查询词典 dynamical friction

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Friction are many ways to fitness, with a dry towel friction body, known as "dry cloth friction"; with a soft brush friction, known as "brush friction"; with a cold towel wrung friction is called "cold-water friction"; also can be used "hand-rub the Law" and so on.

磨擦健身的方法很多，用干毛巾磨擦全身，叫作&干布磨擦&；用柔软的刷子磨擦，称为&刷子磨擦&；用拧干的冷毛巾磨擦叫&冷水磨擦&；此外还可以采用&手擦法&等等。

The rule of dry sliding friction wear of vermicular iron was analyzed. The influence of working conditions, composition and structure on dry sliding friction characteristics was investigated, 3D morphologies of friction surfaces of vermicular iron and temperature characteristics of friction surface were discussed. The results showed that, compared with nodular and gray irons, vermicular iron has lowest wear rate, highest friction coefficient and lowest friction coefficient attenuation, so it is suitable to be as the material of braking device.

分析了蠕墨铸铁的干滑动摩擦磨损规律，研究了工况条件、成分、组织对蠕墨铸铁干滑动摩擦学特性的影响，探讨了蠕墨铸铁摩擦表面二维形貌与摩擦表面温度特性，结果表明：蠕墨铸铁与球墨铸铁和灰铸铁相比具有最低的磨损率和最高的摩擦系数与最低的摩擦系数衰减量，适合于作为制动器材料。

The law of factors' affecting degree, which influences the parameters between geogrids and soils in the pulling-out procedure, is obtained. With the concept of 'equivalent pull-out displacement' brought forward, the whole process of pull out tests is divided into two process-" main process (when x 1.0)" and "residual process (when x 1.0)", and three stages-static friction resistance stage, slip friction resistance stage, and residual friction resistance stage.2 The value of friction coefficient between reinforcement and soil varies with their definitions of friction, but each factor' s affecting degree influencing friction pa

将模糊控制理论引入了岩土工程过程分析，考虑影响因素影响程度的变化及其规律，提出了一套可供岩土工程过程分析中参数选择的分析方法，并在筋土界面相互作用参数选取的拉拔试验过程控制中获得实施，为应用有限元法对加筋土结构进行过程中南大学博士论文摘要分析提供了参数选择的新方法；将模糊聚类分析方法应用于加筋土陡边坡状态评定，并提出侧向位移可作为加筋土边坡状态评定的量化指标，而不同类型边坡的侧向位移允许控制值可仿效此法结合工程经验确定。

In the last chapter, on the basis of theories in paper [4, 5], the notions of strong mixing, weak mixing, generator and expansion of the variable-parametric dynamical system are introduced, it turns out that in variable-parametric dynamical system strong mixing implies weak mixing and then implies transitivity; it is proved that if and both are variable-parametric dynamical system, F conjugates with G , the members of F are communicate with each other and the members of G are also communicate with each other, what's more, they are both homeomorphism, then F is strong mixing implies G has the same properties; futhermore, we prove that F is strong mixing implies F Devaney chaos in the sense of modification in variable-parametric dynamical system and that F Devaney chaos in the sense of modification if and only if G Devaney chaos in the sense of modification when semi-conjugate with and they both are communicate and homeomorphism; at last, we illustrate that F has generator if and only if it has weak generator, and we also prove that if F is expansion, then F has generator.

在第三章中，我们在文[4，5]的基础上，提出了变参数动力系统拓扑强混合、拓扑弱混合以及变参数动力系统的生成子、扩张的概念；证明了变参数动力系统拓扑强混合蕴含拓扑弱混合，进而蕴含拓扑传递；证明了：如果，为两个变参数动力系统，F与G拓扑半共轭，且F两两可交换，G两两可交换，它们均为同胚映射，那么F拓扑强混合，则G也有同样的性质；本章还证明了变参数动力系统拓扑强混合蕴含F在修改的意义下Devaney混沌；在此基础上得出了：如果变参数动力系统与变参数动力系统拓扑半共轭，它们都两两可交换，并且它们均为同胚映射，那么F在修改的意义下Devaney混沌当且仅当G在修改的意义下Devaney混沌；得出了F有生成子当且仅当F有弱生成子；如果F是扩张的，则F有生成子。

Rumjantsev used Hamilton's principle with Lagrange's multipliers to generate the dynamical equations of a rigid-fluid coupled system in 1954 and the dynamical equations and their dynamical boundary conditions of a fluid-elastic coupled system in 1969, where the fluid is incompressible and inviscid. In 1990, Liu used Jourdain's principle with Lagrange's multipliers to generate the dynamical equations of a rigidfluid coupled system, where the fluid is incompressible and viscid.

Rumjantsev利用带Lagrange乘子Hamilton变分原理于1954年建立了刚—流耦合系统的动力方程，于1969年建立了流—弹耦合系统的动力方程及其动力边界条件，其中所考虑的流体是不可压无粘液体；Liu利用带Lagrange乘子Jourdain变分原理于1990年建立了刚—流耦合系统的动力方程，其中所考虑的流体是不可压粘性液体。

The friction performances of carbon face were investigated with an inertia friction tester. The torque curve of carbon face was ideal, the coefficient of static friction was lower than that of dynamic in 0.28 MPa, the friction coefficient of static and dynamic decreased with the braking pressure increasing. To the fiber face, the coefficient of dynamic friction of carbon face was more stable in cycle braking process, the wear rate was lower, and it was efficient to protect the couple plate not to be worn.

结果表明：碳质层的摩擦力矩在制动初期上升较快，中间过渡区平稳，尾部翘起较小；在制动压力小于0.28 MPa时静摩擦系数小于动摩擦系数，且动、静摩擦系数均随制动压力增加而减小；相对纤维层而言，采用碳质层摩擦时摩擦力矩曲线形态更好，连续制动时摩擦系数波动较小，磨损率低且能够有效保护偶件，是1种静/动摩擦系数比较低且适用于高载荷工况条件下使用的摩擦材料。

It is difficult to measure the static friction coefficient of the material like polyurethane. The state of friction under very low velocity with small sliding distance is a special state between static and dynamic friction. This state of friction can be called initial stages'friction.

聚氨酯弹性体材料的静摩擦系数是比较难以确定的，本文建议把滑动量较小而滑动速度又很低的这一时期的摩擦称为"初期摩擦"，它是界于静摩擦与动摩擦之间的一种特殊的摩擦状态。

And more, the article dissects the friction of the joggle, notarizes that the character of the friction is mixed friction which is near boundary friction, and get a conclusion that the rolling part of friction can be neglect through a c...

继而对该处的摩擦问题进行剖析，确认滑动性质为接近边界摩擦的混合摩擦，并且通过一个实例计算得出滚动摩擦部分可忽略不计的结论。

The test shows that the butt friction welding process of copper and stainless steel bar can be divided into the following stages approximately: the adhesion at the beginning of friction,friction inside the copper,the expansion of the plastic ring and the friction on the bound surface of copper-stainless steel and the friction in stainless ...

结果表明铜与不锈钢棒料的对接摩擦焊过程大致可分为初始摩擦的粘着；铜内摩擦、塑性环扩展；铜、不锈钢界面摩擦及不锈钢体内摩擦3个主要阶段。在接头形成过程中经历了两次摩擦面的转移。其内容对促进异种材料摩擦焊的接头形成机理研究有积极的作用。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。