等谱AKNS方程的约化

通过对等谱AKNS方程的约化,构造出非线性Schrodinger和mKdV方程的新双Wronskian解;分别推导出这2个方程的双Wronskian形式的有理解。     

月壤采样冲击破碎过程的影响参数分析

针对月球表面的月壤采样过程中遇到不同粒度的块状月岩会对钻探取样工作造成不同程度的影响和阻碍的问题，提出了一种通过有限元仿真模型结合类月岩材料力学特性进行有效分析的方法，作为提高效率的依据。首先通过实验和仿真拟合，得到硬度接近于月岩的两种类岩石材料红砖和砂岩的材料模型参数。在此基础上，用实际尺寸的机构有限元模型进行仿真，得到采样冲击机构冲击过程中不同参数的影响。基于该参数分析，对于冲击机构及其冲击过程提出改进建议，可有效提高采样过程中冲击破碎岩石效率。     

Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split, and frequency split can cause gyroscope to drift. Therefore, it is of great significance to analyze the relationship between mass non-uniformity and frequency split, which can provide a theoretical basis for mass balance of imperfect resonator. The starting point of error mechanism analysis for gyroscope is the motion equations of resonator. Firstly, based on the Kirchhoff-Love hypothesis in the elastic thin shell theory, the geometric deformation equations of resonator are deduced. Secondly, the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell. Thirdly, the kinetic energy equation of resonator is deduced by the Coriolis theorem. Finally, the motion equations of resonator are established by the Lagrange mechanics principle. The theoretical values of precession factor and natural frequency are calculated by the motion equations, which are substantially consistent with the ones by the finite element method and practical measurement, the errors are within a reasonable range. Simultaneously, the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis. The above conclusions prove the correctness and rationality of motion equations. Similarly, the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping, and the state equations with respect to the velocity and displacement of vibration system are derived, then two natural frequencies are solved by the characteristic equation. It is concluded that one of reasons for frequency split is the 4th harmonic of mass non-uniformity, and thus much attention should be paid to minimizing the 4th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.     

侧向随动力作用下大展弦比柔性机翼的稳定性

 随动力能够诱发弹性结构发生颤振失稳。以侧向随动力和集中质量分别模拟发动机推力和外挂质量,考虑机翼垂直弯曲-扭转刚度比、集中质量大小、侧向随动力和集中质量的位置以及机翼后掠角和上反角的影响,研究了受侧向随动力作用的大展弦比柔性机翼的气动弹性稳定性。数值模拟所采用的大展弦比柔性机翼非线性气动弹性模型耦合了几何精确完全本征运动梁模型和ONERA动失速非定常气动力模型,该模型考虑了几何非线性、动失速和材料各向异性。模拟结果表明,侧向随动力对机翼颤振可以具有稳定作用,其具体表现依赖于若干变参数的影响,如：减小机翼垂直弯曲-扭转刚度比;发动机吊舱靠近翼根布置;使发动机推力作用点在法向上与机翼弹性轴靠近;单纯的集中质量避免布置在柔性机翼中部,且布置在机翼弹性轴之前或下方,这些设计或布置均有利于提高带发动机吊舱/有效载荷外挂的柔性机翼的气动弹性稳定性。     

Constructing G~2 Continuous Curve on Freeform Surface with Normal Projection

This article presents a new method for G～2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with prescribed tangent direction and curvature vector,respectively,at every point.First,a G～2 continuous curve is constructed in three-dimensional space.Then the curve is projected normally onto the given surface.The desired interpolation curve is just the projection curve,which can be obtained by numerically solving the initialvalue problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit case.Several shape parameters are introduced into the resulting curve,which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand.The presented method is independent of the geometry and parameterization of the base surface.Numerical experiments demonstrate that it is effective and potentially useful in numerical control (NC) machining,path planning for robotic fibre placement,patterns design on surface and other industrial and research fields.     

面向稀薄流非线性本构预测的机器学习方法

稀薄非平衡流域内连续介质假设已经失效,主要围绕Boltzmann方程及模型方程对稀薄非平衡流开展理论与计算研究,统一气体动理论格式（UGKS）是其中一种代表性方法。在稀薄非平衡流数值模拟中,Navier-Stokes （N-S）方程连续介质假设已经失效,不能有效描述流场非平衡特征。UGKS方法虽然计算精度高,但速度空间离散导致计算效率低下,多维高速条件下数值计算难以开展。基于数据驱动的思想,在N-S方程与UGKS方法的研究基础上发展出了一种稀薄非平衡流非线性本构关系求解方法（DNCR）。该方法以N-S与UGKS求解器获得的流场数值模拟计算结果作为训练数据集,基于流场特征参数采用极端随机树算法生成机器学习模型,对预测流场中线性黏性应力项与热流项进行非线性修正,并耦合非线性本构关系求解宏观守恒方程得到目标状态稀薄非平衡流动数值解。针对DNCR方法中所采用的机器学习方法-极端随机树模型,通过二维顶盖驱动方腔流算例对高维非线性建模涉及的特征参数选取、参数调优开展了相关验证工作,选取若干典型状态对极端随机树模型的泛化性能开展研究,并评估了相关模型与方法的计算精度与计算效率。     

非结构混合网格高雷诺数流动计算中一种改进的LU-SGS隐式格式(英文)

The lower-upper symmetric Gauss-Seidel (LU-SGS) implicit relaxation has been widely used because it has the merits of less dependency on grid topology,low numerical complexity and modest memory require...     

旋翼翼型定常-非定常特性综合优化设计新方法

旋翼翼型对直升机旋翼及全机气动特性有至关重要的影响。结合直升机飞行特性及旋翼工作气动环境,本文提出了一种新的旋翼翼型设计理念,即定常优化设计同非定常设计相结合的方法来开展直升机旋翼专用翼型的优化设计。首先,建立旋翼翼型非定常气动特性的高精度CFD求解方法,以获得旋翼翼型在相应状态下的升力、阻力和力矩等气动参数。其次,针对旋翼翼型优化状态的特点,对于翼型静态优化及动态失速优化分别采用遗传算法和序列二次规划算法。在上述方法建立基础上,首先针对定常状态下的原始翼型(SC1095)进行优化设计,获得一个满足设计要求的静态优化翼型,进一步着重对该翼型在非定常状态下进行优化设计,成功地得到一种新翼型,并具有非常规外观。结果表明,在设计状态下,新翼型在保持良好定常气动特性的同时,明显减弱了动态失速状态下的分离涡,从而显著改善了翼型的动态失速特性。     

高纬极区离子速度分布函数多项式解及非相干散射谱计算

为更准确描述高纬极区电离层离子分布函数, 分别采用弛豫碰撞模型和麦克斯韦分子碰撞模型描述玻耳兹曼方程的碰撞项, 通过求解两种模型下的输运方程, 分别得到两种模型基于麦克斯韦分布下离子分布函数的13矩近似和基于双麦克斯韦分布下离子分布函数的16矩近似. 进一步根据Sheffield理论, 利用两种模型下离子分布函数的13矩和16矩近似, 计算了非相干散射谱, 并对结果进行对比分析. 结果表明, 相对于弛豫碰撞模型, 麦克斯韦分子碰撞模型能更好地描述电离层E层中离子与中性成分的相互作用. 相对于离子分布函数的13矩近似, 16矩近似更适合描述由于电场增加导致的离子温度各向异性特征.      

高超声速飞行器非线性纵向运动稳定性研究

针对研究高超声速飞行器飞行动力学稳定性时忽略方程非线性影响的问题,建立了保留非线性特征的六自由度动力学方程组和非线性活塞理论耦合模型。研究了初始迎角和活塞理论非线性项对高超声速飞行器纵向稳定性的影响,并在稳定巡航中施加瞬时扰动,分析其姿态响应。仿真结果表明:高超声速飞行器姿态收敛速度比常规低速飞行器慢很多;对迎角施加扰动后,飞行器姿态变化主要影响短周期模态,且偏离平衡位置越远,收敛越快;改变气动力非线性项时,其姿态变化主要影响长周期模态,且收敛较慢;两种扰动均对振荡周期无明显影响。