杆系结构的几何非线性分析──Ⅰ．平面问题

本文以三维连续体的虚功增量方程为基础，采用平动、转角位移分别插值的方法，导出了梁结构大位移、大转动问题内力分析的ＵＬ法。本文考虑了轴向、剪切和弯曲效应，提出了新的几何刚度矩阵。算例表明，依本文方法编制的程序具有分析结构强几何非线性行为的能力；在满足本文位移假定（即每次加载增量中转角增量是小量）的条件下，可以描述任意大角度的刚体转动。     

杆系结构的几何非线性分析──Ⅱ．三维问题

以三维连续体的虚功增量方程为基础，采用平动、转角位移分别插值的方法，导出了空间Ｔｉｍｏｓｈｅｎｋｏ梁大位移、大转动问题内力分析的ＵＬ法（ＵｐｄａｔｅｄＬａｇｒａｎｇｉａｉ１Ｆｏｒｍｕｌａｔｉｏｎ）。本文考虑了轴向、剪切、弯曲和扭转效应，提出了新的几何刚度矩阵，并建立了描述大转动规律的坐标转换矩阵。算例表明，依本文方法编制的程序具有分析结构强几何非线性行为的能力；在满足本文假定（即每次加载增量中转角增量是小量）的条件下，可以描述任意大角度的刚体转动。     

杆系结构的几何非线性分析：Ⅰ.平面问题

本文以三维连续体的虚功增量方程为基础，采用平动、转角位移分别插值的方法，导出了梁结构大位移、大转动问题内力分析的ＵＬ法。本文考虑了轴向、剪切和弯曲效应，提出了新的几何刚度矩阵。算例表明，依本文方法编制的程序具有分析结果强几何非线性行为的有能力；在满足本文位移假定的条伯下，可以描述任意大角度的刚体转动。     

双质量解耦硅微陀螺仪的非理想解耦特性研究和性能测试

为了分析双质量解耦硅微陀螺结构中的机械耦合误差,对微陀螺结构的非理想解耦特性进行了研究。首先,阐述了双质量解耦硅微陀螺仪的结构原理,推导了双质量解耦硅微陀螺仪的检测位移;接着构建检测框架在驱动模态下非理想的解耦模型,推导了由非理想解耦导致检测框架的平动位移与转动位移的公式;然后进行了结构非理想解耦特性仿真分析,对驱动模态时检测框架和检测模态时驱动框架的非理想运动特性进行仿真,结果表明检测框架的残余平动位移达到驱动位移的0.86%,最大转动残余位移达到了驱动位移的2.7%,而驱动框架的平动残余位移达到了检测位移的1.36%,转动残余位移达到了检测位移的0.87%;最后,对加工的双质量解耦硅微陀螺结构芯片的非理想解耦误差进行了测量,结果表明非真空封装下的正交误差达到158.65(o)/s,失调误差为19.03(o)/s,偏置稳定性达到12.01(o)/h。     

复合型裂纹位移场的分析

本文分析了复合型裂纹尖端v向位移场的特点,即v=0的位移线和切点连线(等位移线斜率为零的切点的连线)均为直线,它们的斜率与K_Ⅱ∶K_Ⅰ有关.在裂纹两岸的v向位移大小相等符号相反.当纹尖有刚性转动时,裂纹两岸同x处的v向位移不同.利用它们的代数和可消除变形位移,而得到两倍的刚性转角位移,从而求出刚性转角,并找到无刚性转角时的v=0位移线和切点连线. 作者利用上述特点,由贴片云纹干涉法得到有刚性转角的条纹图中求出转角、纹尖精确位置、和应力强度因子K_Ⅰ、K_Ⅱ.与文[4]的计算值一致,实验与计算的条纹图吻合得很好,结果令人满意.     

杆系结构的几何非线性分析：Ⅱ.三维问题

以三维连续体的虚功增量方程为基础，采用平动、转角位分别插值的方法，导出了空间Ｔｉｍｏｓｈｅｎｋｏ梁大位移、大转动问题内分力分析的ＵＬ法（ＵｐｄａｔｄｅＬａｇｒａｎｇｉａｎＦｏｒｍｕｌａｔｉｏｎ）。本文考虑了轴向，剪切、弯曲和扭转效应，提出了新的几何刚度矩阵，并建立了描述大转动规律的坐标转换矩阵。算例表明，依本方方法编制的程序具有分析结果强几何非线性行为的能力；在满足本文假定的条件下，可以描述任意大     

基于非线性微振动流体阻尼隔振器的Octo-strut隔振平台的动力学特性研究

针对一种新型非线性微振动流体隔振器的Octo-strut平台进行研究,基于隔振器的非线性五参数模型及牛顿-欧拉方法建立了Octo-strut隔振平台的动力学模型,并对平台的振动耦合性、安全冗余性等动力学特性进行了理论分析和数值仿真验证。研究结果表明:隔振平台垂直平动z方向、绕垂向转动θ_s方向动力学特性独立,径向平动x方向与径向平动y方向相互垂直,径向平动x方向与绕径向转动θ_y方向、径向平动y方向与绕径向转动θ_x方向的动力学特性相互耦合。隔振平台具有振动耦合性、安全冗余性、非线性温变特性,在工程实际应用时应避免失效隔振器的出现并关注隔振器温变特性,以保证隔振的安全可靠性。     

超声散斑数字相关法应用于刚体面内转动测量的研究

在激光数字散斑相关法测量理论的基础上,阐述了超声散斑相关法测量的基本原理,并建立了相应的超声散斑数字相关实验分析系统。在实验分析时,首先应用模拟测量的方法对刚体面内转动对散斑场相关性的影响进行了分析;然后应用实验测量的方法再对此进行了分析;最后对刚体未知面内转角进行了实测。实验结果表明,刚体面内转动可测量的最大转角为9°,当转动角度为10°时,误差大于9%。实验中分别应用了爬山搜索法和相关系数拟合法来分别搜索整像素的位移和亚像素的位移。     

超声散斑数字相关法应用于体面内转动测量的研究

在激光数字散斑相关法测量理论的基础上,阐述了超声散斑相关法测量的基本原理,并建立了相应的超声散斑数字相关实验分析系统。在实验分析时,首先应用模拟测量的方法对刚体面内转动对散斑场相关性的影响进行了分析;然后应用实验测量的方法再对此进行了分析;最后对刚体未知面内转角进行了实测。实验结果表明,刚体面内转动可测量的最大转角为9°,当转动角度为10°时,误差大于9%。实验中分别应用了爬山搜索法和相关系数拟合法来分别搜索整像素的位移和亚像素的位移。     

爆炸荷载作用下结构冲量的测量

冲击摆是间接测量爆炸荷载下瞬态冲量的一种有效装置。常用的冲击摆为典型的复摆模型,设计、加工和数据处理复杂,质心难以准确测定,对冲量测定的精度影响较大。特别是测量爆炸载荷试验中的冲量时,遇到较大的困难。文中引入一种冲击摆的改进装置,将传统的冲击摆简化为等效单摆,限制了传统冲击摆的转动效应,考虑了阻尼对冲量计算的影响,减小了不确定性因素产生的试验误差。对比分析两种冲击摆在爆炸荷载下冲量的测量原理,改进装置具有设计加工简单、试验精度高、数据处理方便等优点。最后将改进装置应用于泡沫铝夹芯壳的爆炸试验中,通过测量其最大平动位移得到了待测冲量。试验结果也证明了改进装置的可行性．     

边坡岩体结构的三维失稳形式及稳定性分析研究

由两组结构面控制的四面体块体是岩体中最基本的结构体, 其稳定性取决于块体所受荷载及结构面上的摩阻力。正确判定边界面上摩阻力分布是评价块体稳定性的关键。本文提出的块体稳定性分析适用于岩体所受荷载为三维非共点力系。在不同外力作用下块体可产生平动、转动、翘扭及倾倒等各种三维失稳组合形式, 从而得到更为合理的块体稳定性评价。     

Existence of Weak Solutions for the Three-Dimensional Motion of an Elastic Structure in an Incompressible Fluid

We study here the three-dimensional motion of an elastic structure immersed in an incompressible viscous fluid. The structure and the fluid are contained in a fixed bounded connected set Ω. We show the existence of a weak solution for regularized elastic deformations as long as elastic deformations are not too important (in order to avoid interpenetration and preserve orientation on the structure) and no collisions between the structure and the boundary occur. As the structure moves freely in the fluid, it seems natural (and it corresponds to many physical applications) to consider that its rigid motion (translation and rotation) may be large. The existence result presented here has been announced in [4]. Some improvements have been provided on the model: the model considered in [4] is a simplified model where the structure motion is modelled by decoupled and linear equations for the translation, the rotation and the purely elastic displacement. In what follows, we consider on the structure a model which represents the motion of a structure with large rigid displacements and small elastic perturbations. This model, introduced by [15] for a structure alone, leads to coupled and nonlinear equations for the translation, the rotation and the elastic displacement.     

圣地亚结构动力学问题模型确认与评估

考虑模型的不确定性与建模误差等因素, 是现代模型确认的研究特点. 为了 研究现代模型确认过程中的建模、模型确认准则等核心问题, 以圣地亚提出的结构动力 学挑战问题为研究实例, 采用正态分布和非参数核密度估计研究了参数不确定性建模, 并且 通过所采用的两条确认准则对所建立的数学模型进行了确认研究, 并最终得到了较好的数学 模型. 通过该实例的具体开展, 发现联合使用多条确认准则可对所建原始模型进行更科学 的评估确认.     

INTERACTION MODEL OF THE ENCLOSED AIR AND THE OUTER MEMBRANE

将充气膜结构内充气体假定为势流,推导得到速度势表示的内充气体小幅波动方程,并采用Galerkin法离散得到内充气体的有限元动力学方程。引入界面协调条件,建立了内充气体结点速度势与外部膜材结点位移的关系,然后联立薄膜动力方程和气体动力学方程得到充气膜系统内充气体与外部膜材的共同作用理论模型。在该理论模型基础上,建立了两类典型充气结构的数值模型进行分析,通过将数值结果与试验结果对比,验证了共同作用理论模型的准确性和合理性。     

Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap

The aerodynamic forces and flow structures of two airfoils performing “fling and subsequent translation“ and “translation and subsequent clap“ are studied by numerically solving the Navier-Stokes equations in moving overset grids. These motions are relevant to the flight of very small insects. The Reynolds number, based on the airfoil chord length c and the translation velocity U, is 17. It is shown that: (1) For two airfoils performing fling and subsequent translation, a large lift is generated both in the fling phase and in the early part of the translation phase. During the fling phase,a pair of leading edge vortices of large strength is generated; the generation of the vortex pair in a short period results in a large time rate of change of fluid impulse, which explains the large lift in this period. During the early part of the translation, the two leading edge vortices move with the airfoils;the relative movement of the vortices also results in a large time rate of change of fluid impulse, which explains the large lift in this part of motion. (In the later part of the translation, the vorticity in the vortices is diffused and convected into the wake.) The time averaged lift coefficient is approximately 2.4 times as large as that of a single airfoil performing a similar motion. (2) For two airfoils performing translation and subsequent clap, a large lift is generated in the clap phase. During the clap, a pair of trailing edge vortices of large strength are generated; again, the generation of the vortex pair in a short period (which results in a large time rate of change of fluid impulse) is responsible for the large lift in this period. The time averaged lift coefficient is approximately 1.6 times as large as that of a single airfoil performing a similar motion. (3) When the initial distance between the airfoils (in the case of clap, the final distance between the airfoils) varies from 0.1 to 0.2c, the lift on an airfoil decreases only slightly but the torque decreases greatly. When the distance is about lc， the interference effects between the two airfoils become very small.     

单侧界面条件下弹性波传播规律的研究

界面是介质间的分界面,把界面看成是双侧的,只是真实界面模型表述的一个极端,在很多情况下,它的另一个极端,即单侧界面模型可能更近于实际．在单侧界面条件下弹性波的传播问题,与双侧界面问题相比,还是一个尚未充分研究的领域．本文意在对这一领域的研究现状及问题作一评述和展望      

Set-values filtering for discrete time-delay genetic regulatory networks with time-varying parameters

We propose a new discrete-time model for genetic regulatory networks (GRNs) in this paper. The new model includes time-varying degradation rates, translation rates of mRNA, and protein as well as time-delay and bounded external noise, which better approximates the practical GRNs. The aim is to estimate the concentrations of mRNA and protein in the proposed model. Due to the unknown external noise and time-varying parameters in this model, the set-values filtering is adopted. The so-called set-values filtering problem is to find an upper bound for the quadratic estimation error of the filtering dynamics and minimize this bound at each time step provided that the external noise is bounded. A recursive linear matrix inequality (RLMI) based optimization approach is developed to compute the filter gains. The effectiveness of the design method is illustrated via two numerical examples.     

EQUIVALENCE OF TWO METHODS FOR AIRDROP DYNAMICS

定义了空投系统的两个元素，即“载机”和“装载物”。介绍了用来研究空投问题的两种动力学建模方法，即“整体法”和“多体法”。证明了两种方法对于平动动力学是等价的，但对于转动动力学是不等价的，原因是整体法并非总是存在的。     

N-space collision model for rotation-translation energy exchange in DSMC collisions

A new discrete simulation Monte Carlo (DSMC) collision model for molecules possessing an integer number of classical degrees of freedom for molecular structure energy is proposed. The total molecular energy (translation plus molecular structure) is represented by a velocity in five-dimensional space. Each collision is an elastic N-sphere collision in N-space, where N= 3, 4, or 5. For N=5, there is a maximum chance of exchange of energy between the two components of velocity, which represent the rotation energy and the three components that represent the translational velocity. For N=3, there is no change in the rotation energy of each molecule, and for N=4, there is an intermediate chance that rotation and translation energy will be exchanged. The exchange probability ϕ can be set to give the desired rotational relaxation rate. To achieve any realistic viscosity μ(T), the N-space model must be coupled with a modified collision procedure known as ν-DSMC. The new model is shown to match the results of molecular dynamics calculations for the internal structure of a Mach 7 shock, with a saving of about 20% in CPU time compared to standard DSMC using the standard Borgnakke-Larsen exchange model.     

多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象, 其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要. 静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法, 在多体系统碰撞动力学中存在诸多共性与差异. 本文分别从上述两类接触模型的发展历程入手, 详细介绍了两类模型的区别与联系. 首先, 根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型, 讨论了能量指数与Hertz接触刚度之间的关系, 阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题. 其次, 着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段), 分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点. 同时, 以恢复系数为桥梁和借助线性化的弹塑性接触刚度, 避免了Hertz刚度对弹塑性接触刚度的计算误差, 根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子. 探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系, 数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性. 另外, 为了避免阻尼项分母中初始碰撞速度在计算颗粒物质动态性能时导致的数值奇异问题, 通过求解等效的线性单自由度欠阻尼非受迫振动方程获得了阻尼项分母中不含初始碰撞速度的连续接触力模型, 并以一维球链为例, 证明了该模型相比EDEM软件使用的连续接触力模型具有更高的精度. 最后, 本文分析了当前多体系统碰撞动力学的研究现状, 并简要展望了多体系统碰撞动力学中接触力模型的发展趋势与面临的挑战.