Group properties of utt=[F(u)ux]x

The group properties and the associated Lie algebra are developed for the subject quasilinear wave equation, for arbitrary f[fεC²(R), f > 0, f ≠ 0]. From the resulting information sets of explicit invariant solutions are constructed for wave propagation in gases and for the transonic equation.     

Exact solution of the non-linear differential equation RR̈ + 32R2 − AR−4 + B = 0

The non-linear equation $\text{R}\text{R}\text{?}\text{+}\text{3}\text{2}\text{R}{}^2\text{- AR}{}^{\mathrm{?4}}\text{+ B = 0}$ is shown to represent simply periodic motion with a minimum at R₁ and a maximum at R₁R₀ or a maximum at R₁ and a minimum at R₁R₀^?1. R₀ is a function of the ratio $\text{A}\text{B}$ and is greater than 1 for $\text{A}\text{B}$ > 1 and less than 1 for $\text{A}\text{B}$ > 1. The period of the motion satisfies the simple relation T(R₀^?1) = R₀^?1T(R₀). The exact solution to the above equation is represented in terms of elliptic integrals of the first and second kinds and a simple algebraic function.     

Explicit expressions of S(v), H(v) and L(v) for anisotropic elastic materials

The three matrices L(v), S(v) and H(v), appearing frequently in the investigations of the two-dimensional steady state motions of elastic solids, are expressed explicitly in terms of the elastic stiffness for general anisotropic materials. The special cases of monoclinic materials with a plane of symmetry at x₃ = 0, x₁ = 0, and x₂ = 0 are all deduced. Results for orthotropic materials appearing in the literature may be recovered from the present explicit expressions.     

惯导／GNSS／罗兰C／航姿系统组合导航方案

为保证飞行器的导航精度及可靠性,采用了惯导/GNSS/罗兰C/航姿系统的组合导航。该组合导航采用开环组合方式,将多系统导航信息在计算机中进行综合,提高导航信息精度。仿真试验结果说明,所设计的组合导航系统是可行的,能满足任务要求。     

Phase portraits and bifurcations of the non-linear oscillator: ẍ + (α + γx2 + βx + δx3 = 0

The non-linear oscillator ? + αx + γx²x + βx + δx³ = 0 is studied using the methods of differentiable dynamics to obtain qualitative behaviour. The case x, β<0; γ, δ> 0 is considered in some detail; it has physical relevance as a simple model in certain now-induced structural vibration problems in which the structural non-linearities act to maintain overall stability. The presence of local and global bifurcations is detected and their physical significance discussed.     

Rheology/morphology/flow conditions relationships for polymethylmethacrylate/rubber blend

Viscoelastic behavior, phase morphology and flow conditions relationships in polymer/rubber blends have been investigated. The importance of such correlations is illustrated on polymethylmethacrylate (PMMA)/rubber blends subjected to different flow conditions both under small and large deformations. In small-amplitude oscillatory shear (the morphology does not change during the flow) the elastic modulus G of the concentrated blends shows a secondary plateau, G _p , in the low frequency region. This solid-like behavior appears for rubber particle contents beyond the percolation threshold concentration (15%). Morphological observations revealed that for concentrations higher than 15%, the particles are dispersed in a three-dimensional network-type structure.In capillary flow it was found that the network-type structure was destroyed and replaced by an alignment of particles in the flow direction. This morphological modification resulted in a decrease in both viscosity and post-extrusion swell of the blends. Morphological observations revealed that the ordered structure in the flow direction was concentrated only in the skin region of the extrudate, where the shear stress is higher than the secondary plateau, G _p . A simple kinetic mechanism is proposed to explain the observed morphology.Similarly, steady shear measurements performed in the cone-and-plate geometry revealed alignment of particles in the flow direction for shear stress values higher than G_p.Presented in part at the Symposium Recent Developments in Structured Continua Montréal (Canada) 26–28 May 1993 and at the 45th Canadian Chemical Engineering Conference, Quebec, October 15–18 (1995)     

溅射沉积WSx/Ni/a-C/Ni多层膜的微结构及大气环境摩擦学性能

采用磁控溅射技术在硅基体上交替沉积WS₂、Ni及非晶碳(a-C)层制备出不同Ni层厚度的WS_x/Ni/a-C/Ni多层膜. 利用扫描电子显微镜、X射线衍射仪、拉曼光谱仪、X射线光电子能谱仪等研究了多层膜的成分及微观结构；通过纳米压痕仪、划痕仪和球盘式摩擦磨损试验机等评价了薄膜的力学及大气环境中的摩擦学性能. 结果表明:随着Ni层厚度的增加，WS_x/Ni/a-C/Ni多层膜的致密度下降，n_s/n_w值(S与W原子百分数之比)由0.84降至0.73，WS_x层以微晶或非晶的形式存在. 多层膜的硬度和磨损率均随Ni层厚度的增加先降低后升高，但摩擦系数由0.22升至0.38，结合力先增大后减小. Ni层厚度为6 nm的多层膜的硬度可达13.4 GPa，抗氧化性能和耐磨性最优，磨损率仅为9.47×10–14 m3/(Nm).      

机翼-机身-挂架-短舱复杂流场数值模拟

本文采用分区搭接网格技术,对机翼/机身/挂架/短舱复杂组合体进行网格分布,通过分析计算网格对结果的影响,探讨了网格的划分.基于Roe的近似黎曼解的方法,采用S-A湍流模型,通过求解N-S方程,对该组合体外流场/发动机短舱内流场进行一体化数值模拟,与相应风洞实验数据进行了比较与分析,取得了与实验数据较为吻合的结果.与无发动机短舱的组合体的气动特性进行比较,分析了短舱对翼身组合体的气动干扰.     

On free energy-based formulations for kinematic hardening and the decomposition F = fpfe

Within the framework of linear plasticity, based on additive decomposition of the linear strain tensor, kinematical hardening can be described by means of extended potentials. The method is elegant and avoids the need for evolution equations. The extension of small strain formulations to the finite strain case, which is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, proved not straight forward. Specifically, the symmetry of the resulting back stress remained elusive. In this paper, a free energy-based formulation incorporating the effect of kinematic hardening is proposed. The formulation is able to reproduce symmetric expressions for the back stress while incorporating the multiplicative decomposition of the deformation gradient. Kinematic hardening is combined with isotropic hardening where an associative flow rule and von Mises yield criterion are applied. It is shown that the symmetry of the back stress is strongly related to its treatment as a truly spatial tensor, where contraction operations are to be conducted using the current metric. The latter depends naturally on the deformation gradient itself. Various numerical examples are presented.     

SINS/SAR/北斗组合导航系统

针对SINS/SAR/北斗组合导航系统中,图像匹配定位和北斗定位具有一定延迟的问题进行研究.首先,提出了采用曲线拟合的方法解决量测滞后问题.然后,在联邦滤波理论的基础上,研究并给出了一种基于故障检测函数的信息分配新方法.最后,将以上两种方法运用到SINS/SAR/北斗组合导航系统中进行了计算仿真.仿真结果表明:采用曲线拟合的方法和动态调整信息分配系数的方法后,可使系统位置误差由几十米减小为几米,并提高了系统的抗干扰能力.     

智能车辆SINS/DGPS/视觉/数字地图组合导航技术

为适应自主驾驶车辆的高精度、高频率与高可靠性的导航要求,提出了一种机器视觉/数字地图/CP-DGPS共同辅助SINS的智能车辆组合导航方法,建立了组合导航系统的滤波模型。该滤波模型的量测信息不仅包括GPS与SINS形成的位置与姿态观测信息,还包括机器视觉/数字地图/SINS形成的横向偏差观测信息。通过对SINS的多重冗余辅助,使得导航系统具备容错能力。仿真结果表明,该组合导航系统能为智能车辆提供其空间位置、速度、加速度与姿态角等众多导航信息,并具有100Hz的高频输出、厘米级的导航精度和容错性能,当GPS较长时间中断时,通过SINS/视觉/数字地图的组合仍能为智能车辆提供可靠的导航数据。     

Group theoretic methods for approximate invariants and Lagrangians for some classes of y″+εF(t)y′+y=f(y,y′)

Some recent results on the Lie symmetry generators of equations with a small parameter and the relationship between symmetries and conservation laws for such equations are used to construct first integrals and Lagrangians for autonomous weakly non-linear systems, y″+εF(t)y′+y=f(y,y′). An adaptation of a theorem that provides the point symmetry generators that leave the invariant functional involving a Lagrangian for such equations is presented. A detailed example to illustrate the method is given (and other examples are discussed). The (approximate) symmetry generators, invariants and Lagrangians maintain the perturbation order of the ‘small parameter’ stipulated in the equation — first order in this case.     

双K断裂模型粘聚韧度KcIc实用插值计算方法

为了配合《水工混凝土断裂试验规程》在工程界的推广使用,提出了双K断裂模型中在临界状态时分布在虚拟裂缝上的粘聚力σ(x)产生的粘聚韧度KcIc的二元拉格朗日插值计算方法,进而由准脆性材料韧度三参数定律计算了混凝土起裂韧度KiInci。与粘聚韧度KcIc积分计算和简化计算方法的比较,表明此插值计算方法具有很高的精度,计算过程简化,使用计算器即可实现,便于工程人员实际使用。     

基于SINS/TAN/ADS/MCP的无人机组合导航系统

为实现无人机高精度高可靠性导航,提出了一种以捷联惯性导航系统(SINS)为主,以地形辅助导航(TAN)、大气数据系统(ADS)及电子磁罗盘(MCP)为辅的组合导航方式。通过分析SINS、TAN、ADS及MCP单一系统的工作原理及输出误差模型,构建了SINS/TAN、SINS/ADS及SINS/MCP系统的状态方程及观测方程,最后采用联邦卡尔曼滤波方式实现了对各组合系统的信息融合。仿真数据对比表明:SINS/TAN系统位置误差较小,但航向误差较大;SINS/ADS系统速度误差较小且比较稳定,但位置误差随时间发散;SINS/MCP系统航向误差方差可达0.3783’,但其位置和速度估计精度不理想;而SINS/TAN/ADS/MCP系统能够克服上述不足,实现所有导航参数误差估计的高精度。     

基于P-S-N曲线的强度退化随机模型

强度退化一般具有随机性和不可逆性,而Gamma过程是一个独立非负的增量过程,具有描述强度退化特性的基本属性。由于强度退化过程中,表征退化状态(磨损、裂纹、腐蚀等)的数据很难直接测量,属于典型的缺失数据,而表征材料疲劳性能的P-S-N曲线一般易于获得。因此,本文假定Gamma过程的形状参数为线性函数,并利用材料的P-S-N曲线对Gamma过程的特征参数进行估计,由此建立基于P-S-N曲线的强度退化随机模型。最后,利用20CrMnTi钢的疲劳试验数据对所建模型的有效性进行验证和分析。结果表明,所建模型能够有效描述材料强度退化的宏观趋势。     

Mo/Al2O3复合材料的耐磨性

无压烧结制备了不同组分的Mo/Al2O3复合材料样品,对样品的磨损行为和磨损机理进行了研究,并用电子探针分析了其磨损形貌.结果表明:Mo/Al2O3复合材料的磨损率随Mo含量的增加呈上升趋势,在30vol.%Mo时出现峰值;摩擦系数随着Mo含量的增加而增大,20vol.%Mo样品的摩擦系数较小;Mo含量不超过60%时,当出现Mo的连续相或者Al2O3的连续相时复合材料表现出较好的耐磨性;Mo含量较低时磨损机理表现为脆性脱落,而Mo含量较高时材料的磨损机理主要为磨粒磨损.     

On Anisotropic Elastic Materials for which Young''s Modulus E ( n ) is Independent of n or the Shear Modulus G ( n , m ) is Independent of n and m

It is shown that, among anisotropic elastic materials, only certain orthotropic and hexagonal materials can have Young modulus E(n) independent of the direction n or the shear modulus G(n,m) independent of n and m. Thus the direction surface for E(n) can be a sphere for certain orthotropic and hexagonal materials. The structure of the elastic compliance for these materials is presented, and condition for identifying if the material is orthotropic or hexagonal is given. We also study the case in which n of E(n) and n, m of G(n,m) are restricted to a plane. When E(n) is a constant on a plane so are G(n,m) and Poisson's ratio ν(n,m). The converse, however, does not necessarily hold. A plane on which E(n) is a constant can exist for all anisotropic elastic materials. In particular, existence of such a plane is assured for trigonal, hexagonal and cubic materials. In fact there are four such planes for a cubic material. For these materials, not only E(n) is a constant, two other Young's moduli, the three shear moduli and the six Poisson's ratio on the plane are also constant.     

开放空间H2/CH4/空气爆炸实验与数值模拟研究

近年来氢的使用范围逐渐发展到各个领域, 含氢多元混合物气体在工业生产及生活燃料中被普遍使用. 为了保障含氢气体在生产、运输、使用等各个环节的安全性, 构建了开放空间混合气体爆炸测试实验系统, 研究了H₂/CH₄/空气混合气体爆炸压力及火焰传播特性, 给出了不同氢摩尔分数(100%, 75%, 66.67%, 50%, 33.33%)、混合气体当量比(0.8, 1.0, 1.1, 1.2, 1.4)、可燃云团尺寸(1 m3, 4 m3, 8 m3)及障碍物约束等因素对混合气体爆炸压力及火焰的影响规律. 基于经典TNT当量法, 建立了考虑混合气体组分比及可燃云团尺寸的最大爆炸超压预测模型, 修正了爆炸火焰传播半径理论模型. 结合高精度数值模拟技术揭示了加气站内建筑结构对混合气体爆炸的影响. 研究表明, 氢气的加入能够明显增强气体爆炸强度, 最大爆炸超压、火焰传播速度均随氢摩尔分数的增加而增大, 随当量比的增大先增大后减小, 当量比为1.1~1.2时最大; 通过对大尺度混合气体爆炸数值仿真与分析发现, 加气站内不同建构筑物条件下爆炸火焰传播距离、传播速度、最大爆炸超压等关键参数明显不同, 顶部和背部同时约束时, 爆炸伤害范围及事故后果最严重, 因此在划定加气站安全距离时, 应充分考虑不同建筑结构的影响.