两自由度振动系统的斜碰撞分析

研究斜碰撞振动系统动力学的一个关键问题是对系统在碰撞前后的状态进行合理描述和正确计算．针对两弹性体斜碰撞问题，基于瞬间碰撞假设，提出了采用步进冲量来分析和求解斜碰撞前后的状态关系；并以弹簧摆和振子组成的两自由度斜碰撞振动系统为例，具体介绍了该算法如何实现．用解析方法讨论了该系统在斜碰撞过程中可能出现的各种力学现象，将冲量步进算法得到的数值解与解析结果进行对比，取得了完全一致的结果．该数值方法能适应多种斜碰撞问题的计算．     

摩擦学系统条件转化研究

通过对摩擦学系统条件转化的研究和转化实例分析 ,提出了解决摩擦学系统条件转化问题的新思路和方法 .人工智能技术为摩擦学系统条件转化研究提供了有效的手段 ,从而使得将某些摩擦系统条件下获得的摩擦学特性转化到其它系统条件下使用成为可能     

Applications of the group of equations of motion of a polytropic gas

The machinery of Lie theory (groups and algebras) is applied to the system of equations governing the unsteady flow of a polytropic gas. The action on solutions of transformation groups which leave the equations invariant is considered. Using the invariants of the transformation groups, various symmetry reductions are achieved in both the steady state and the unsteady cases. These reduce the system of partial differential equations to systems of ordinary differential equations for which some closed-form solutions are obtained. It is then illustrated how each solution in the steady case gives rise to time-dependent solutions.     

A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method （DEM）. Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.     

A version of modeling of nonlinear-hereditary viscoelasticity of polymer materials

We propose a version of the mathematical model of nonlinear-hereditary viscoelasticity of polymer materials, which is used to predict strain processes of various complexity, from simple relaxation and simple creep processes to complicated strain recovery processes and reverse relaxation processes with alternating loading and unloading.     

Dynamic behavior and prevention of the damage of material of the massive hammer of the scrap shredding machine

Shredders are used for comminuting the metallic scrap fed to the electric arc furnace and consist of a set of hammers connected to a main rotor, whose rotation converts the kinetic energy into a strong impact. Design of the hammer is still based on some daily practice, but often it looks insufficient to predict the effects of wear and the cracks monitored in service. To reduce costs and improve the product quality manufacturers of shredders urgently need for a design tool suitable to predict the hammer dynamic behavior, the damage of material and to locate the stress concentration. Unfortunately no comprehensive design approach was yet proposed in the literature. This paper investigates the behavior of an industrial prototype of shredder to develop such as design tool. A first rotor-dynamic analysis was combined with a numerical investigation, performed through the Multi Body Dynamics and Finite Element Method, respectively. Results were then compared to some experimental evidences. Damage effects were tentatively related to some design parameters, the material properties and the loading conditions of the hammer. Results were used to increase the performance of a new shredder hammer being designed by refining the cutting edge profile and by selecting a different material.     

Experiments of free vibration of shells of revolution

This paper presents experimental techniques used in and results obtained during a series of experiments performed to investigate the free-vibration behavior of 15-in. base-diameter spherical and paraboloidal shell models of various geometric parameters and boundary conditions. The models were manufactured from polyvinyl-chloride (P.V.C.) sheets by a thermo-vacuum process using special molds and templates. To provide the necessary excitation power, a variable control amplitude/frequency audio oscillator was used to drive a loudspeaker which was mounted underneath the models. A recently developed noncontact fiber-optics instrument, referred to as the “Fotonic Sensor”, was employed in determining the motion of the models. Thirty-two models of different configurations and boundary conditions were tested in the series. The natural frequencies were observed for all models, while the mode shapes associated with the first four-to-six resonant frequencies were mapped only for some of the models, using special scanning devices.     

Analysis of the mechanics of perforation of projectiles in metallic plates

A mathematical model has been developed to describe the mechanism of normal perforation of projectiles in metallic targets. The perforation process is considered to be divided into three interconnected stages. The analysis accounts for an effective mass of the bullet due to part of the target material moving with the bullet, the deformation of the bullet during penetration, and the increased strength of the target material at high rates of loading. The analysis enables the residual velocity to be calculated as a function of the target thickness and its mechanical and physical properties, and of the mass, geometry and impact velocity of the projectile. The geometry of the cavity, i.e. entrance and exit diameters and plug thicknesses, are factors in the analysis and are empirical quantities. The present theory can also predict the force-time curve and the contact time for the perforation process.     

沙漠地貌演化过程的湍流大涡模拟研究

采用大涡模拟和混合粒径群体沙粒运动算法结合内置边界方法来模拟沙波纹与沙丘的演化和发展,在平坦沙区形成沙波纹的同时,在沙丘上同样也出现了沙波纹的结构,即沙波纹的发展出现了多尺度现象.此外,还分析了粒径对沙波纹与沙丘自身形态演化和发展的影响,以及沙丘对平坦沙区沙波纹形成发展的作用.     

Instability of sintering of porous bodies

Sintering models are discussed and used to analyze flow instabilities that may arise during preliminary compaction of powders. These instabilities can be at the origin of heterogeneities in the densification. The material is modeled as a viscoplastic thermal sensitive porous material. The modeling includes the limit case of a linear viscous material. The effects of sintering conditions (temperature and pressure in the case of pressure sintering) and the effects of material characteristics such as porosity, heat capacity, theoretical density, surface tension, particle size and creep parameters on stability of sintering are investigated. The heat release associated with the plastic flow is shown to sometimes have an important role. Stability criteria are derived and applied to the analysis of sintering and hot isostatic pressing, using various sintering models. These stability criteria can be used to optimize the densification process; one can control, for example, temperature so as to avoid any instability. Stability maps enabling an optimization of temperature–pressure regime in hot isostatic pressing are built for sample metal (nickel) powder.     

Studies of effect of dynamic preloads on mechanical properties of steel

In order to determine the effect of load history upon the yield characteristics of a low-carbon steel, specimens of low-carbon steel have been subjected to initial dynamic compressive or tensile loads. The load-time function was approximately that of a sine wave of half-period duration with a half-period time of about 1 msec. The intensity of the load was varied; scme specimens were subjected to elastic strains for loads in excess of the static yield stress but less than the dynamic yield stress, while in others gross yield was initiated. These specimens were then aged for a short time at temperatures ranging from 68 to 250°F and then retested dynamically or in static tension. Upper and lower yield stresses and the inelastic microstrain which preceded gross yield on the retest have been used to evaluate the extent of damage and recovery. The results of these studies tend to confirm a yield phenomenon predicted by dislocation theory.     

Homogenization of the equations of the Cosserat theory of elasticity of inhomogeneous bodies

The paper deals with the homogenization of a boundary value problem for an inhomogeneous body with Cosserat properties, which is referred to as the original problem. The homogenization process is understood as a method for representing the solution of the original problem in terms of the solution of precisely the same problem for a body with homogeneous properties. The problem for a body with homogeneous properties is called the accompanying problem, and the body itself, the accompanying homogeneous body. As a rule, a constructive homogenization procedure includes the following three stages: at the first stage, the properties of the inhomogeneous body are used to find the properties of the accompanying homogeneous body (efficient properties); at the second stage, the boundary value problem is solved for the accompanying body; at the third stage, the solution of the accompanying problem is used to find the solution of the original problem. This approach was implemented in mechanics of composite materials constructed of numerous representative elements. A significant contribution to the development of mechanics of composites is due to Rabotnov [1–3] and his students. Recently, the homogenization method has been widely used to solve problems for composites of regular structure by expanding the solution of the original problem in a power series in a small geometric parameter equal to the ratio of the characteristic dimension of the periodicity cell to the characteristic dimension of the entire body. The papers by Bakhvalov [4–6] and Pobedrya [7] were the first in the field. At present, there are numerous monographs partially or completely dealing with the method of a small geometric parameter [8–14]. Isolated problems for inhomogeneous bodies with nonperiodic dependence of their properties on the coordinates were considered by many authors. Most of such papers published before 1973 are collected in two vast bibliographic indices [15, 16]. General methods were considered, and many specific problems of the theory of elasticity of continuously inhomogeneous bodies were solved in Lomakin’s papers and his monograph [17]. The theory of torsion of inhomogeneous anisotropic rods was considered in [18]. In 1991, in his Doctoral dissertation, one of the authors of this paper proposed a version of the homogenization method based on an integral formula representing the solution of the original static problem of inhomogeneous elasticity via the solution of the accompanying problem [19, 20]. An integral formula for the dynamic problem of elasticity was published somewhat later [21]. This integral formula was used to develop a constructive method for the homogenization of the dynamic problem of inhomogeneous elasticity, which can be used in the case of both periodic and nonperiodic inhomogeneity of the properties [22]. The integral formula in the case of the Cosserat theory of elasticity was published in [23]. The present paper briefly presents constructive methods for homogenizing the problems of the Cosserat theory of elasticity based on the integral formula.     

Mechanical properties of nanostructure of biological materials

Natural biological materials such as bone, teeth and nacre are nanocomposites of protein and mineral with superior strength. It is quite a marvel that nature produces hard and tough materials out of protein as soft as human skin and mineral as brittle as classroom chalk. What are the secrets of nature? Can we learn from this to produce bio-inspired materials in the laboratory? These questions have motivated us to investigate the mechanics of protein-mineral nanocomposite structure. Large aspect ratios and a staggered alignment of mineral platelets are found to be the key factors contributing to the large stiffness of biomaterials. A tension-shear chain (TSC) model of biological nanostructure reveals that the strength of biomaterials hinges upon optimizing the tensile strength of the mineral crystals. As the size of the mineral crystals is reduced to nanoscale, they become insensitive to flaws with strength approaching the theoretical strength of atomic bonds. The optimized tensile strength of mineral crystals thus allows a large amount of fracture energy to be dissipated in protein via shear deformation and consequently enhances the fracture toughness of biocomposites. We derive viscoelastic properties of the protein-mineral nanostructure and show that the toughness of biocomposite can be further enhanced by the viscoelastic properties of protein.     

Modeling of forming of wing panels of the SSJ-100 aircraft

Problems of inelastic straining of three-dimensional bodies with large displacements and turns are considered. In addition to the sought fields, surface forces and boundary displacements have also to be determined in these problems. Experimental justification is given to the proposed constitutive equations of steady creep for transversely isotropic materials with different characteristics under tension and compression. Algorithms and results of the finite-element solution of the problem are presented for these materials.     

混凝土搅拌车搅拌筒磨损数值分析

混凝土运输过程中搅拌筒的磨损一直是一种常见潜在危害,磨损严重时会导致叶片失效,对搅拌的质量和出料匀质性产生影响。通过实验获取搅拌筒内部的磨损费时费力,因此有必要采取一种数值分析方法对搅拌筒的磨损进行预测并提出改进。本文采用摩擦磨损实验的方法来标定颗粒与搅拌筒之间的Archard磨损常数,采用JKR接触模型表征混凝土的流动性能,采用离散元方法(DEM)对搅拌筒筒体及叶片磨损进行预测分析。通过法向接触能量与切向接触能量的对比,证明搅拌筒中的磨损主要为伴有冲击作用的磨粒磨损,搅拌车搅拌筒中搅拌叶片顶部的磨损较为严重。针对磨损比较严重的叶片顶部进行改进,采用T型耐磨结构等改进叶片结构,叶片顶部结构改进后搅拌筒使用寿命能得到明显提升。     

Integration of linear and some model non-linear equations of motion of incompressible fluids

We suggest a new exact method that allows one to construct solutions to a wide class of linear and some model non-linear hydrodynamic-type systems. The method is based on splitting a system into a few simpler equations; two different representations of solutions (non-symmetric and symmetric) are given. We derive formulas that connect solutions to linear three-dimensional stationary and non-stationary systems (corresponding to different models of incompressible fluids in the absence of mass forces) with solutions to two independent equations, one of which being the Laplace equation and the other following from the equation of motion for any velocity component at zero pressure. To illustrate the potentials of the method, we consider the Stokes equations, describing slow flows of viscous incompressible fluids, as well as linearized equations corresponding to Maxwell's and some other viscoelastic models. We also suggest and analyze a differential-difference fluid model with a constant relaxation time. We give examples of integrable non-linear hydrodynamic-type systems. The results obtained can be suitable for the integration of linear hydrodynamic equations and for testing numerical methods designed to solve non-linear equations of continuum mechanics.     

Experimental verification of the theory of thixotropy of viscoelastic polymer media

Previous studies [1, 2] were devoted to the formulation of a phenomenological theory of the reversible changes (thixotropy) in the physicomechanical properties of viscoelastic media, in particular, polymer systems. The basis of this theory is the idea that the reversible changes in the structure and properties of viscoelastic thixotropic media under the influence of mechanical action are due to a change in their relaxation spectrum. In this case the behavior of the mechanical properties is entirely and uniquely determined by two material functions which completely characterize the given material: the relaxation time (frequency) distribution function, which describes the behavior of the material in the linear region of deformation, and the thixotropy function, which determines the nature of the changes compression) of the relaxation spectrum on transition to the nonlinear region. The object of this approach is to reflect the effect of the change in supramolecular and molecular structures associated with the flow of polymer system, or in the bonds and orientation of the particles in disperse systems, on the viscoelastic and viscosity properties of the systems concerned. The essential validity of this approach was demonstrated in [3], where it was shown that at sufficiently high strain rates changes occur in the structure of the polymer leading to a change in mechanical properties. In [4] the basic structural functions were found. These, in conjunction with the proposed theory of thixotropy, characterize the behavior of a broad group of polymer systems in both the linear and the nonlinear regions of deformation. In this connection it should be noted that whereas for the linear region the accuracy of the laws obtained lies within the limits ± 100%, on transition to the nonlinear region the error may increase, Therefore, for the purposes of a rigorous quantitative verification of the theory we shall use not the universal functions obtained in [4], but the more precise characteristics of the specific material on which the experiments are performed, since those effects with respect to which it is desired to test the theory usually lie within the limits of 30% of the measured quantities.The authors thank G. V. Vinogradov for organizing and discussing their work.     

The solution of the variational problem of the construction of the contour of a two-regime pipe

This paper is devoted to the problem of the optimal shaping of the supersonic part of a pipe in those cases when the engine is designed to operate in two essentially distinct regimes. The different regimes may be determined, for example, by a difference in fuel consumption, in the configuration of the pipe, which may be a consequence of some adjustment in the conditions of the external medium, etc. We consider two cases. In one of these the pipe may be controlled by a central body moved into it, and in this case only two regimes are possible for such a pipe, i.e., when there is a central body and when the central body is absent. In the second, the flow parameters at the inlet of the pipe, which has no subsonic part, vary for some reason while the configuration of the pipe is fixed (for example, due to a change in fuel consumption or in the parameters at the entrance to the air intake, etc.). We obtain the necessary conditions determining the shape of the optimal contour, and to construct it we develop a numerical algorithm. We give examples of optimal pipes, the contours of which are constructed by the abovementioned algorithm and compare them with pipes chosen in accordance with other considerations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 96–103, July–August, 1973.The author wishes to thank A. N. Kraiko for drawing his attention to the problem.     

Analysis of evaporative cooling and enhancement of condenser efficiency and of coefficient of performance

The graphical method to determine with the aid of a Mollier i - x diagram (psychrometric chart) combined heat and mass transfer is simulated by a computer program. Heat rejection rates from a plate-fin tube type condenser are determined for various flow rates and inlet state conditions of air and for different degrees of wetting of the heat transfer surfaces. The presence of water and the cooling by latent heat makes it possible to exchange more heat than the unwetted exchanger would even for idealized conditions of infinite heat transfer coefficient of the air. The evaporative cooled condenser also can exchange heat with ambient air which has much higher temperature than the condensing fluid. Evaporative cooling increases heat transfer by a factor of more than three for saturated inlet air and greater than five for lower inlet humidities. Wetted heat exchangers require less extended surfaces and can operate effectively with bare tubes only. Wetting the condenser of a refrigeration or heat pump system makes it possible to exchange the condenser load at lower temperatures. This yields an increase of COP of the order of 30 to 60% and therefore a substantial decrease in compressor power and its energy consumption.