共查询到19条相似文献,搜索用时 236 毫秒
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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. 相似文献
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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. 相似文献
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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. 相似文献
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<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 相似文献
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多自由度结构各支座运动所引起的振动 总被引:1,自引:0,他引:1
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). 相似文献
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Steven Cranford Haimin Yao Christine Ortiz Markus J. Buehler 《Journal of the mechanics and physics of solids》2010,58(3):409-10047
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). 相似文献
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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。 相似文献
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Subharmonic steady vibrations of a non-linear damper with two degrees of freedom and viscous damping
Riccardo Riganti 《International Journal of Non》1980,15(3):173-183
The steady-state. 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. 相似文献
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Dj. S. Djukic 《International Journal of Non》1981,16(5-6):489-498
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. 相似文献
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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. 相似文献
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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. 相似文献