论经典力学中的参考系

力学最本质的问题是物体的受力与其运动的关系问题,本文对经典力学中的参考系进行了梳理和讨论,主要得到了以下结论：(1)探讨了牛顿第一运动定律在物理学和力学上的基础意义,利用该定律既可以对惯性参考系进行定义,同时也能够对时间进行度量;(2)指出了\绝对静止坐标系" 未必存在,但近似的\绝对静止坐标系" 却很容易找到;(3)分析了质心平动参考系的特殊性,总结了其对惯性参考系动力学理论在形式上的影响。     

多点碰撞的力学模型

在理论力学的教科书中,一般只讨论均质的、表面光滑的球形物体之间的碰撞问题.本文将讨论任意形状的,表面光滑的物体之间的碰撞问题,并且参与碰撞的物体可以是任意多个.在碰撞前或碰撞后,我们把物体视作刚体.但是在碰撞过程中,必须考虑物体的变形并利用相应的变形协调条件.定义1 在两个物体的碰撞过程中,物体发生最大变形的时刻叫做临界时刻.     

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.      

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.     

论理论力学中摩擦力和摩擦角概念的引入

从逻辑的和有利于学生对问题的理解的角度出发,对理论力学教学中摩擦力和摩擦角这些概念的引入,给出了另一种引入方法,得到了物体失去平衡的两种临界状态．这种方法对初学者在理解相关的概念上有所帮助,讨论了物体的状态与受力之间的关系,并对这种引入方式的优点进行了分析．     

读者·作者·编者

教学中常参考《力学与实践》的"教育研究"一栏中的文章,并介绍给学生.学生反应很好.希望编辑部可以把1989年之前的文章也上载,让会员可以下载这些"老"文章,这些"老"文章中很多讨论(如"功"的定义及很多老师对此的热烈讨论),即使在今天的教学中也很有参考价值.(澳门,罗健豪)2008-1-27     

小问题 (十七)

《小问题》栏欢迎来稿出题,题目(附解答)请寄北京大学力学系《小问题》组,采用者将致薄酬。37.自由运动的"魔方"有几个自由度?(复旦大学数学系陈 ...     

小问题

《小问题》栏欢迎来稿出题,题目(附解答)请寄北京大学力学系《小问题》组,采用者将致薄酬。37.自由运动的“魔方”有几个自由度?(复旦大学数学系陈     

关于滑动摩擦力的方向问题——与周庆华老师商榷

<正> 《力学与实践》1987年第3期发表了周庆华老师的一篇文章,题为《摩擦力的方向问题及其判断方法》.本人持不同意见,在此和您商榷.文中(指《摩擦力的方向问题及其判断方法》一文,下同)所说的第一种情况是:“主动力大小未知,求物体或物体系平衡时主动力的范围,此时静滑动摩擦力的方向不能任意假设,必须经分析后确定其正确方向,否则不能解出正确的值.”实际上,此时只要约束充许,静滑动摩擦力的方向是可以假设的,而且对于不易确定静摩擦力的方向的问题,假设其方向是方便的,甚至     

多自由度结构各支座运动所引起的振动

过去对于在动荷载作用下结构振动的分析做了很多工作.但是,对于有限个支座运动引起结构振动的分析,相对来说成果较少.1964年笔者在文中,讨论了有阻尼多自由度体系各支座发生不同运动所引起体系的强迫振动.该文曾在1965年中国建筑学会和土木工程学会联合召开的房屋结构和动力机械基础振动学术会议上提出.1971年日本学者青柳史郎也研究了相同的问题,其成果于1974年被编入著作、1980年被编入著作,并在工程设计中得到广泛地应用.青柳史郎所研究的问题和力学模型与笔者完全相同.但是,由于他列出的振动微分方程不成立,致使所得结果不正确(详见后面的讨论).     

A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

自由度对鱼类自主游动数值模拟结果的影响

采用自适应浸没边界方法,数值模拟了仿生鱼在不同自由度个数情况下的游动,对比分析了自由度个数对仿生鱼受力、能耗、推进效率以及尾涡结构的影响。研究结果表明,推进效率随着自由度个数的增加而略有降低;当仿生鱼在自主游动过程中没有侧向运动速度时,侧向受力幅值会大幅度提高。另外,当采用"六自由度模型"进行模拟时,仿生鱼很难沿直线运动,从而导致定量分析的困难。     

带转动自由度的内参型非协调元研究

非协调元虽然破坏了单元间位移的连续性，却能很好地反映弯曲类变形，然而在不增加单元结点自由度的情况下，非协调元的计算精度总是滞留在某一水平，无法得到较大改变。基于修正后的位移型Reissner泛函中引入独立转动场的变分原理，采用连续介质力学中的转动自由度的定义，转动场采用结点真实转角来插值，结合平面四结点单元讨论了有效附加非协调位移的合理形式，引入了适用于任何四边形单元的非协调位移函数，从而建立了一种带转动自由度的平面四结点内参型非协调元模型。本文单元能通过分片检验，并易于与带转动自由度的梁单元相容．教值算例表明具有较高的计算精度。     

Subharmonic steady vibrations of a non-linear damper with two degrees of freedom and viscous damping

The steady-state. $\text{1}\text{3}$ subharmonic vibrations of a dynamic damper (or vibration absorber) with two degrees of freedom, sinusoidal forcing function and internal viscous damping. are presented. The study of these oscillations leads to the determination of suitable “form functions” of the solutions, by following a methodology recently introduced by Nocilla for studying the harmonic vibrations of non-linear systems with one and two degrees of freedom. The proposed theory. which is valid even if the non-linearity is large, gives satisfactory results in all the cases in which the subharmonic component is predominant in the steady-state oscillation of the system.     

一个简洁有效的带旋转自由度的平面三角形单元

从原始的Allman单元[1]出发,构造出一个简洁有效的带有旋转自由度的平面三角形单元。该单元基本保持了Allman单元的精度,同时消除了多余的零能模式,而且使转动自由度等同于连续介质力学中关于旋转分量的定义,并对旋转自由度自身的正确性进行了考核。     

Adiabatic invariants for dynamical systems with one degree of freedom

Adiabatic invariants for dynamical systems with one degree of freedom, whose equation of motion is (1), and where the existence of the corresponding Hamilton action integral is not imposed, are established. The adiabatic invariants may vary according to their structure. Using the theory a few particular problems, including non-autonomous Duffing and Van der Pol oscillators, are analysed. Finally, it is indicated how the adiabatic invariants can be used for finding approximate solutions, stability analyses and for plotting phase curves.     

Motion control of the flexible manipulator via controllable local degrees of freedom

In order to improve motion accuracy of the flexible manipulator, an idea of using its topological characteristics to suppress vibration is suggested. The concept of controllable local degree of freedom is proposed and introduced to the topological structure of the flexible manipulator. It is shown that the arbitrary motion provided by the controllable local degrees of freedom plays an important role in eliminating undesired effects of the flexibility. On this basis, a method for reducing motion error of the flexible manipulator is put forward. By planning the motion of controllable local degrees of freedom, the appropriate control force can be constructed to increase the damping force and eliminate the exciting force of the flexible manipulator, thereby improving the end-effector accuracy. The results, demonstrated by the numerical simulations, are highly promising and suggest that controllable local degrees of freedom can be a useful tool in combating the undesired vibration deformation of the flexible manipulator.     

A meshfree-based local Galerkin method with condensation of degree of freedom for elastic dynamic analysis简

Condensation technique of degree of freedom is first proposed to improve the computational efficiency of meshfree method with Galerkin weak form for elastic dy- namic analysis. In the present method, scattered nodes with- out connectivity are divided into several subsets by cells with arbitrary shape. Local discrete equation is established over each cell by using moving Kriging interpolation, in which the nodes that located in the cell are used for approxima- tion. Then local discrete equations can be simplified by con- densation of degree of freedom, which transfers equations of inner nodes to equations of boundary nodes based on cells. The global dynamic system equations are obtained by as- sembling all local discrete equations and are solved by using the standard implicit Newmark＇s time integration scheme. In the scheme of present method, the calculation of each cell is carried out by meshfree method, and local search is imple- mented in interpolation. Numerical examples show that the present method has high computational efficiency and good accuracy in solving elastic dynamic problems.