空间站大型伸展机构的运动稳定性分析

从空间站大型伸展机构的运动特点和系统动力学方程出发，着重分析了该系统的稳定性判据。这一问题又可分为五个方面：姿态-伸展-振动耦合系统的分析方法，复杂大系统的分解集结方法，时滞系统和滞后系统的稳定性问题，Stick-Ship运动对系统对系统稳定性的影响，非线性非定常系数稳定性的一般解。其中还对接触、摩擦、碰撞问题，变拓扑系统，非光滑动力学系统等进行了专门的研究，分析了Lyapunov指数方法在这些特殊系统中的适应性。本文对空间站大型伸展机构的稳定性问题进行了较全面的分析，指出了目前在处理这类复杂大系统时存在的一些难点问题，为其设计和研制工作提出了理论基础。     

转子系统不平衡故障的再现方法浅析

针对转子系统不平衡特征再现设计问题,提出1种基于动力学相似关系的模型再现方法。根据转子系统的振动微分方程,通过积分模拟法和量纲分析法建立转子系统中转轴、转盘、弹性支承和不平衡量的相似关系。根据相似关系,设计了原型不平衡转子系统的动力学相似模型,利用有限元方法仿真验证了所得相似关系的正确性。试验采用最小二乘三点法识别原型与模型不平衡转子试验台的不平衡量,给出再现原型不平衡特征的过程,验证了不平衡特征再现设计方法的有效性。总结了基于动力学相似关系的转子系统不平衡特征再现设计方法。     

M数缩尺法旋翼颤振动力相似模型设计

本文以延-2复合材料桨叶旋翼为例,用M数缩尺法尝试设计了缩尺比为1/5的颤振相似模型。设计从旋翼颤振微分方程开始,应用π定理得出10个独立相似准则数,列出各有关物理量缩尺因子后进行模型结构设计,从而得出了若干有益的结论。     

Diversity of Comets: Formation Zones and Dynamical Paths

The past dozen years have produced a new paradigm with regard to the source regions of comets in the early solar system. It is now widely recognized that the likely source of the Jupiter-family short-period comets (those with Tisserand parameters, T > 2 and periods, P, generally < 20 years) is the Kuiper belt in the ecliptic plane beyond Neptune. In contrast, the source of the Halley-type and long-period comets (those with T < 2 and P > 20 years) appears to be the Oort cloud. However, the comets in the Oort cloud almost certainly originated elsewhere, since accretion is very inefficient at such large heliocentric distances. New dynamical studies now suggest that the source of the Oort cloud comets is the entire giant planets region from Jupiter to Neptune, rather than primarily the Uranus-Neptune region, as previously thought. Some fraction of the Oort cloud population may even be asteroidal bodies formed inside the orbit of Jupiter. These comets and asteroids underwent a complex dynamical random walk among the giant planets before they were ejected to distant orbits in the Oort cloud, with possible interesting consequences for their thermal and collisional histories. Observational evidence for diversity in cometary compositions is limited, at best. This revised version was published online in June 2006 with corrections to the Cover Date.     

Periodic relative orbits of two spacecraft subject to differential gravity and electrostatic forcing

Coulomb forces between charged close-flying satellites can be used for formation control, and constant electric potentials enable static equilibria solutions. In this work, open-loop time-varying potential functions, which produce periodic, two-craft, Coulomb formation motions are demonstrated for the first time. This is done in the rotating Hill-Frame, with linearized gravity, and craft position components assumed in the form of simple harmonic oscillators. Substitution of the oscillatory functions into the dynamics, further constrains these functions, and yields necessary potential histories, to produce the periodic flow. The assumed position functions, however, are not arbitrary, since the dynamical model restricts what oscillatory trajectories are allowed. Specifically, a Hill-Frame integral of motion is derived, and this is used to show certain candidate periodic functions to be inadmissible. The system dynamics are then linearized to expose stability properties of the solutions, and it is established that asymptotic stability is impossible for all orbit families. Finally, the degree of instability in the assumed motions, over free parameter ranges, is determined numerically via the Floquet multipliers of the associated full-cycle state-transition matrices.     

Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

A large set of simulations, including all the relevant perturbations, was carried out to investigate the long-term dynamical evolution of fictitious high area-to-mass ratio (A/M) objects released, with a negligible velocity variation, in each of the six orbital planes used by Global Positioning System (GPS) satellites. As with similar objects discovered in near synchronous trajectories, long lifetime orbits, with mean motions of about 2 revolutions per day, were found possible for debris characterized by extremely high area-to-mass ratios. Often the lifetime exceeds 100 years up to A/M ∼ 45 m²/kg, decreasing rapidly to a few months above such a threshold. However, the details of the evolution, which are conditioned by the complex interplay of solar radiation pressure and geopotential plus luni-solar resonances, depend on the initial conditions. Different behaviors are thus possible. In any case, objects like those discovered in synchronous orbits, with A/M as high as 20–40 m²/kg, could also survive in this orbital regime, with semi-major axes close to the semi-synchronous values, with maximum eccentricities between 0.3 and 0.7, and with significant orbit pole precessions (faster and wider for increasing values of A/M), leading to inclinations between 30° and more than 90°.     

模拟中性大气边界层中污染物传输与扩散的动力相似讨论

文章从湍流雷诺数相等出发,推导出风洞中模拟中性大气边界层动力相似准则一充分发展的湍流中,运动相似的流动动力也相似。文章还讨论了模拟烟流抬升和扩散的相似准则,概述了国内外一些主要实验室应用的近似模拟技术。     

Multiscale eigenelement method for periodical composites: A review

Based on the eigenvector expansion idea, the Multiscale Eigenelement Method (MEM) was proposed by the author and co-workers. MEM satisfies two equivalent conditions, one condition is the equivalence of strain energy, and the other is the deformation similarity. These two equivalent conditions character the structure-preserving property of a multiscale analysis method. The equivalence of strain energy is necessary for achieving accurate macro behaviors such as lower order frequencies, while the deformation similarity is essential for predicting accurate micro behaviors such as stresses. The MEM has become a powerful multiscale method for the analysis of composite structures because of its high accuracy and efficiency. In this paper, the research advances of MEM are reviewed and all types of eigenelement methods are compared, focusing on superiorities and deficiencies from practical viewpoint. It is concluded that the eigenelement methods with smooth shape functions are more suitable for the analysis of macro behaviors such as lower order frequencies, and the eigenelement methods with piecewise shape functions are suitable for the analysis of both macro and micro behaviors.     

现代对策论研究

对策论是研究斗争局势中冲突问题的数学理论,笔者长期以来在此领域进行了大量的研究探讨,本文概要介绍了主要工作。     

压气机叶片气动阻尼的改善设计

针对气动阻尼在强迫响应分析中的应用现状,提出了一种在叶型基本确定的条件下进一步设计气动阻尼的方法.该方法只对叶片基元级的积叠轴做微小的调整,这种调整对叶栅流场气动特性和固有频率的影响很小,可以忽略不计.研究了积叠轴调整对叶片气动阻尼的影响,得出在不需要大量流场计算的条件下,即可判断如何调整叶片积叠轴以达到增加气动阻尼目的的结论.在分析中用振型相似度衡量叶片模态振型与气动阻尼比的关系,相似度越小气动阻尼比越大.