具有可移动弹性支承输流管道的稳定性分析

研究了具有可移动弹性支承的输流管道的稳定性问题。建立了分段表示的运动微分方程以及弹性支承处的连续条件和边界条件,采用有限差分法导出了复特征方程,分析了弹性支承处的弹性常数、支承位置对输流管道振动频率和稳定性的影响,给出了稳定性区域图,指出了发散和颤振区域。     

Oscillating Tangential Forces on Cylindrical Specimens in Contact at Displacements within the Region of No Gross Slip

The effects of oscillating tangential forces on cylindrical specimens at relative displacements within the no-gross-slip region have been studied experimentally. It is shown that within the no-gross-slip region there is a well-defined region at the onset of tangential displacement within which a primarily elastic deformation is indicated. Energy dissipation studies indicate that in this region the behavior is essentially visco-elastic, confirming the results of published work. This “limit of elastic behavior” has been found and measured for a number of metallic and non-metallic materials including diamond and plastics. At amplitudes below this limit no discernable wear is observed, even after millions of cycles of rubbing. However, at larger amplitudes, wear is rapid and characteristic of fretting corrosion, especially above the gross slip amplitude. Values of elastic tangential compliance at the limit of elastic behavior are determined which are in agreement with published theoretical work.     

Fundamental frequency and testing mode of complicated elastic clamped-plate vibration

Aimed at the modal analysis of complicated elastic clamped-plates, a trigonometric interpolation method of conformal mapping is applied to set up the mapping function between a complicated region and a unit dish region, and the fundamental frequency of the complicated vibrating region is analyzed with the help of the Galerkin method. Taking an elastic rectangle-plate with arc radius as an example, the testing mode frequency band of plates is determined by analyzing the fundamental frequency; meanwhile, according to hamming testing method of multi-point excitation to the single-point response, and by signal processing technology and its software programming, modal parameter recognition of the elastic clamped-plate is completed. Comparing the first order modal frequency with the theoretical fundament frequency, the validity of the testing mode method and theoretical analysis are verified.     

Fundamental frequency and testing mode of complicated elastic clamped-plate vibration

Aimed at the modal analysis of complicated elastic clamped-plates, a trigonometric interpolation method of conformal mapping is applied to set up the mapping function between a complicated region and a unit dish region, and the fundamental frequency of the complicated vibrating region is analyzed with the help of the Galerkin method. Taking an elastic rectangle-plate with arc radius as an example, the testing mode frequency band of plates is determined by analyzing the fundamental frequency; meanwhile, according to hamming testing method of multi-point excitation to the single-point response, and by signal processing technology and its software programming, modal parameter recognition of the elastic clamped-plate is completed. Comparing the first order modal frequency with the theoretical fundament frequency, the validity of the testing mode method and theoretical analysis are verified.     

The topography of the core-region around cracks under modes I, II and III of fracture

The core region, defined as the limiting zone of validity of the various brittle fracture criteria, has been intuitively assumed as a circle. Its experimental determination is based here on a simple asymptotic elastic theory and a verification by the method of reflected caustics. This definition covers the three modes of deformation at the surroundings of the crack tip. For each mode the initial curve of the caustic, which for isotropic elastic materials is always a circle, yields the limits of validity of the linear elastic theory and corresponds to the boundary of the core region. Experimental evidence with profilometers and projected-grating techniques indicates a similar nature of the deformed surfaces adjacent to the crack tip, as this given by the asymptotic analysis theory of stress and displacement distribution around the crack-tip.     

两接触粗糙表面的椭圆弹塑性模型

视两单峰的接触区为椭圆,给出了两接触相糙表面的椭圆弹性通解.根据两单峰塑性接触时单个相糙峰的椭圆抛物面体积守恒推导了椭圆塑性通解.临界弹性干涉量随有效半径比增加而减小.塑性指数越小,临界弹性干涉量减小量越大.临界弹性干涉量随表面粗糙度增加、材料硬度减小而减小.椭圆、GW模型的临界弹性干涉量之比随有效半径比增加而减小.GW模型高估了临界弹性干涉量.椭圆、GW模型的塑性指数之比随有效半径比增加而增加.GW模型低估了塑性指数.有效半径比越大,偏差量越大.     

Studying the stressed state of a pipe wall with nonuniform residual stresses during bending

The change of the stressed state of pipes with a nonuniform distribution of residual stresses during bending in the elastic region of deformation is studied. The increment of stresses during the bending of a pipe is shown to be almost independent of the initial state. During the bending of a pipe in the elastic region, residual stresses are simply summed with stresses induced by an applied external load. The most stable result of estimating the increment of stresses may be obtained by the annular scanning of a pipe and the averaging of the data on the measurements of a signal over conditionally accepted sectors.     

Elastic moduli and plastic collapse strength of hexagonal honeycombs with plateau borders

The theoretical analysis for the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders is proposed and presented here. The variation of cell edge thickness in real honeycombs is taken into account in deriving their elastic moduli and plastic collapse strengths. A repeating element, composed of three cell edges connected at a vertex with Plateau borders of constant radius of curvature and width, is employed to calculate the elastic moduli and plastic collapse strength of hexagonal honeycombs. Results suggest that both the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders depend on their relative density and the volume fraction of solid contained in the Plateau border region. Meanwhile, effects of solid distribution on the elastic moduli and plastic collapse strength of hexagonal honeycombs are investigated, providing a guideline for the optimal microstructure design of honeycombs.     

弹性支承双跨碰摩故障转子系统非线性特性

建立了弹性支承双跨碰摩及油膜故障20自由度转子系统的非线性动力学模型,并进行了数值分析.与刚性支承情况进行了对比,再用仿真试验进行了验证.结果表明,该系统具有明显的混沌特性,且碰摩间隙对弹性支承的非线性特性影响十分明显.弹性支承的转子系统比刚性支承非线性明显增强,混沌区域增大,实际工程中不容忽视.同时,仿真试验结果与数值分析结果基本一致,表明了数值分析结果的可靠性.     

The elastic-plastic wrinkling of rectangular plates subjected to locally uniform tension

After overcoming the difficulty with discontinuity in boundary conditions, the pre-buckling elastic stress field for a rectangular plate subjected to locally uniform tension is given. An iteration procedure for solving an elastic-plastic plane stress problem is developed, so as to obtain the pre-buckling elastic-plastic stress field for the same plates. The effects of the aspect ratio of plates, tensile non-uniformity and material properties upon the stress field are also discussed. By assuming the shape of wrinkling region and the wrinkling mode in it, the dependences of critical wrinkling load and the size of wrinkling region upon the material and geometrical parameters are revealed. It is found that wrinkling is dominant by a combined parameter in elastic case or in plastic case.     

四参数非牛顿流变模型

作者分析总结了现有的流变模型，并提出了一个能全面描述弹流接触区润滑油粘性、粘弹性、弹塑性特征的四参数非牛顿流变模型。     

Experimental measurements of load and strip profile in thin strip rolling

Experiments are described in which plasticine strips are rolled using elastomer rolls. Conditions cover the range from “thick strip” behaviour, in which roll elastic deformations are small, to “thin strip rolling”, in which elastic deformations of the rolls are very significant. Results provide the first direct experimental confirmation of the thin strip rolling model proposed by Fleck et al. (Proc. Instn Mech. Engrs B206 (1992) 119–131). Strip profiles clearly show a short region of reduction at the inlet to the bite and a central region which is relatively flat, in accord with the theory. The profiles do not however show a short region of reduction at the exit as predicted. For intermediate strip thicknesses the measured loads are in reasonable agreement with theory. For the thinnest strips, although the form of the dependence of load on reduction and inlet strip thickness is as predicted by theory, the measured loads are almost an order of magnitude lower than predicted. It is suggested that this is caused either by differences between the assumed rigid–perfectly plastic strip and the real constitutive behaviour of the plasticine, or by errors in treating the rolls as elastic half-spaces, an approximation which is accurate for industrial metal rolling, but is not good for the conditions of these experiments.     

变速旋转圆盘的弹塑性分析及其安定性

本文研究了等厚度变速旋转圆盘的弹塑性分析问题,给出了用角速度和角加速度表示的弹性极限和塑性极限分界曲线以及安定载荷区域。     

板厚对不同胶粘剂胶焊单搭接头中应力分布影响的数值分析

采用三维弹塑性有限元分析方法,研究了板厚对胶焊单搭接头中有效应力分布的影响。计算结果表明,板厚对不同胶粘剂胶焊接头中的有效应力分布有不同影响。对酚醛树脂胶粘剂胶焊接头,搭接区边缘应力高于焊点边缘,搭接区边缘是裂纹的起裂位置;随板厚增加,搭接区边缘的峰应力减小而焊点边缘应力变化不大,使应力分布趋于均匀,对提高接头强度有利。对丙烯酸酯胶粘剂胶焊接头刚好相反。     

The contact of elastic regular wavy surfaces

A complete solution in closed form to the elastic contact of a one-dimensional sinusoidal surface with a flat surface was presented by Westergaard in 1939. This paper is concerned with the elastic contact of a two-dimensional sinusoidal surface with a flat. In this case the stress distribution within the elastic solids is three-dimensional. As the load is increased the contact areas change in shape from being circular to square and finally leave a circular region of no contact when the waves are almost squashed flat. The problem is solved in general using a numerical method due to Kalker, but asymptotic solutions in closed form have been found for light loads and also for heavy loads at which contact is almost complete. The variation of the mean separation with load, which determines the volume of the space trapped between the two surfaces, is also found.     

Coercive-force hysteresis of carbon steels during elastic cyclic tensile deformation

Dependences of the coercive force and mechanical stresses on cyclic tensile in the region of elastic deformation of steel samples with various carbon contents (Armco iron, 3, 8) are investigated. It is shown that the dependence of the coercive force on cyclic elastic tensile deformation is reversible for well-annealed samples. The dependence for plastically deformed steels has a hysteresis loop that is significantly determined by the carbon content and increases with an increasing degree of plastic deformation. It is assumed that the hysteresis of the coercive force as a function of elastic cyclic tensile deformations in plastically deformed carbon steels is caused generally by the appearance “free” carbon atoms, i.e., those not bound in carbide phases, which act as interstitial impurity atoms in the lattice of α-iron.     

鱼雷壳体与试验台架的接触刚度分析

在试验台架上对鱼雷进行冷、热车试验时,试验台架与壳体之间的接触刚度对试验结果有很大影响,同时也是考察台架是否压坏鱼雷试件的一个重要因素,本文中使用ABAQUS软件对鱼雷壳体与台架的接触刚度进行有限元建模计算,并与理论计算结果进行对比。对结果中的接触应力集中及接触应力曲线不连续等现象进行了分析,讨论了壳体弹性模量对接触应力曲线不连续性的影响。结果表明:在壳体上存在应力集中区域的附近同时存在着接触应力曲线沿环向的分布不连续现象,进一步的研究表明接触应力曲线的不连续程度与壳体弹性模量有关,弹性模量越大,该曲线的不连续程度越大。     

圆柱面过盈连接的应力分析

综合以往轴毂过盈连接分析中,只考虑了弹性变形的问题,在此基础上,进一步分析轴毂结构及配合过盈量对应力的影响,以及在怎样的条件下导致其发生塑性变形。根据屈瑞斯卡塑性条件,找出过盈连接由弹性变形过渡到塑性变形的条件,推导了在弹性与塑性情况下连接体内的应力计算公式,完善和丰富过盈配合的应力分析理论。计算实例分析了轴毂结构参数对许用过盈量的影响规律,并通过对毂内应力的分析,发现随着过盈量的增加,毂内塑性区变大,按弹性变形和按弹塑性变形计算的应力结果的差异变大。     

Macroscopic elastic constants of pure metal based on the interactions between microscopic particles

The research activities of the calculation of the elastic constants of metal are mainly focused on the elastic constants of crystal at the micro level. To the calculation of the macroscopic elastic constants of metal, although molecular dynamics method and quasicontinuum method can be used, but there are shortcomings in them, such as a large amount of computation and that the spatial scale of the study model is limited. Therefore, with a pure metal thin plate composed of a single layer of microscopic particles as research object, a new mechanical model is established after the interactions between microscopic particles of the thin plate are applied on the continuum mechanics model of the thin plate. According to this model, the calculation formulas for the microscopic elastic constants, which are the elastic constants of any triangle region in the model, are obtained. After the concept of the ideal micro structure is presented, the calculation formulas for the macroscopic elastic constants, the elastic modulus and the Poisson’s ratio of pure metal are obtained, where the Poisson’s ratio is the constant that is equal to 1?3. As an example, the elastic constants and the elastic modulus of pure copper are solved, where c11 is 175.811 GPa, c12 is 58.604 GPa, c33 is 58.604 GPa and E is 156.277 GPa, the rationality and the correctness of the model are verified. The model presented fully embodies the discreteness of the microstructure of solid, is a development to the continuum model, and is more suitable to reality, more simplified and more new to the study of the macroscopic elastic constants of pure metal.     

Conformal analysis of fundamental frequency of vibration of elastic clamped plates

To calculate the fundamental frequency of vibration of special-shaped and elastic clamped plates, the conformal mapping theory is adopted to separate the interpolating points of a complicated boundary into odd and even sequences, both of which can be mutually iterated, so that the conformal mapping function between the complicated region and the unit dish region is established. Trigonometric interpolation and convergence along the normal direction methods are provided, and the complex coefficients of the conformal mapping function are calculated. Galerkin method is used to obtain the solution of fundamental frequency in the vibrating differential function of the complicated vibrating region. Finally, taking ellipse elastic clamped plates as an example, the effects on fundamental frequency coefficient caused by eccentric ratio e and area size are analyzed. __________ Translated from Engineering Mechanics, 2006, 23(10): 73–76 [译自: 工程力学]