一类非线性非自治振动系统的同步派生系统建立方法

对于一类非线性非自治振动系统,给出了建立派生系统,使得两个系统最终达到完全同步的方法.派生系统的耦合项包含常数矩阵与函数矩阵,常数矩阵使得系统的线性方程零解渐近稳定,函数矩阵使得非线性部分变成幂函数的形式,这样可以保证派生系统与原系统通过控制实现完全同步.对于具体的参数激振与外激励同时存在的Mathieu系统,以及Φ6-Duffing方程分别进行了仿真,由计算结果可以看出实现了系统之间的完全同步,证明了此方法是有效的.     

基于偏振光及红外传感器的辅助定姿方法

为了满足无人飞行器自主导航需求,提出了一种偏振光及红外传感器辅助惯导定姿方法。该方法选取了姿态四元数和陀螺误差模型构建滤波状态向量,采用偏振光传感器、红外传感器测量的三维姿态角作为量测向量建立卡尔曼滤波模型;融合后的最优姿态四元数转换为姿态矩阵反馈至惯性导航系统中,修正位置、姿态信息的解算。在分析了捷联惯导力学编排的基础上,参考常见的惯导系统参数进行了动态仿真。结果表明:偏振光、红外传感器可以有效地修正惯导姿态误差,修正后输出精度与偏振光、红外传感器输出精度相当,分别保持在±0.2°和±1°。提出的新型辅助定姿方法为提高惯导系统精度提供了一种新思路,具有广阔的应用前景。     

非半单分叉的Normal Form计算

在文［１］基础上，提出一种仅知道派生线性系统零实部特征值时求解非线性系统非半单分叉ＮｏｒｍａｌＦｏｒｍ的方法．通过适当的分类，将要求解的线性代数方程组分为若干相互独立的方程组．将所求系数向量按字典序列排列后，各独立方程组的系数矩阵是上三角矩阵．在非共振情形，各系数向量可按反字典序列递推求出．在共振情形，根据文中的二个定理，巧妙地由一简单的常数矩阵的最大秩子矩阵，定位其系数矩阵的满秩子矩阵，解决了这类方程组的降维简化．通过消元法，把简化后的方程化成类似于半单分叉ＮｏｒｍａｌＦｏｒｍ求解过程中方程的形式，其解法也类似．该方法非常易于在计算机代数软件平台上程序化．     

求解结构动力学方程的一种辛格式及其优化

论文将四阶隐式高斯勒让德辛龙格库塔法应用于线性结构动力学方程,并对其进行了算法优化.针对n个自由度的动力学初值问题,先通过消元得到n阶线性代数方程组,利用其系数矩阵稀疏对称正定的性质,采用预处理共轭梯度法求解,其中预条件子由系数矩阵的不完全Cholesky分解得到.通过与中心差分法、Newmark-β法及Runge-Kutta法相比,论文方法在计算量未显著增加的前提下给出了更高的计算精度.     

非参数概率系统非平稳随机响应研究

对复杂系统的测量和知识的有限性造成的不确定很难完全由随机参数模型进行描述,采用随机矩阵模型更具有一般性和合理性.本文应用随机矩阵模拟不确定线性动力系统有限元模型中质量阵、阻尼阵和刚度阵的概率不确定性.综合运用虚拟激励法和精细时程积分法建立了非参数概率系统非平稳随机响应的有效计算方法.数值模拟结果表明,对于高精度制造,模型的不确定性是不能忽略的.本文提出的算法为此类问题求解提供了一条有效途径.     

对《光弹性矩阵理论》的讨论

Theocaris 和 Gdoutos 所著《Matrix Theory of Photoelasticity》是采用矩阵理论讲述光弹性基本原理的一本著作.本文拟对该书某些不足之处进行讨论,这里包括:Poincare'球操纵的普遍情况,等效定理,三维光弹性基本方程,椭园偏振光的测定以及对该书某些错误的改正.希望通过补充讨论使光弹性矩阵理论更加完善.     

无网格局部Petrov-Galerkin方法中本质边界条件的处理

鉴于无网格局部Petrov-Galerkin方法(MLPG)形函数的非插值性质,将一种新的本质边界处理方案——完全变换法与MLPG结合,通过变换矩阵修正形函数,使其满足Kronecker-δ条件,实现了本质边界的精确实施。进一步与MLPG中通常处理边界的罚方法作了比较研究,数值结果表明新方法的可靠性与精确度。     

层状弹性半空间非轴对称动力问题的奇异解

在柱坐标系下，利用关于方位角的Ｆｏｕｒｉｅｒ变换及关于径向的Ｈａｎｋｅｌ变换，将弹性力学基本方程组转化为非齐次的一阶常微分方程组的标准形式．采用求解微分方程组的矩阵法，建立了介质层的传递矩阵．由层间完全接触条件，导出了在任意埋藏源作用下层状弹性半空间频域奇异解，时域奇异解可通过关于频率的Ｆｏｕｒｉｅｒ积分得到．该方法可应用到固体、流体层的情况     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

弹性力学中的一种非协调数值流形方法

通过引入数学和物理双重网格，将插值域与 积分域分别定义在不同的覆盖上，即在数学网格上进行插值函数的构造，物理网格上完成 系统能量泛函积分运算，最后通过覆盖权函数将二者联结在一起. 它的优点是单元网格划 分随意，不受复杂边界形状和二相材料界面的限制，单元可以是任意形状，是较之于有限 元方法更一般的数值模拟方法. 在4节点四边形数值流形方法中，由于单元总体位移函数 包含的完全多项式不完全，使得计算精度不够精确，为此，在单元总体位移函数上附 加非协调位移基本项，使之趋于完全，提出了弹性力学问题的一种改进的数值流形 方法------非协调数值流形方法. 通过内部自由度静力凝聚处理，导出了消除内参后的单元应变矩阵 和单元刚度矩阵，使得在不增加广义节点自由度的前提下，大大提高了数值流形方法的计 算精度和计算效率. 同时对非协调项进行了显式处理，可以对工程实践起到更切实的帮助. 数值试验表明，它们能够保证收敛，有较高的精度，对畸变不敏感，从而证明了该方法的 可行性.     

A matrix method for describing unpolarized light and its applications

A matrix method for describing fully depolarized light is proposed. According to the properties of fully depolarized light it is proved theoretically that this column matrix (Jones vector) can be used to describe unpolarized light as well. Thus, it enables the problems of holographic photoelasticity, including holographic photoelasticity of unpolarized light, to be simply treated by using a unified matrix calculus (Jones calculus).     

Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.     

A neoteric interferometer for use in holographic photoelasticity

A shortcoming of the conventional holographic interferometer used in photoelasticity is that, for the double-exposure cases, the resulting fringe patterns are a complex combination of conventional isochromatic and isopachic fringes. This paper describes a holographic interferometer that may be used to obtain separate but simultaneous isochromatic- and isopachic-fringe patterns for photoelastic models in states of plane stress. The method requires a model with a partially reflecting front surface. Isopachics, which are proportional to the thickness change, are recorded using holographic interferometry from the transmitted light. The isochromatics are obtained from the transmitted light by conventional means. General equations relating the surface displacement of the specimen to the observed fringe patterns are developed, and examples of static and dynamic loadings are shown.     

Holographic velocimetry for flow diagnostics

Currently, there are a number of flow diagnostic tools available for the evaluation of fluid dynamic systems. In spite of its great potential, holographic velocimetry is one technique which has not been widely used. It does, however, have great potential in this area due to its inherent three-dimensionality. As demonstrated in this study of fully developed turbulent flow in a pipe, full three-dimensional mapping can be achieved at any instant in a flow cycle. Comparisons of holographic results with analytical predictions and laser-Doppler-anemometry (LDA) measurements demonstrate the accuracy of the technique as well as some of its advantages and disadvantages relative to LDA. Although relatively poor spatial resolution is obtained, the fact that holographic velocimetry is both an instantaneous and full volume measuring tool makes it useful for a range of complex and high-speed flow-measurement applications.     

用白光散斑的直接记录法测量曲面变形

本文提出以物体表面精细光学结构在白光照射下辐射率随机分布函数作为散斑场,以全息软片为记录介质,采取无镜头成象技术,得到宽频域的散斑底片,并用有一定带宽的准单色光进行全场分析,测量可展曲面变形,其结果不仅具有较高的灵敏度,较大的灵敏度调节范围,而且其中的准备过程、记录过程和分析过程比现有的各种测量曲面变形的散斑法都要简单,该方法将可展曲面变形问题简单地转化为平面问题处理,保留了白光散斑直接记录法在测量平面变形时的全部优点,并能脱离暗室在工程现场中应用。     

Strain determination on curved surfaces by objective white light speckles

A close-range objective white light speckle method has been used for strain determination on simply curved surfaces. The speckle field is not the artificially printed random dots but only the radiance distribution of object surface which was slightly treated before the test to produce fine structure of optical details. The holographic film, instead of holographic plate, is attatched to the curved surface when illuminated by a flash light. Whole field fringe patterns are obtained with high sensitivities and large adjustable range. There is no longer a requirement to derive the speckle movement on the image plane from the object surface. Defocusing problem has been avoided. It can be practically applied to engineering problems with considerable convenience because of the very simple recording system and little demand for environmental stability.     

二维变线距光栅密度的检测

变线距全息光栅平面单色仪由于具有自动聚焦、消像差、高分辨率以及减少杂散光等能力，因而在同步辐射装置、激光核聚变装置以及太空望远镜等设备中有着重要的应用。由于变线距全息光栅的制作及检测存在着相当的难度，制约了变线距全息光栅的推广应用。因此，变线距全息光栅的制作及检测研究，具有十分重要的理论及应用意义。变线距全息光栅的制作必须有高精度的密度检测技术相配合。比如，在变线距全息光栅的制作过程中，需要对用于形成变线距光栅的全息干涉条纹的线密度进行检测；对于已经制成的变线距全息光栅的线密度也需要进行检测，以检查光栅的制作质量。因此，变线距全息光栅线密度的检测，对提高变线距全息光栅的制作质量起着十分关键的作用。文中给出了二维变线距光栅的密度描述公式，讨论了干涉条纹的物理意义；应用干涉云纹法和条纹图像处理技术，对二维变线距光栅的密度分布进行了检测研究，给出了光栅密度的全场分布，并讨论了检测精度。     

Simplifications for scattered-light photoelasticity when using the unpolarized incident beam

A method is presented for obtaining scettered-light photoelastic data in three-dimensional problems using an unpolarized incident light beam. Using simplifying optical assumptions, the scattered-light observation path is considered tobe a series of half-wave retarders. Data are obtained through rotation of the optical analyzer and translation of the incident light beam with respect to the model. The method is applied to obtain data in problems where the secondary principal directions are: (1) fixed and (2) rotate. Results compare favorably with those obatained using a polarized incident beam.     

Model interferometry with air-holograms

An “air-hologram” is formed by the superposition of collimated object and reference light beams in a standard transmission holographic bench. Since no model is initially placed in the system, the reconstruction is simply the collimated beam that had passed through the model space. Insertion of transparent model material changes the optical path-length profile causing interference between the existing beam, which traverses the model, and the reconstructed beam which had traversed air only—hence, the designation “air-hologram”. Using this method, model material can be inspected and selected for optical flatness. Interference in the unloaded models can then be eliminated by simple rotation of the hologram. Real-time holographic interferometry is performed in the same manner as is photoelasticity. Further, it is shown how errors caused by large model displacements can be minimized.