Un modèle discret du couplage entre les fils dans une structure tisséeA discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yarns is introduced, the potential energy of which is calculated. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yarn. The contact force is then expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yarn are analysed. The consideration of the coupling enhances the rigidity of the response of the yarn; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yarn. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 331 (2003).     

活性流体流变行为的布朗动力学模拟研究

活性流体在用于开发新材料方面具有巨大潜力, 满足这一需求就要定量掌握活性流体所表现的特殊力学行为, 特别是流变行为. 扩展布朗运动方程, 建立自驱动活性粒子的运动模型, 基于反向非平衡法确定活性流体的黏度, 考察活性粒子体积分数、直行速度和转向扩散系数对活性流体流变行为的影响规律, 确定活性流体特殊流变行为的形成机理. 结果表明, 活性流体的流变曲线可被划分为黏度下降区、过渡区和牛顿区; 活性粒子体积分数越高, 活性流体的非牛顿特性越显著, 活性粒子的直行运动引起活性流体在低剪切速率区域黏度下降, 直行运动和转向运动的耦合作用导致中剪切速率区域流变曲线非单调变化, 活性粒子频繁发生转向运动会导致活性流体非牛顿特性受到抑制; 活性流体的宏观流变学特性和粒子的涨落直接相关, 活性粒子体积分数越高、直行速度越快和转向扩散系数越小, 活性流体中活性粒子越容易产生显著的涨落; 低剪切速率区域内活性粒子涨落明显, 随着剪切速率增大, 活性粒子的涨落逐渐被削弱, 粒子的聚集结构不断被破坏, 最终体系的流变行为类似一般被动流体.      

Influence of an acoustic wave on a system of two spheres in a viscous fluid

In this article we formulate and solve the problem of the influence of radiation forces (forces created by the radiation pressure) on two spheres in a viscous fluid during the transmission of an acoustic wave. On the basis of these forces we investigate the nature of the interaction between the spheres as determined by the mutual disturbance of the flow fields around them as a result of interference between the primary and secondary waves reflected from the spheres. A previously proposed [2] approach is used in the investigations. The radiation force acting on one of the spheres is filtered by averaging the convolution of the stress tensor in the fluid with the unit normal to the surface of the sphere over a time interval and over the surface of the sphere. The stresses in the fluid are represented, to within second-order quantities in the parameters of the wave field, in terms of the velocity potentials obtained from the solution of the linear problem of the diffraction of the primary wave by the free spheres. The diffraction problem is formulated and solved within the framework of the theory of linear viscoelastic solids [6]. The case of an ideal fluid has been studied previously [3–5, 7]. Radiation forces are one of the causes of the relative drift of solid particles situated in a fluid in an acoustic field.S. P. Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 33–40, February, 1994.     

A contribution to the theory of streamer breakdown

The development of a systematic theory of streamer breakdown of a gas requires the consideration of the transport of the region of ionization toward the ionized gas in an electric field depending on the form of the streamer, which in turn is determined by the transport mechanisms [1–3]. In this form the problem is very complicated,and the theory takes the path of investigation of different qualitative models of a streamer [4]. It is assumed in [4] that the rates of anode-directed and cathode-directed streamers are determined by the drift velocity of the electrons. The mechanism of propagation of anode-directed streamers is taken to be the development of avalanche from the leading front of the electrons traveling to the anode. On the side of the cathode, electrons before the front of the cathodedirected streamer are produced due to the transport of radiation from the ionized region [1]. It is shown in [5] that direct photo-ionization is ineffective because of the small range of the quantas, and a mechanism of development of cathode-directed streamer related to the associative ionization of excited atoms is proposed. These atoms are formed by long-span resonance photons from the wings of the spectral line. An interesting prediction of the theory [4] was a linear dependence of the velocity of the streamers on their length. This dependence was confirmed in experiments on the study of streamer breakdown initiated at the center of the discharge gap in spark chambers [6, 7]. At the same time, for streamers developing from avalanche initiated at one of the electrodes the velocity of propagation of the breakdown wave remains constant with a good accuracy in gaps having lengths of the order of 1 m. In the present work a qualitative theory is developed which permits one to calculate the velocity of the an ode-directed streamer in the case where it is independent of the length. Since for pressures of the order of atmospheric pressure the diffusion coefficient of excited atoms [8] is comparable with the electron diffusion coefficient, the effect of radiation transport is disregarded. The stability of the front of the streamer to infinitely small perturbations is investigated. It is shown that, when the finite thickness of the front is taken into consideration, the streamer is stable. It is unstable in the approximation of infinitely thin leading fronts.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 56–65, January–February, 1973.The authors thank A. A. Vedenov, E. P. Velikhov, A. P. Napartovich, and O. B. Firsov for valuable discussions.     

On the conditions of formation of population inversion of atomic levels in a thermally heated recombining plasma

A theoretical investigation is made into the recombination of a thermally heated plasma of a monatomic gas which undergoes gas-dynamic cooling in a supersonic nozzle. A method of approximate analytic calculation makes it possible to determine the necessary conditions for the existence of an effective recombination regime of the flow out of the nozzle that makes possible population inversion of the excited electronic levels of the atom. The conditions of occurrence of inversion are studied as functions of the parameters characterizing the state of the plasma in the reservoir in front of the entrance to the nozzle, the shape of size of the nozzle, and the working substance. Use of the method of blocks of levels made it possible to calculate the degree of expansion needed for the formation of inversion between transitions with different wavelengths, and also to estimate the gain and the specific radiation energy in these transitions. Numerical estimates of the values of the parameters for the case of an argon plasma are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–97, November–December, 1979.We thank S. A. Losev for discussing the results and for helpful comments.     

Flow of an anomalously viscous liquid between two rotating cylinders

One of the most important problems of the theory of processing polymer materials is the investigation of the flow of thermoplasts in the region of deformation of rolling machines. In this paper, an analysis is carried out of this process, based on equations for an anomalously viscous liquid, including the energy equation in the bipolar system of coordinates. An analytical solution is given for this system of equations, and also given are the results of the solution obtained by numerical methods of analysis, taking account of the dependence of the rheological coefficients on the temperature. The dependence of the maximum temperature rise in the region of deformation on the speed of rotation of the rollers, the coordinates of the material feed in the region of deformation, and the rheological coefficients, is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 17–24, March–April, 1976.In conclusion, the authors thank S. A. Regirer for critical comments.     

Resonant interaction of wave packets in a boundary layer

The space-time evolution of resonance-coupled triads of wave packets in a Blasius boundary layer is studied within the framework of weakly nonlinear stability theory. The amplitude behavior of the packet envelopes is determined in relation to their initial shape, the carrier frequency and the region of propagation. As in the case of triads with a discrete spectrum, interaction leads to parametric pumping of the low-frequency fluctuations and explosive nonlinear growth of the packet maxima. The space-time evolution characteristics are expressed in the deformation of the shape and the spectra of the disturbance. Parts of the envelopes are amplified, depending on the local values of the parameters. This leads to sharp discrimination of the peaks and the equalization of their propagation velocities. These effects make it possible to explain the broadening of the spectrum, the stable distribution of the visualization pattern, and the appearance of irregularities in the oscillograms observed in the S transition. In order to analyze the nonlinear evolution of a disturbance initiated by an instantaneous point source, the interaction of a two-dimensional wave train with variable carrier frequency and pairs of three-dimensional low-frequency packets is examined. (The train frequency corresponds to the local maximum of the linear growth rate with respect to R.) The possibility of the progressive parametric excitation of fluctuations over the entire band of frequency parameters is established. This may explain the acceleration of the transition process in the presence of an impulsive disturbance of the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 67–71, November–December, 1988.The authors are grateful to I. I. Maslennikov for useful discussions.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

基于阻抗法的矩形截面均压槽气浮支承静态性能分析

针对CFD仿真方法效率低下的状况,提出利用阻抗法来提升气浮支承承载性能的计算速度. 以矩形截面均压槽气浮支承为研究对象,研究了当均压槽高度、角度、数量、半径和供气压力变化对气浮支承承载性能的影响. 结果表明:与CFD仿真方法相比,阻抗法在保证计算结果精度的前提下可提高气浮支承承载力的计算速度. 当均压槽高度、角度、数量、半径和供气压力增大时,阻抗比会增加,气浮支承的承载力和刚度峰值对应的阻抗比也会增加. 当气膜厚度增加时,阻抗比会增加,但承载力会相应地减小. 本文作者通过阻抗法推导了气浮支承承载力简化计算公式,解决了气浮支承在均压槽方向上简化计算的难点,并为阻抗法在均压槽中的研究与应用提供了理论依据.      

Parameters of a stationary radially symmetrical jet of vapors heated by laser radiation

The solution [1] of the problem of the stationary radially symmetrical movement of vapors heated by monochromatic radiation is generalized for the case of an arbitrary (tabular) dependence of the coefficient of absorption and the adiabatic index on the temperature and density. The calculations of thermodynamical and optical properties of vapors of a number of elements carried out in a wide range of densities and temperatures and the solution referred to made it possible to determine the parameters of a stationary jet of vapors in a wide range of radiation flux densities and characteristic dimension. Some results of the calculations for carbon and aluminum are presented. It turns out that a characteristic property of the distribution pattern of parameters in a jet of vapors is the presence on the surface of a zone of cold vapors and a zone of their heating — the heating wave front. However, for large radiation flux densities the extent of the zone of cold vapors is not large. A rough estimate of the intensity of reradiation of the heated vapors is derived. It is shown that for characteristic dimensions of the vapor layer on the order of 0.3–1 cm the intensity of reradiation can be high enough that the pattern of movement found without considering reradiation can change somewhat. It is shown that the solution examined can be generalized also to the case where the transfer of energy by radiation of the continuous spectrum is taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 58–75, September–October, 1972.The authors are grateful to V. V. Novikova for great assistance in conducting the calculations for the stationary state problem and analyzing their results and to L. P. Markelova and V. A. Onishchuk for help in conducting the calculations of the thermodynamic and optical properties of the vapors.     

球形颗粒遮弹层对高速侵彻弹体的作用机理

在钻地弹威慑之下,重要目标工事外覆盖遮弹层是常见加固和防护手段。硬质球形颗粒（以下简称颗粒）是常见的遮弹层组成结构。本文中将研究高速侵彻弹体与颗粒作用机理,分析遮弹效率的控制因素。首先,基于动态空腔膨胀理论,计及靶的自由面效应和颗粒强度差异,建立了靶对弹体侵彻阻力的表征模型。然后,采用弹靶分离计算方法,模拟并分析了斜侵彻含球形颗粒有限大高强混凝土时弹体的运动与变形,研究颗粒的强度、位置及尺寸对来袭弹侵彻行为的影响规律。结果表明,颗粒的遮弹作用主要取决于与其作用时弹体的姿态,其随颗粒位置变化无明显规律;颗粒强度越高,遮弹效果越好;颗粒半径从1倍到10倍弹径变化时,颗粒对弹体的作用机理从弹道偏转为主转变为弹道偏转与侵彻阻力增加两者耦合。因此,为达到良好的遮弹效果,单层球形颗粒密排遮弹层的颗粒半径建议在5倍弹体直径之上;若采用较小颗粒制作遮弹层,建议采用多层错排方式,且遮弹层厚度须在10倍弹径之上。     

Impact on the surface of a compressible liquid

The evolution of a weak, nearly plane shock wave produced by the impact on the plane boundary of a compressible liquid is considered. At the initial moment the liquid is at rest and occupies the lower half-plane. Then the points of its boundary get instantly velocities directed into the liquid domain. This leads to the formation of a shock wave the intensity of which is non-uniform due to a non-uniform distribution of the impact velocities. Initially the shock wave is plane but then it bends due to the non-linear effects and can later be focused. To analyze the liquid flow, the method of matched asymptotic expansions is used. For finite times the flow and the evolution of the shock wave are described within the framework of the acoustic approximation. For large times the flow becomes non-linear, and the form of the shock front depends essentially on the characteristics of the liquid flow behind it. If the non-uniformity of the impact velocity distribution is slight then the focusing of the shock wave is shown not to occur. The influence of viscosity of the liquid on the structure of its motion is discussed.     

Calculation of plane electric fields in channels of magnetohydrodynamic instruments

The local and integral characteristics of flat MHD channels are studied with allowance for longitudinal and transverse edge effects and heterogeneities in the distributions of conductivity and stream velocity. An analysis is made of the effect of the finite dimensions of the insulating inserts in the longitudinal edge effect and of the modular construction of the side wall in the transverse edge effect on the output parameters of MHD channels. The solution of the problem is based on reduction of the initial quasilinear elliptical equation for the electrical potential with allowance for Ohm's law to an integral equation of the Fredholm type relative to the current density.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 8–16, March–April, 1974.In conclusion the authors thank L. A. Vulis, A. V. Gubarev, and A. L. Genkin for discussion of the formulation of the problem and the results of the work.     

柔性铰柔性杆机器人动力学建模、仿真和控制

本文探究了铰柔性对机器人动力学响应和动力学控制的影响. 首先, 建立由$n$个柔性铰和$n$个柔性杆组成的空间机器人模型, 运用递推拉格朗日动力学方法, 得到柔性机器人系统的刚柔耦合动力学方程. 在动力学建模过程中, 除了考虑杆件的拉伸变形、弯曲变形、扭转变形以及非线性耦合变形对机器人系统动力学行为的影响, 还考虑了铰的柔性对机器人动力学响应和控制的影响. 其中, 柔性铰模型是基于Spong的柔性关节简化模型, 将柔性铰看成线性扭转弹簧, 不仅考虑了铰阻尼的存在, 还考虑了柔性铰的质量效应. 其次, 编写了空间柔性铰柔性杆机器人仿真程序, 研究铰的刚度系数和阻尼系数对系统动力学响应的影响. 研究表明: 随着柔性铰刚度系数的增大, 柔性机器人的动态响应幅值减小, 振动频率变大. 随着柔性铰阻尼系数的增大, 柔性机器人的动态响应幅值减小, 振动幅值的衰减速度变快. 可通过调节柔性铰的刚度和阻尼来减小柔性铰柔性杆机器人的振动, 因此铰阻尼的研究具有重要工程意义. 最后, 研究了铰柔性在机器人系统动力学控制中的影响. 在刚性铰机械臂和柔性铰机械臂完成相同圆周运动时, 通过逆动力学方法求解得到两种情况下的关节驱动力矩. 研究表明: 引入柔性铰会使控制所需的驱动力矩变小, 对机器人控制的影响显著.      

DYNAMICS AND CONTROL OF RIGID-FLEXIBLE COUPLING FLEXIBLE SPACECRAFT WITH JOINT CLEARANCE1)

大型柔性航天器展开锁定后,运动副中仍存在大量无法消除的间隙. 铰链间隙直接影响柔性航天器的姿态 运动和有效载荷的指向精度及稳定度,会对航天器的动力学特性造成较大的影响. 针对这一问题, 提出一种含间隙铰 接的航天器刚柔耦合动力学建模与控制方法. 首先建立含间隙的铰链精确动力学模型,从而构建含间隙铰接的柔性结构 动力学模型. 然后利用哈密顿原理和模态离散方法,建立含间隙铰接柔性航天器离散形式的刚柔耦合非线性动力学 模型,采用 Newmark 算法对非线性动力学方程进行求解. 基于压电纤维复合材料 (macro fiber composite, MFC) 驱动器 构建航天器的刚-柔-电耦合动力学方程,采用最优控制设计控制律. 分析了铰链参数、中心刚体转动惯量、间隙尺寸和间隙数目对航天器动力学特性的影响,着重研究了铰链间隙对航天器姿态运动和结构振动的影响作用. 最后采用 MFC 驱动器对航天器施加主动控制. 结果表明,铰链参数和中心刚体转动惯量影响航天器的固有频率;随着铰链间隙尺寸的增大及间隙数目的增多,航天器的整体刚度逐渐减小,而航天器的姿态角和振动位移响应不断增大;通过基于 MFC 的主动控制,能够实现含间隙铰接航天器姿态运动与结构振动的协同控制,并缓解间隙对系统动态特性造成的影响.     

剪切增稠液体液舱侵彻实验

为研究剪切增稠液体(shear-thickening fluid, STF)液舱对弹体的防护性能,制备特定规格剪切增稠液体,并开展弹体侵彻剪切增稠液舱实验研究。实验中采用高速相机记录液舱侵彻过程中空泡的演化情况,并测试得到了弹体的剩余弹速以及前后靶板变形数据。实验结果显示,剪切增稠液体可有效抑制液舱侵彻过程中空泡的增长,从而降低液舱结构的损伤程度。结合空泡扩展理论模型,并考虑液体密度以及黏度变化对空泡增长的影响,验证了剪切增稠液体在高速冲击下产生的局部密度增大以及固化现象是抑制空泡扩展的主要原因。此外,剪切增稠液体对弹体速度的衰减作用明显,且相同初始弹速下,剪切增稠液体液舱前后靶板变形明显小于水体液舱。将剪切增稠液体填充于舰船液舱防护结构,可显著提高液舱结构的防护性能。     

基于粗粒化方法的类超级碳纳米管自由振动研究

超级碳纳米管是在碳纳米管结构基础上，将每一根碳-碳键替换为碳纳米管而形成的新型结构。类超级碳纳米管是超级碳纳米管对应的宏观结构，在保持外观结构的基础上将尺度放大到宏观尺度。本文建立了类超级碳纳米管的粗粒化模型。基于粗粒化方法，研究了类超级碳纳米管的自由振动。分析了内外管半径以及长度对类超级碳纳米管振动行为的影响。与原结构有限元进行对比，结果表明粗粒化方法能有效的计算类超级碳纳米管的振动行为。     

基于粗粒化方法的类超级碳纳米管自由振动研究

超级碳纳米管是在碳纳米管结构基础上,将每一根碳-碳键替换为碳纳米管而形成的新型结构。类超级碳纳米管是超级碳纳米管对应的宏观结构,在保持外观结构的基础上将尺度放大到宏观尺度。本文建立了类超级碳纳米管的粗粒化模型。基于粗粒化方法,研究了类超级碳纳米管的自由振动。分析了内外管半径以及长度对类超级碳纳米管振动行为的影响。与原结构有限元进行对比,结果表明粗粒化方法能有效的计算类超级碳纳米管的振动行为。     

Microstructural Changes in Surface Layers of Metal During Running-in Friction Processes

Studies of the dislocation structure of surface layers of some FCC and BCC metals, such as copper and steel, after sliding-friction tests for various lengths of time are reported. The results of the transmission electron microscopy and X-ray investigations show that each material is characterized by its own definite state of surface layer structure, which corresponds to the conditions of the friction, such as load, materials of counterbody and others. A sequence of microstructural changes for increasing test time consists of an increase in dislocation density and formation of dislocation pileups and a fragmented structure. It is established that under constant conditions of friction, the characteristics of the microstructure only vary in the running-in period. The kinetics of microstructure formation in the surface layers during friction predetermine the hardening and negative hardening processes and the wear of material. Comparison of the results of investigation of the structure with wear data and the data on roughness changes, shows that the time of transition to stable wear and equilibrium roughness of the surface coincides with the time of stabilization of the structure. The changes of the surface roughness in the running-in period occur simultaneously with those of the microstructure. These two processes are interrelated. First, when the equilibrium roughness is reached, the pressure on the contact spots decreases. Second, the fragmented structure, formed during the running-in period, strengthens the surface layers. Both these phenomena lead to a reduction in the wear rate. The results of this investigation can be used for development of structural methods of tribosystem diagnostics. They show that the running-in period is characterized by the change of microstructural state of surface layers. Consequently, the parameters of the microstructure can be used to determine this period.     

Stability analysis of helical rod based on exact Cosserat model

Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff's kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff's theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler's angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov's stability of the helical equilibrium is discussed in static category. Euler's critical values of axial force and torque are obtained. Lyapunov's and Euler's stability conditions in the space domain are the necessary conditions of Lyapunov's stability of the helical rod in the time domain.