On the free-vibration of rotating composite beams using a higher-order shear formulation

The free vibration behavior of rotating blades modeled as laminated composite, hollow (single celled) boxed beams is investigated. To this end, geometrically nonlinear structural model incorporating a number of non- classical effects such as anisotropy, heterogeneity, transverse shear flexibility, and warping inhibition is developed. Centrifugal and Coriolis force field effects are also considered in the formulation. However, Coriolis effect is discarded during the solution process. It is assumed that in-plane cross-sectional distortion is negligible. In contrast to the existing structural blade models, the traction free boundary conditions on the external surfaces of the beam are identically satisfied. The linearized dynamical equations and numerical results addressing the problem of the free vibration are supplied. Results obtained for the present higher-order shearable model are compared with those of the existing first-order shearable and the non-shearable structural models. Tailoring studies using the present model reveal an enhancement of eigenfrequency characteristics.     

稀薄流到连续流的气体运动论统一算法研究

通过引入碰撞松弛参数和当地平衡态分布函数对BGK模型方程进行修正，确定含流态控制参数的各流域均适用的气体分子速度分布函数简化控制方程。发展和应用离散速度坐标法于气体分子速度空间，利用一套在物理空间和时间上连续而在速度空间离散的分布函数来代替原分布函数对速度空间的连续依赖性。基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散格式，建立直接求解气体分子速度分布函数的气体运动论有限差分数值方法。发展可用于速度空间宏观取矩的离散速度数值积分方法，获取物理空间各点的流动参数，由此发展一套能有效模拟各流域三维绕流问题的气体运动论统一算法。研究气体运动论数值算法所适合的并行方案，基于统一算法的HPF并行实现，建立一套能有效模拟不同流域复杂外形体绕流的HPF并行算法软件。通过对不同Knudsen数的一维、二维、三维气体绕流问题进行数值计算表明，计算结果与有关实验数据及其它途径得到的研究结果吻合较好，证实了本文发展的统一算法在求解稀薄流到连续流不同流域复杂绕流问题方面的可行性。     

自由漂浮空间机器人的运动学分析及仿真

自由漂浮空间机器人与地面机器人最大的区别是其末端执行器的运动不仅仅和各个关节的运动有关,而且与各个连杆、基座的质量分布及其运动轨迹紧密相关.因此,自由漂浮空间机器人的运动学与其动力学是密不可分的.运用螺旋理论、动量守恒定律对这样的机器人系统进行分析,得到了包含系统质量在内的运动雅可比矩阵,并给出了系统运动的图形仿真结果.     

影响图的基础理论和发展

概述了影响图起源，理论基础和应用进展，ＩＤ是复杂的不确定性决策问题的一种新颖有效的图形表征语言，数学概念完整，关于概率估计，备选方案，决策者偏好和信息状态的说明完备，具有决策树不可比拟的优点，作为不确定性问题的辅助构模手段，表征和推理的工具以及概率计算的有效结构，广泛适用于许多领域的决策分析和不确定性推理问题。     

Applying the mathematical theory of stochastic processes to lunar and planetary science: the ancient oceans on Mars case

The Mathematical Statistics Theory (MST) and the Mathematical Theory of Stochastic Processes (MTSP) are different branches of the more general Mathematical Probability Theory (MPT) that represents different aspects of some physical processes we can analyze using mathematics. Each model of a stochastic process according to the MTSP can provide one or more interpretations in the MST domain. The importance of MTSP is that each such interpretation can provide large amount of new information. While large body of work on the impact crater statistics according to MST has already been done, it is yet to be investigated as to how we can model a stochastic process according to MTSP; for example, bombardment of the planetary surface or something else in a Lunar and Planetary Science (LPS) domain. In order to show possible achievements, the possible existence of a Martian ocean was chosen as a query that could be addressed through computations using presumptions according to MTSP, including probability of existence as well as lateral and vertical extent and duration of time. While the presumptions for this particular case will also be addressed in certain degree, this will be done primarily to show complexities of some physical process that can be modeled, rather than to prove correctness of the concrete values computed here. While this in itself can be the objective in some future work toward the formal proof of the probability, extent, and timing of oceans on Mars, the basic idea here is to show the basic principles of MTSP, and its potential for addressing LPS-related phenomena. Here, I attempt to show how this approach can: (1) provide large amounts of previously unknown information about physical processes on the surface of the planet, (2) lead to a better understanding of the processes that have shaped the surface of the planet, and/or (3) help constrain the amount of resurfacing. Coupled with other current methodologies, MTSP can result in a better understanding of the history of Mars, as well as other lunar and planetary bodies.     

重心坐标应用于几何定理的机械化证明

用机械化方法证明几何定理,适当选取坐标系是一个关系到问题解决得难易程度的重要步骤。本文是在重心坐标下,用机械化方法证明非平凡几何定理。     

关于遗传算法模糊控制的研究

在控制对象的数学模型由于受非线性的时变的影响很难精确确定时，模糊控制是一个比较好的方法，但模糊控制规则易受人的因素的影响而归纳得不完善，并且不能自学习影响了模糊控制的效果。遗传算法可以搜索整个空间，不易陷入局部最优解，不受搜索空间的性假设的约束。可以解决非常困难的寻优问题，本文提出关于遗传算法的模糊控制，使控制规则得到优化，从而改善了控制性能。仿真实例表明这种方法是可行的。     

无穷观问题的研究（Ⅰ）—历史的回顾与思考

本组系列论文（Ⅰ）－（Ⅴ）从数学和认识论的角度系统地研究了无穷观问题的历史发展和现状，确立了无穷观背景世界的三分法原则，指出了两种无穷观相五排斥的局限性，形成了统一两种无穷于同一框架中的基本观点，并建立了一个统一实无限与潜无限于同一框架中的公理集体论系统APAS。     

航空材料的冲击疲劳问题研究进展与展望

材料的冲击疲劳问题在航空工程中大量存在,舰载机的弹射起飞、拦阻着舰都是典型的冲击疲劳问 题。本文梳理了冲击疲劳概念的早期发展历程,综述了自2000年以来冲击疲劳领域的主要研究进展,包括材 料冲击疲劳性能的主要影响因素、材料冲击疲劳试验方法、冲击疲劳的损伤表征和寿命预计以及冲击疲劳问题 的数值计算方法等,指出材料的微观结构、边界条件、使用环境、冲击载荷类型等对冲击疲劳性能有显著影响。 总结了航空工程中冲击疲劳问题面临的主要挑战,并结合未来工程结构设计的需求,展望了航空领域冲击疲劳 技术的未来发展方向。     

基于Lyapunov最优反馈控制的月球中继卫星转移轨道设计

摘要： 随着电推进器及小推力转移变轨的研究逐渐深入,在深空探测领域应用电推力器是必然的发展趋势.文章基于以月球中继卫星的运行轨道地月L2点Halo轨道为目标轨道的轨道转移任务,采用Lyapunov最优反馈控制方法,计算单一轨道根数的局部最优控制率,通过遗传算法调整五个轨道根数的权重,得到时间最优的月球中继卫星小推力轨道转移方案,具有工程应用意义.