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.     

悬丝支撑加速度计标度因数温度系数补偿方法研究

温度是影响加速度计标度因数的最主要因素,标度因数的温度系数是评价标度因数随温度变化的程度.本文根据悬丝支撑的摆式加速度计工作原理,分析了温度变化对标度因数的影响,同时给出了标度因数温度系数的补偿原理和方法,并通过试验进行了验证.     

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。     

直升机空气动力学中的几个疑点

提出了在直升机空气动力学的某些文献里存在的三个疑点：(1)滑流理论能否用于微观分析；(2)叶素理论(即使在处理垂直飞行问题时)中沿半径的诱导速度分布能否认为独立于桨叶安装角分布；(3)前飞时沿方位角的诱导速度分布究竟如何?通过分析讨论，本文给出了一些结论。     

直升机旋翼空气动力学的发展

本文分两大部分，即旋翼理论分析的发展（认识旋翼）及旋翼浆叶外形的发展（改造旋翼）。在第一部分中，阐述了旋翼滑流理论、叶素理论、涡流理论（其中又包括固定尾迹的经典涡流理论、预定尾迹的半经验涡流理论、自由尾迹的现代涡流理论）和旋翼CDD方法。在第二部分中，讨论了旋翼桨叶的翼型、浆尖形状、扭转角分布等的变化历程。最后，作为总结，提出了旋翼理论分析和浆叶气动外形的四代发展阶段的划分。     

关于级数δ_α~θ(a_v,f)的收敛性

主要研究一类较Ｎｅｖａｎｌｉｎｎａ亏值更为广泛的α＝亏值的亏量关系，对于α的不同取值，讨论了由其相应的亏量构成级数的收敛性．作为本文结论的一个佐证，构造一个函数来说明一个亚纯函数的α－亏值个数可以大于Ｎｅｖａｎｌｉｎｎａ亏值个数。主要结论如下：设ｆ（ｚ）是开平面｜ｚ｜＜＋∞上级ρ为有穷的亚纯函数，α１，α２，．．．，αｎ是ｆ（ｚ）的α－亏值，则     

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。