a set of the Green's function sources (including the known sources in the plate region and the unknown sources in the fictitious region), satisfy the prescribed conditions on specially chosen boundary matching points, and the corresponding semi-analytical and semi-numerical solution can be obtained, which is free from the restraint of boundary forms and boundary conditions. The more matching points there are on the boundary, the better the accuracy of results is. Finally, in static bending problems a set of linear algebraic equations has to be computed; in buckling problems the minimum value of buckling eigenvalue equation has to be found; in natural vibration problems the eigenvalues of the frequency equation have to be calculated. Numerical examples are given and the results are compared with those by the analytical method and other methods. It can be seen that they are very close to each other.     

Superposition principle for short-term solutions of Richards' equation: Application to the interaction of wetting fronts with an impervious surface

The interaction of a wetting front with an impervious layer is described by adding a reflected solution to the incoming solution for a semi-infinite medium. It is shown and checked by comparison with a numerical solution that the result is accurate during the early times of the interaction between the front and the impervious surface. This superposition principle is quite general and should prove especially useful to initiate numerical schemes by this analytical approximation as in the early times singularities are difficult to describe numerically.     

设置连接阻尼器的相邻结构随机地震动响应的简明封闭解

针对两相邻结构间设置连接阻尼器对结构的减震影响问题,研究了基于Kanai-Tajimi谱地震动激励下的Kelvin型粘弹性阻尼器与相邻结构形成的组合体系的随机地震动系列响应(绝对位移及层间位移)的简明封闭解。首先,利用Kelvin型粘弹性阻尼器本构关系及Kanai-Tajimi谱的滤波方程,将组合体系基于复杂地震动激励精确转化为基于简明白噪声激励的运动方程;其次,利用复模态法获得了组合结构相对于地面的绝对位移、层间位移等系列响应方差及0阶～2阶谱矩的统一简明封闭解。最后,通过算例及与虚拟激励法进行对比,证明本文方法的正确性和简明性;通过与未设置阻尼装置结构体系的动力响应对比,说明了阻尼装置对相邻结构具有良好的减震效果,但局部楼层的层间位移及层间剪力会有所增加。