大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

秦沈客运专线高速列车构架蛇行波标准差的试验研究

国内外大多采用轨道横向不平顺作为列车—桥梁(轨道)时变系统横向振动的激振源。实际上，引起此系统横向振动的因素很多，诸如轨道横向不平顺、车轮踏面锥度、轮轨缺陷、车轮与钢轨的制造误差、车辆质量及其载重的偏心等。仅仅考虑轨道横向不平顺，会忽略其他很多因素的影响。相反，机车车辆构架蛇行波反映了引起此系统横向振动所有因素的影响，同时还反映了轮轨实际接触状态。研究证明，构架蛇行波标准差是输入此系统横向振动的能量，因此，有关它的研究十分重要。本文根据秦沈客运专线高速列车(中华之星)构架蛇行波现场测试结果，采用工程概率数值分析方法，对高速列车构架蛇行波标准差进行了统计分析，得出具有99％概率水平的高速列车构架蛇行波标准差与车速的关系曲线，为高速列车—桥梁(轨道)时变系统横向振动随机分析激振源的确定提供了基础资料；同时还列出了具有代表性的高速列车构架蛇行波实测波形图。     

工程因素对围岩稳定性影响三维数值模拟分析

结合某地下工程实际,运用FLAC^3D模拟了巷道断面形状、开挖面距离以及开挖顺序对巷道围岩稳定性的影响,并模拟了围岩深部多点位移规律。结果表明,相同围岩条件下,不同断面形状其力学效应不同,同一断面在不同围岩条件下变形不一样;围岩水平位移曲线随开挖面的距离呈“S”形,围岩水平最大位移主要发生在距开挖面后方 2倍巷道长径的范围内;Ⅲ级围岩深部位移影响范围约 2 .8～ 4 .3m,Ⅳ级围岩影响范围 6 .9～ 7.8m;对较大断面,分步开挖有利于围岩控制。     

基于最大熵方法的水下航行体结构动力响应概率建模

水下航行体结构承受的水动力外载荷具有显著的时空分布不确定性,其引发的结构动力响应,诸如结构最大内力、最大内力发生时刻、最大内力发生位置等也由此产生了不确定性;同时,水下航行体的动力响应还会因其连接或分离结构的拉压刚度不同而出现非线性特征. 为了在水动力外载荷样本有限的基础上,分析水下航行体结构连接非线性对动力响应统计特性的影响, 利用水下航行体结构的简化动力学模型,计算了水动力横向载荷作用下响应的样本统计矩,采用最大熵方法实现了动力响应的概率建模. 在分别求出结构最大内力、最大内力发生时刻、最大内力发生位置的概率密度函数后,通过与蒙特卡洛模拟结果对比验证了最大熵方法拟合的响应概率密度函数精度;而后,基于这些结构响应概率密度曲线讨论了系统连接非线性参数变化对结构动力响应的影响. 最终得出如下结论:连接非线性会导致结构在只有横向力的作用时产生的轴力响应,并且最大轴力概率密度函数峰值会因连接结构非线性程度增大而逐渐增大;连接非线性对不确定性传播有显著影响,当连接非线性比较强时,输入正态分布的载荷所得到的内力响应不是正态分布的;最大内力响应的发生位置也会受到连接非线性程度的影响. 上述结果可以为结构优化提供技术支持.      

Trajectory and Global Attractors of the Boundary Value Problem for Autonomous Motion Equations of Viscoelastic Medium

We introduce the concept of minimal trajectory attractor generalizing the known concept of trajectory attractor of an abstract evolution equation. We obtain several results on existence and properties of minimal trajectory and global attractors without assumptions of any invariance of the trajectory space of an equation. With the help of these results we prove existence of minimal trajectory and global attractors for weak solutions of the boundary value problem for autonomous motion equations of an incompressible viscoelastic medium with the Jeffreys constitutive law. The work was partially supported by grants 04-01-00081 of Russian Foundation of Basic Research, VZ-010-0 of the Ministry of Education and Science of Russia and CRDF and MK- 3650.2005.1 of President of Russian Federation.     

Effects of gas flow and turbulent diffusion on the centrifugal classification of fine particles

Tthe mass movement of fine particles and changes in their trajectories under the effect of centrifugal, gravitational, and aerodynamic forces is studied by numerical modeling of turbulent swirling flow. The effect of turbulent migration of solid particles due to pulsating gas flow velocities on the aerodynamics of particles and, consequently, on the efficiency of the process of separation of particles by size is analyzed. The studies revealed the behavior laws of probability curve of separation of particles by size and showed the effect of regime and geometric parameters on the process of classification of fine powders.     

Propagation of Perturbations in Plane Poiseuille Flow between Walls of Nonuniform Compliance

The evolution of small perturbations in longitudinally nonuniform flows is studied with reference to the problem of the propagation of flow perturbations in a plane channel with walls of variable elasticity. Using the solution of the problem of the receptivity of the flow to local vibrations of the walls, the problem considered can be reduced to the solution of an integral equation for a single function, namely, the complex vibration amplitude of the walls. A numerical method for solving this equation on the basis of a piecewise-linear approximation of the unknown function is proposed. It is shown that the instability wave amplitude changes discontinuously at the junction of the rigid and elastic channel sections. A second method of investigating the process of propagation of perturbations in the flow considered is proposed. This method is based on laws of evolution of perturbations in nonuniform flows and an analytic solution of the problem of perturbation scattering on the junction of walls with different compliance. On the basis of this method the classical stability theory is generalized to include the case of nonuniform flows.     

Free electrogasdynamic flows under conditions of unsaturation

An experimental study was made of electrogasdynamic flows behind sources of charged particles, working under conditions of unsaturation, for the purpose of studying the flow of unipolar reactive jets from present-day-airplane engines, which in a number of cases can work under these conditions. A special corona source was developed, with a change in the take-off current of the electrogasdynamic jet over wide limits; this source was used for the laboratory modelling of such processes. It is shown that the floating potential of an insulated source of charged particles is practically independent of the degree κ of saturation of the electro-gas-dynamic jet, i.e., of the value of the take-off current with a constant velocity of the flow; under these circumstances, the time required for establishment of the floating potential is inversely proportional to the value of κ. An investigation was made of the effect of the surrounding conditions on the characteristics of electrogasdynamic jet with different degrees of saturation κ. It was observed that a decrease in κ brings about an appreciable weakening of this effect.     

Calculation of the explosion of a trotyl bar of infinite length

The dynamics of the explosion of spherical, cylindrical, or flat charges of explosive has been thoroughly studied [1–6]. The form of these charges is such that the energy evolved is distributed under the condition of the instantaneous character of the detonation or of its initiation at the center, along the axis, or at the plane of symmetry of the charge, uniformly over the surface of the charges, which, with an explosion in a homogeneous medium, leads to one-dimensional not fully established motions. It is of interest to investigate the process of the explosion of charges of more general form, where the above distribution of energy ceases to be uniform, and the corresponding motion of the medium ceases to be one-dimensional. An example can be the explosions of charges having the form of a cube, a parallelepiped, an ellipsoid, etc. The study of such cases makes it possible to clarify the resulting redistribution of the energy of the explosion, which can be of importance from the point of view of the search for possibilities of improving the use and the control of this energy. Such investigations have been carried out experimentally (see, for example, [7]); however, up to the present time there has been no rigorous theoretical analysis, which is connected with the great complexity of the corresponding gasdynamic problems. The article discusses the natural generalization of the problem of the explosion of an infinitely long cylindrical charge.     

Investigation of heat transfer at the critical point of a sphere around which flows a hypersonic flow of carbon dioxide gas

The article gives the numerical results of an investigation of flow near the leading critical flow line with the hypersonic flow of carbon dioxide gas around a sphere. The investigation was made on the basis of a simplified system of Navier-Stokes equations for a five-component model of the gas, taking account of dissociation-recombination relaxation processes of the components of the gas, as well as of the excitation and deactivation of the vibrational degrees of freedom of molecules of carbon dioxide gas. The calculations were made in a range of values of the pressure in the oncoming flow from 10^?7 to 10^?3 atm, and of the velocity from 4.5 to 8 km/sec for a sphere of radius 2 m. The surface of the sphere was assumed to be either ideally catalytic or chemically neutral. The dependence of the heat-transfer parameter on the determining parameters of the flow is obtained.     

Stress-strain state of non-thin plates and shells. Generalized theory (survey)

Conclusions Thus, this part of our survey has presented the main approaches that have been taken to the construction of two-dimensional (in terms of the space coordinates) equations of a generalized theory of plates and shells. The solutions of these equations represent a certain approximation of the solution of the initial three-dimensional problem. They are based on expansion of the sought functions into Fourier series in Legendre polynomials of the thickness coordinate. Studies completed on the basis of the given variants of plate and shell theory were systematized and analyzed. In terms of the method of its construction, the theory involves a regular process of replacing the solution of the three-dimensional problem by the solution (or sequence of solutions) of two-dimensional boundary-value problems or initial-boundary-value problems. Numerical results illustrating the convergence of the successive approximation were presented. It should be noted that to make comparison with the results of classical or applied theories, several of the studies cited here presented solutions of problems for thin plates and shells with allowance only for the initial terms of expansions of the stress and displacement components into base functions (Legendre polynomials).S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 3–34, November, 1993.     

动力学与控制论力学系统的自由度

力学系统的自由度定义源自描述系统位形的独立坐标数.在分析力学发展过程中,人们通过对非完整约束的研究,将其拓展为独立的坐标 变分数.本文指出,对于含非完整约束的力学系统,该定义存在不妥之处,给出的自由度会过度限制系统的力学行为.文中研究力学系统在状态空间中的可达流形,指出可达流形维数与描述系统动力学的一阶常微分方程组的最少未知函数个数一致,例如Gibbs-Appell方程与广义速度方程联立的未知函数个数,进而将可达流形维数的一半定义为系统自由度.通过含黏弹性支承的振动系统、在倾斜平面上运动的冰橇等案例,讨论了单个非完整约束导致的半自由度概念,指出其力学意义和与相邻整数自由度的关系.此外,文中还给出两个非完整约束导致系统减少一个自由度的案例,讨论了系统的切丛和余切丛维数.      

基于X-射线CT方法的岩石小裂纹扩展过程分析

岩石的小裂纹起裂及扩展过程是岩石力学研究的一个关键问题。对软硬两种砂岩进行单轴加载试验,同时用高分辨率的螺旋CT扫描机进行实时扫描。通过对获得的CT图像的分析处理发现,CT差值图像中的方差值与小裂纹的扩展速率有密切的关系,建立CT差值图像中的方差值与应力关系曲线,可以直观地看出:1)岩石样品中小裂纹起裂门槛值:软砂岩样品小裂纹扩展的门槛值为岩石强度的55%,小裂纹的扩展强度占整个强度的73%。硬砂岩小裂纹扩展的门槛值为岩石强度的64.5%,小裂纹的疲劳强度占整个强度的79%;2)小裂纹的扩展规律,即:在加载的初期岩石中小裂纹的扩展速率缓慢增大,在小裂纹扩展的门槛值出现之前快速下降,小裂纹扩展的门槛值出现之后又快速增加,最后当裂纹长度达到一定值时与长裂纹扩展速率基本一致。     

导流板对腔口流体自持振荡影响的研究

腔口流体动力自持振荡的频率和导流板的长度有一定关系。本文通过对跨越腔口非稳定层和自持振荡的理论分析，并通过对不同长度导流板的腔、低速流激自持振荡均方压力谱分析的实验研究，给出流激自持振荡的频率与导流板长度之间的关系。流体动力振荡和腔的声驻波共振耦合时，腔内振荡的均方压力达到最大值。根据流速变化时，均方压力谱峰值频率的偏移，分析了导流板长度对流引起的流一腔系统耦合共振的影响。     

Long-term shock loading of solids by a combined charge with explosive initiation

A method and results of calculation of parameters of long-term shock loading of solids, generated by a gas-dynamic former containing a combined charge with explosive initiation, are described. A calculation model based on the concepts of the hydrodynamic theory of detonation and on the theory of combustion of condensed substances is considered. The forcing pressure and the physical laws of combustion of the combined charge are determined in calculations and experiments. The dynamics of the process is studied by an example of calculation of parameters of the loaded solid acceleration pulse in the case of initiation and combustion of a charge consisting of two batches of high explosives: black powder and pyroxylin powder. The effect of the combined charge parameters and combustion-chamber size on the parameters of the shock loading pulse is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 3–10, July–August, 2009.     

高层框架分析的状态变量传递法

取高层框架柱端位移和对应的柱端力作为状态变量,利用传递矩阵和逐层分析的方法来分析以框架。文中取框架的每一层作为基本单元,建立基本单元端部的状态变量与相邻基本单元端部状态变量之间的转换关系。分析过程中,框架烽的增加仅增加上乘的次数,而待求的基本未知量的数目始终保持不变,从而提高了计算机分析问题的能力。     

Entropy generation of radial rotation convective channels

The exchange of heat between two fluids is established by radial rotating pipe or a channel. The hotter fluid flows through the pipe, while the cold fluid is ambient air. Total length of pipe is made up of multiple sections of different shape and position in relation to the common axis of rotation. In such heat exchanger the hydraulic and thermal irreversibility of the hotter and colder fluid occur. Therefore, the total entropy generated within the radial rotating pipe consists of the total entropy of hotter and colder fluid, taking into account all the hydraulic and thermal irreversibility of both fluids. Finding a mathematical model of the total generated entropy is based on coupled mathematical expressions that combine hydraulic and thermal effects of both fluids with the complex geometry of the radial rotating pipe. Mathematical model follows the each section of the pipe and establishes the function between the sections, so the total generated entropy is different from section to section of the pipe. In one section of the pipe thermal irreversibility may dominate over the hydraulic irreversibility, while in another section of the pipe the situation may be reverse. In this paper, continuous analytic functions that connect sections of pipe in geometric meaning are associated with functions that describe the thermo-hydraulic effects of hotter and colder fluid. In this way, the total generated entropy of the radial rotating pipe is a continuous analytic function of any complex geometry of the rotating pipe. The above method of establishing a relationship between the continuous function of entropy with the complex geometry of the rotating pipe enables indirect monitoring of unnecessary hydraulic and thermal losses of both fluids. Therefore, continuous analytic functions of generated entropy enable analysis of hydraulic and thermal irreversibility of individual sections of pipe, as well as the possibility of improving the thermal–hydraulic performance of the rotating pipe consisting of n sections. Analytical modeling enabled establishing of a mathematical model of the total generated entropy in a radial rotating pipe, while the generated entropy of models with radial rotating pipe were determined by experimental testing, with comparisons of the achieved results.