Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a laval nozzle

Within the framework of a two-liquid (two-velocity and two-temperature) model of a continuous medium, the article considers the flow of a mixture of a gas and foreign particles in the subsonic, transonic, and supersonic parts of a Laval nozzle. In the case of a thin layer of pure gas near the wall, the problem is solved in two stages. First, the method of establishment is used to calculate the core of the flow, where the gas with the particles is flowing; under these circumstances, the parameters in the layer of pure gas are determined approximately; then simplified equations (of the type of the equations of the boundary layer) are used to find the distribution of the parameters in the zone of pure gas, and the flow in the core of the stream is refined. Examples of the calculation are given. Use of the method developed permitted establishing some of the special characteristics of the flow of a mixture of gas with particles in a Laval nozzle in the case of Stokes flow around the foreign particles.     

半圆柱壳挠曲问题解析解精确性的研究

壳体力学已于上世纪由多位专家发展成熟,其中简支柱壳挠曲问题采用改进莱维解法的三角级数法解出,但是其解法复杂,手算难以完成．为讨论其结果的精确性,通过编写运行基于MATLAB的运算程序导出实例化解析解,与基于力学基本理论的推想假设对比,再引入有限元计算结果进行比较研究．最终发现,理论解析解应力和位移具有分布形式大致准确性,但仍存在不容忽视的细节与局部性问题．研究表明,理论解法工程意义有限,结果尚需改进．     

Investigation of the microstructure a turbulent jet in a wake

The study of the characteristics of the turbulence in the boundary layer and in free jets is one of the most important problems of the aerodynamics of viscous fluids. The accumulation of information on the pulsation characteristics of jet flows and the establishment of the corresponding governing laws may serve to verify the basic hypotheses of the semiempirical theories of turbulence, and also for the development of more advanced computational methods. In many cases the measurement of the pulsation characteristics of turbulent jets is of practical interest.The studies made up till now [1–5] of the microstructure of turbulent flow in the primary region of submerged axisymmetric jets have made it possible to obtain several interesting results. In particular, in addition to the average velocity profiles, hot-wire anemometric equipment has been used to measure the normal and tangential Reynolds stresses and also the intermittency factor in cross sections of the jet, the distribution of the intensity of the longitudinal and lateral velocity pulsations along the axis, the correlation coefficients and the corresponding integral turbulence scales, etc. These measurements have made it possible to draw several important conclusions on the mechanism of turbulent exchange, on the order of the terms omitted in the equation of motion, and on the semiempirical theories of turbulence [6–9].The common deficiency of the studies mentioned above is that near the boundary of a submerged jet, where the average velocity is practically equal to zero, the intensity of the pulsations is so great that it makes the reliability of the results obtained by means of the hotwire anemometer questionable. In this connection Townsend [6] indicated the advisability of studying the microstructure of a turbulent jet issuing into a low-velocity ambient flow.The present study had as its objective the investigation of the microstructure of the primary region of an axisymmetric jet in a wake flow over quite a broad range of the flow ratio parameter m=u/u₀;here u₀ is the average velocity at the nozzle exit, u is the velocity of the ambient stream. For various values of the parameter m in the primary region of the jet measurements were made of the profiles of the three components of the pulsation velocity and the Reynolds shear stresses, and also the values of the average velocity and two components of the pulsation velocity at a large number of points on the jet axis. The measured profiles of the Reynolds shear stresses were compared with the corresponding profiles calculated on the basis of the boundary layer equations from the experimentally determined average velocity profiles. For two values of the parameter m, in one of the sections of the jet measurements were made of the correlation coefficients of the longitudinal components of the pulsation velocity and the variation across the jet of the integral turbulence scale was determined.The results obtained give an idea of the influence of the parameter m on the characteristics of the turbulent jet in an ambient stream.     

Experimental investigation of the atomization of drops of liquid under conditions of a gradual rise in the external forces

The article gives the results of an experiment on the effect of the physical properties of the liquid and the phase-contact time on atomization of drops under conditions of a gradual rise in the aerodynamic forces of the flow. It is shown that the value of the critical Weber number and the mechanism of the atomization of a drop are determined both by the conditions of the change in the relative velocity of the gas flow at the moment preceding atomization of the drop and by the values of the viscosity complex and the phase-contact time.     

含界面相Voronoi单元的等效弹性常数的计算

采用含界面相Voronoi单元有限元法,根据广义胡克定律,计算了在给定边界条件下,颗粒增强复合材料的等效弹性常数。建立了含多个随机分布的椭圆形夹杂及界面相的VCFEM模型,分析了夹杂体分比,界面相厚度和界面相弹性模量等因素对颗粒增强复合材料等效弹性常数的影响,并利用普通有限元方法对比验证。结果表明,当界面相弹性模量小于基体与夹杂时,材料的等效弹性模量会随着界面相厚度的增大而减小,随着夹杂体分比的增大而减小,并且界面过薄时,材料的等效弹性模量会随着夹杂体分比的增大而增大;当界面相弹性模量大于基体或夹杂时,材料的等效弹性模量会随着夹杂体分比和界面相厚度的增大而增大。而界面相的厚度和弹性模量对材料的等效泊松比的影响较小,材料的等效泊松比主要受夹杂体分比的影响,与其呈反比关系。     

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half-space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of (sub-) hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of (sub-) soft beam and hard half-space but are similar to each other for the system of (sub-) hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity (the shear wave velocity of the beam for the system of soft beam and hard half-space). The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave radiation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.     

EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION

本文首先将以前所得到的关于两个轴对称塑性平面应力问题(薄圆环和旋转盘)的有关方程和计算结果作了一个简单的叙述.这些计算结果是根据两种不同硬化特性的材料和一种理想塑性材料的应力应变曲线在不同负荷下计算得到的.这些结果指出这三种不同材料的应力应变曲线和负荷对于这两个问题的主应力比值和比例应变的影响很小,而对于比例应力的影响则很大.之后,分析了二维的塑性平面应力问题的方程;这些方程考虑了大应变,但不包括体积力(body force).分析这些方程中的包括材料应力应变曲线项和载荷数项的结果,认为假若在边界上的主应力的比值和比例应变不变,则材料的应力应变曲线和载荷对于主应力比值和比例应变的分布的影响可能不大,而对于比例应力的影响则很大.这种边界条件在实际问题中的普通加减下,满足的可能想是很大的.薄圆环和旋转盘的边界条件及所得的结果和这分析的结果是完全一致的.从这些结果并可提出一个简单而相当准确的近似解,最后并将本文所得的结果和依留辛(Ильюшии)的理论——关于小应变下三维问题形变理论的应用条件——作了比较.     

复合柔性结构全局模态函数提取与状态空间模型构建

随着航空航天等领域中实际工程结构的大型化和柔性化,结构的非线性振动和主动振动控制问题越来越凸显.分析和处理此类结构出现的复杂振动问题的关键在于建立系统的非线性动力学模型与状态空间模型.对于由柔性部件、刚体、连接部件构成的复合柔性结构,由于各部件之间的振动耦合效应,单个柔性部件在悬臂、简支和自由等静定边界下的模态与结构的真实模态有较大差异.为此,本文提出复合柔性结构全局模态的解析提取方法,通过全局模态离散得到系统非线性动力学模型,从而构建状态空间模型.该方法采用笛卡尔坐标描述系统的运动,建立系统的运动方程;结合描述柔性部件的偏微分方程、刚体的常微分运动方程、连接界面处力、力矩、位移和转角的匹配条件以及系统的边界条件,利用分离变量法给出统一形式的频率方程,获取系统的固有频率和解析函数表征的全局模态.这里提出的全局模态提取方法不仅便于复合柔性结构固有频率和全局模态的参数化分析,而且为建立复合柔性结构低维非线性动力学模型和状态空间模型提供了有效的途径,对于推进这类结构的非线性动力学分析与主动振动控制研究具有重要意义.      

刚性环梁支撑圆形基坑支护结构变形解析解

将圆形基坑支护结构视为弹性圆柱壳，利用广义Delta函数和Heaviside函数，基于圆柱薄壳轴对称弯曲变形的控制方程，利用Laplace变换及其逆变换，得到了具有任意数目刚性环梁支撑的圆形深基坑支护结构变形的解析解．在此基础上，以某一圆形基坑工程为背景，分析了基坑底部混凝土底板、支护结构底部边界条件、基坑开挖深度以及支护结构的几何和物理参数等对支护结构变形和内力分布的影响，结果表明：随着基坑半径和挖掘深度的增大，支护结构的位移和内力增大，但随着支护结构厚度的增加，径向位移减小，而内力增加．同时，随着支护结构弹性模量的增加，基坑位移减小，但内力几乎没有变化，这些结果为圆形基坑支护结构设计提供了理论依据和指导．     

刨削参数对刨刀载荷特性影响研究及其强度分析

为研究刨刀刨削煤岩过程中刨削参数对刨刀载荷的影响,建立了基于碰撞接触模型的刨刀刨削煤岩动力学模型。采用软件模拟、现场试验的手段,对不同工况条件下的刨刀载荷进行了分析,得到刨削速度、刨削深度及煤岩硬度等刨削参数对刀头载荷的影响规律;并基于仿真结果,对刨刀强度进行了分析和预测。研究结果表明:随着刨削深度的增加,刨刀载荷特征值均有较大幅度的增加,刨削速度、煤岩硬度等刨削参数与刨刀载荷特征值也呈正相关关系,但变化幅度较小。根据仿真结果选取一组最恶劣工况条件进行刨刀强度分析,发现除焊缝局部在接触载荷作用下产生强度失效外,其余大部分区域仍可以满足材料强度使用需求,并不会产生失效;在极限测试载荷条件下刨刀焊缝部位也可能发生强度失效,且有较小概率引发刀头、刀体部分发生断裂失效。研究结果可为刨煤机关键零部件设计优化提供一定的理论基础。     

Rarefied gas flow near the forward stagnation point of a blunt body at hypersonic speeds

With reduction of the density in a hypersonic stream the transition of the flow from continuum to free molecule takes place gradually. The transition region may be divided into several regimes, in each of which a definite physical phenomenon is most significant. For the case of the flow in the vicinity of the forward stagnation point of a blunt body these phenomena include increase of the thickness of the detached shock wave and of the boundary layer, the presence of viscous flow in the entire disturbed layer ahead of the blunt body, reduction of the number of collisions between molecules and the associated relaxation effects, the increasing role of the interaction of the stream molecules with the surface, and the phenomena of slip and temperature jump.     

Stability loss of the micro-fiber in the elastic and viscoelastic matrix near the free convex cylindrical surface

This paper studies the stability loss of the micro-fiber which is near the convex cylindrical surface. It is assumed that the material of the cylinder is viscoelastic and the fiber has the infinitesimal initial imperfection in the form of the periodical curving. Within the scope of the piecewise homogeneous body model with the use of the three-dimensional geometrically non-linear field equations of the theory of viscoelasticity, a method is developed for the investigation of the evaluation of such imperfections. Using the initial imperfection criterion for stability loss, the numerical results on the critical deformation and critical times are presented and discussed. The micro-fibers are classified by the values of the ratio of a modulus of elasticity of the fiber material to that of the matrix material.     

Relaxation of a fluidized bed to the state of a continuous medium

The kinetic equation proposed in [1,2] for describing the behavior of a system of particles in a gas flow differs from the usual Boltzmann equation with respect to the additional terms that take into account random variations of the particle velocity under the influence of the flow. As shown in [2], the collision operator and the Brownian-type operator in the starting kinetic equation describe essentially different simultaneous physical processes of change of state of the particle system: equalization of the mean kinetic energy of the particles and change of energy due to the action of the viscous forces associated with the suspending flow. Therefore the method of solving the kinetic equation used in [2], a direct generalization of the Chapman-Enskog method of solving the kinetic equation it is necessary to investigate method of solving the kinetic equation it is necessar y to investigate the relaxation processes in the system. Moreover, the relaxation of systems of the fluidized-bed type to the continuum state is also of independent interest in connection with the analysis of fast processes in the system, i.e., processes with a characteristic duration of the order of the mean free time.     

Hypersonic viscous shock layer in a swirling gas flow on a permeable surface

A hypersonic swirling flow of viscous compressible gas past rotating axisymmetric blunt bodies is considered, its velocity vector being parallel to the axis of rotation of the body. The body surface is assumed permeable, while, in the general case, the gas is not injected (drawn off) along the normal to the body surface. An analytic solution of the problem, valid at small Reynolds numbers, is found in the first approximation of the integral method of successive approximations. On the basis of the results of the numerical solution, obtained in a wide range of variation of the determining parameters of the problem, we investigate the influence of the swirling of the free-stream flow, the angular velocity of rotation of the body, the Reynolds number and the injection (suction) parameter on the structure of the compressed layer, and the coefficients of friction and heat transfer on the body surface. The influence of the swirling of the flow on the nature of the asymptotic behavior of the viscous shock layer equations at large Reynolds numbers is studied. It is shown that the presence of a nonzero peripheral component for the velocity vector of the gas in the shock layer can lead to a qualitative change in the nature of the flow. Deceased Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–37, November–December, 1986. The authors thank G. G. Chernyi for his useful discussion of the results of the work.     

一类带柔性附件充液航天器姿态机动控制

基于Lyapunov稳定性理论研究了用动量轮控制一类带轻质悬臂梁附件的充液航天器的姿态机动控制问题, 其中晃动液体用黏性力矩球摆模型代替, 悬臂梁附件用若干集中质量代替. 用动量矩定理和Lagrange方程分别推导得到航天器主刚体、等效球摆、等效集中质量的动力学方程, 所用反馈控制律包含了与动量轮角加速度密切相关的权重因子, 利用系统初、终状态和到达最终姿态所需时间解析确定此权重因子. 同时利用Lyapunov稳定性理论得到了实现最终姿态机动的稳定性判据. 数值仿真表明所用控制律的有效性, 分析附件的相对主刚体平面的转角、相对系统质心的高度、长度、刚度、质量、阻尼系数和到达最终姿态所需时间等因素对控制过程中航天器剩余章动角的影响大小.      

一类三维随机动力系统的最大Lyapunov指数

基于一维扩散过程的奇异边界理论,使用摄动方法研究了白噪声参激的一类余维二分岔系统的最大Lyapunov指数渐近表达式和数值解,主要讨论了一维相扩散过程同时存在两类奇异边界以及FPK方程存在平稳解的一般性条件. 通过对参激噪声作用项系数矩阵的分析,给出了不变测度的解析解及其相应的Monte Carlo数值仿真结果,并导出了一维相扩散过程P分岔点的确定方法. 对于一类特殊情形,给出了最大Lyapunov指数的渐近表达式;对于参激噪声作用项系数矩阵的一般情形,则给出了系统最大Lyapunov指数的数值结果.      

Gradient surface ply model of SH wave propagation in SAW sensors

Investigation of the propagation of the wave in SAW sensors is a basis for the research and design of the sensors. With the advance of the sensor, both the effect of environment on the surface ply and the geometry of waveguide are complicated. To consider the complication, a model with gradient surface ply and multilayer waveguide of SH wave propagation in sensor is proposed. The equation of wave velocity is derived by a transfer matrix method. Through the equation, the function of wave velocity increment via the change of parameters in the surface ply is obtained. The effect of the inhomogeneity on the function is also studied. Finally, some influencing factors of the behavior of the sensor are discussed. This study was supported by the National Natural Science Foundation of China (No. 59635140), the Doctoral Education Foundation of the Ministry of Education of China and Aeronautics Foundation of China.     

碳／碳复合材料磨损表面碳结构的激光喇曼光谱分析

采用显微激光喇曼光谱及 X射线衍射考察了基体分别为沥青浸渍碳 /少量气相沉积热解碳和全部气相沉积热解碳的航空刹车用碳 /碳复合材料磨损表面碳结构的变化特征 ,并分析了引起这些变化的原因 .结果表明 ,经过 10次模拟飞机正常着陆刹车试验后 ,相对于石墨化程度各异的磨损次表层炭纤维及基体碳 ,磨损表面各处的石墨化程度及石墨微晶在 a轴方向的尺寸 La趋于均匀 .换言之 ,就复合材料磨损表面拉曼图谱上位于波数 1338.94 cm- 1 的谱峰与15 85 .2 2 cm- 1处的谱峰的积分强度比值 R的倒数 1/ R而言 ,低石墨化程度组元的 1/ R值显著升高 ,而高石墨化程度组元的 1/ R值有所降低 .磨损表面高石墨化程度组元中的石墨微晶通过转动使其 c轴沿磨损表面法线方向择优取向 ,在机械力作用下 ,石墨片层脱离、碎断 ,均匀分布于磨损表面上 .因此 ,在模拟飞机刹车过程中 ,不同结构和密度的 C/ C复合材料磨损表面形成石墨化程度相近的碳结构 ,这是导致复合材料摩擦系数对结构和密度不敏感的重要原因