可对角化矩阵特征值的Wielandt型扰动上界

利用矩阵的奇异值分解和Wielandt-Hoffman定理,探讨了可对角化矩阵特征值的扰动问题,得到了可对角化矩阵特征值的Wielandt型绝对扰动上界,而此上界也适用于可对称化矩阵,是可对称化矩阵特征值扰动上界的推广.研究结论还进一步推广了Wielandt-Hoffman定理,得到了比Wielardt-Hoffman定理更一般的形式.     

冲头压入半无限体的矢量分析解法

首先对冲头压入问题进行了矢量分析，建立了速度矢量关系式，证明其散度为零。后经参量积分，广义积分，曲线积分按上界定理得到应力状态系数ｎ＿σ＝２．５７。     

线性规划内点法(续)

<正>1 上界变量问题在单纯形法中对上界变量可按简单直接的方式处理,而它作为约束条件加入到约柬条件系数矩阵中.而对内点法来说,原一对偶法也易于处理这一问题[27].这时对是有上界变量的线性规划问题为:(p);Min c~TX     

关于区间矩阵Hurwitz与Schur稳定之间的关系

运用矩阵特征值性质讨论了区间矩阵Hurwitz稳定与Schur稳定的关系,提出了以区间矩阵Hurwitz稳定来推断Schur稳定的判据,解决了现有结果的相反问题,从而构架了Hurwitz与Schur相互推导的桥梁.     

具有非零元素链的矩阵为H矩阵的判定条件

目的 解决判断一个具有非零元素链的矩阵为H矩阵的条件.方法 采用逻辑推理的方法进行了证明.结果得到了当矩阵含有非零元素链时,判断其为H矩阵的条件.结论 此结果对于控制系统的稳定性、特征值分布、线性方程组迭代解等方面都具有重要的理论意义.     

一种用于磁感应成像中灵敏度矩阵的计算方法

生物组织中的磁感应成像(MIT)是一种通过测量交变磁场中因扰动导体所引起的感应电压来重建复合电导率分布的方法.灵敏度矩阵即是映射电导率分布的变化与接收线圈中感应电压变化的对应关系.基于有限元方法和补偿原理,提出一种快速计算灵敏度矩阵的方法,并应用这种方法进行了多种仿真分析实验.结果表明,通过该方法可以快速地对单个扰动和多个扰动的灵敏度矩阵进行有效求解,即为MIT中逆问题的图像重建提供了有效的方法.     

严格对角占优矩阵与SOR迭代法的收敛性定理

针对线性方程组的系数矩阵为α-链严格对角占优矩阵和双严格对角占优矩阵的情况,讨论了线性方程组求解时常用的SOR迭代方法的收敛性,给出了迭代法收敛性定理,解决了以往估计迭代矩阵谱半径的问题.结果不仅适用于这两类矩阵,还适用于广义严格对角占优矩阵类,最后举例说明了所给结果的优越性.     

具有混合时滞模糊神经网络的全局指数稳定性分析

主要研究一类具有混合时滞的模糊神经网络.运用不动点定理,M-矩阵理论和一些分析技术,得到了唯一平衡点存在和全局指数稳定的充分条件.实例证明了所得结果的有效性.     

矩阵Hadamard积特征值的估计

利用矩阵有向图上的k-path覆盖,给出了非负矩阵Hadamard积的最大特征值上、下界的估计式,改进了相关结果,使估计更具优越性.     

变时滞中立系统的时滞依赖渐近稳定性分析

本文讨论了一类变时滞中立系统的时滞依赖渐近稳定性问题.通过利用Lyapunov-Krasovskii泛函(LKF)和自由权矩阵方法,得到了该系统渐近稳定性的时滞依赖新判据.交叉项间的联系由Leibniz-Newton公式给出.定理的推导没有利用模型转换和交叉项有界方法.由于结果以严格线性矩阵不等式形式给出,所以很容易验证所考虑系统的稳定性.最后的数值实例验证所给判据的有效性和对已有结果的改进.     

Dynamic Response of Closed-Loop System with Uncertain Parameters Using Interval Finite-Element Method

Using the interval finite-element method, the vibration control problem of structures with interval parameters is discussed, which is approximated by a deterministic one. Based on the first-order Taylor expansion, a method to solve the interval dynamic response of the closed-loop system is presented. The expressions of the interval stiffness and interval mass matrix are developed directly with the interval parameters. With matrix perturbation and interval extension theory, the algorithm for estimating the upper and lower bounds of dynamic responses is developed. The results are derived in terms of eigenvalues and left and right eigenvectors of the second-order systems. The present method is applied to a vibration system to illustrate the application. The effect of the different levels of uncertainties of interval parameters on responses is discussed. The comparison of the present method with the classical random perturbation is given, and the numerical results show that the present method is valid when the parameter uncertainties are small compared with the corresponding mean values.     

Modified Sturm Sequence Property for Damped Systems

This technical note presents a method of checking the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues for nonproportionally damped system. A Schur–Cohn matrix is constructed from the coefficients of the characteristic polynomial for the damped system, and LDLT factorized using some standard numerical algorithms. By observing signs of the diagonal elements of the above diagonal matrix D, we can determine the number of complex eigenvalues in some interested regions or the multiplicity of some complex eigenvalues, which is very similar to the well-known Sturm sequence property for undamped systems. To verify the applicability of the proposed method, two numerical examples are considered.     

Perturbation Solutions for Thermal Process of Honeycomb Regenerator

 A parameter perturbation for the unsteady state heat transfer characteristics of honeycomb regenerator is presented. It is limited to the cases where the storage matrix has a small wall thickness so that no temperature variation in the matrix perpendicular to the flow direction is considered. Starting from a two phase transient thermal model for the gas and storage matrix, an approximate solution for regenerator heat transfer process is derived using the multiple scale method for the limiting case where the longitudinal heat conduction of solid matrix is far less than the convective heat transfer between the gas and the solid. The regenerator temperature profiles are expressed as Taylor series of the coefficient of solid heat conduction item in the model. The analytical validity is shown by comparing the perturbation solution with the experiment and the numerical solution. The results show that it is possible for the perturbation to improve the effectiveness and economics of thermal research on regenerators.     

Uncertain Dynamical Systems in the Medium-Frequency Range

This paper presents a novel probabilistic model of random uncertainties for dynamical system in the medium-frequency (MF) range. This approach combines a nonparametric probabilistic model of random uncertainties for the reduced matrix models in structural dynamics with a reduced matrix model adapted to the MF range. The theory is presented and the random energy matrix relating to a given MF band, its random trace, and its random eigenvalues are studied. A numerical example is presented allowing convergence properties and stability of random responses with respect to the bandwidth to be analyzed.     

A Note on Nonproportional Damping

This note deals with three aspects of nonproportional damping in linear damped vibrating systems in which the stiffness and damping matrices are not restricted to being symmetric and positive definite. First, we give results on approximating a general damping matrix by one that commutes with the stiffness matrix when the stiffness matrix is a general diagonalizable matrix, and the damping and stiffness matrices do not commute. The criterion we use for carrying out this approximation is closeness in Euclidean norm between the actual damping matrix and its approximant. When the eigenvalues of the stiffness matrix are all distinct, the best approximant provides justification for the usual practice in structural analysis of disregarding the off-diagonal terms in the transformed damping matrix. However, when the eigenvalues of the stiffness matrix are not distinct, the best approximant to a general damping matrix turns out to be related to a block diagonal matrix, and the aforementioned approximation cannot be justified on the basis of the criterion used here. In this case, even when the damping and stiffness matrices commute, decoupling of the modes is not guaranteed. We show that for general matrices, even for symmetric ones, the response of the approximate system and the actual system can be widely different, in fact qualitatively so. Examples illustrating our results are provided. Second, we present some results related to the difficulty in handling general, nonproportionally damped systems, in which the damping matrix may be indefinite, by considering a simple example of a two degrees-of-freedom system. Last, we use this example to point out the nonintuitive response behavior of general nonproportionally damped systems when the damping matrix is indefinite. Our results point to the need for great caution in approximating nonproportionally damped systems by damping matrices that commute with the stiffness matrix, especially when considering general damping matrices. Such approximations could lead to qualitatively differing responses between the actual system and its proportionally damped approximation.     

Parallel Algorithms for Integrated Structural/Control Optimization

Optimization of combined structural and control systems is a complex problem requiring an inordinate amount of computer‐processing time, especially the solution of the eigenvalue problem of a general unsymmetric square real matrix with complex eigenvalues and eigenvectors, which is frequently used in such problem. The few algorithms presented in the literature thus far have been applied to small structures with a few members and controllers only. Parallel processing on new‐generation multiprocessor computers provides an opportunity to solve large‐scale problems. In this paper, the integrated structural and control optimization problem is formulated by including constraints on displacements, stresses, and closed‐loop eigenvalues and the corresponding damping factors. Then, parallel algorithms are presented for integrated optimization of structures on shared‐memory multiprocessors such as the Cray YMP 8/864 supercomputer. In particular, parallel algorithms are presented for the solution of complex eigenvalue problems encountered in structural control problems using the method of matrix iteration for dominant eigenvalue(s). The solution is divided into two parts. The first part is the iteration for dominant eigenvalue(s) and the corresponding eigenvector(s) and the second part is the reduction of the matrix to obtain the smaller eigenvalue(s) and the corresponding eigenvector(s).     

Curve Veering of Eigenvalue Loci of Bridges with Aeroelastic Effects

The eigenvalues of bridges with aeroelastic effects are commonly portrayed in terms of a family of frequency and damping loci as a function of mean wind velocity. Depending on the structural dynamic and aerodynamic characteristics of the bridge, when two frequencies approach one another over a range of wind velocities, their loci tend to repel, thus avoiding an intersection, whereas the mode shapes associated with these two frequencies are exchanged in a rapid but continuous way as if the curves had intersected. This behavior is referred to as the curve veering phenomenon. In this paper, the curve veering of cable-stayed and suspension bridge frequency loci is studied. A perturbation series solution is utilized to estimate the variations of the complex eigenvalues due to small changes in the system parameters and establish the condition under which frequency loci veer, quantified in terms of the difference between adjacent eigenvalues and the level of mode interaction. Prior to the discussion of bridge frequency loci, the curve veering of a two-degree-of-freedom system comprised of a primary structure and tuned mass damper is discussed, which not only provides new insight into the dynamics of this system, but also helps in understanding the veering of bridge frequency loci. To study this more complicated dynamic system, a closed-form solution of a two-degree-of-freedom coupled flutter is obtained, and the underlying physics associated with the heaving branch flutter is discussed in light of the veering of frequency loci. It is demonstrated that the concept of curve veering in bridge frequency loci provides a correct explanation of multimode coupled flutter analysis results for long span bridges and helps to improve understanding of the underlying physics of their aeroelastic behavior.     

Fast and accurate numerical method for principal components analysis dealing with large image data sets

The principal components analysis has been applied to various imaging studies in nuclear medicine. This technical report describes a fast and accurate numerical method of calculating eigenvalues and eigenvectors in the principal components analysis dealing with larger image data sets. The method employs both data transformation and matrix transpose of original data sets to calculate a variance-covariance or correlation matrix. The method was tested on actual image data sets using a common workstation, confirming faster execution time and efficient accuracy in comparison to a standard method.     

Efficient Model Correction Method with Modal Measurement

An efficient model correction method is proposed by using the modal measurement from a structural system. The method corrects/updates the mass and stiffness matrix without imposing any parameterization. It considers the information from both the nominal finite-element model and the measurement of modal frequencies and mode shapes. The method is computationally very efficient and it does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the nominal eigenvalues and eigenvectors of the modes to be corrected are needed. The Gram-Schmidt orthogonalization process is used to construct a basis that satisfies the mass orthogonality condition. This basis is used to transform the eigenvectors of the nominal model so that the corrected model is compatible with the measurement. A thousand-degree-of-freedom chainlike system and a 1,440-degree-of-freedom structural frame are used to illustrate the proposed method.     

Analytical Solution of a Pressure Transmission Experiment on Shale Using Electrochemomechanical Theory

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a monovalent ionic solution. From the governing equations a coupled diffusion equation is derived for the three electrochemical potentials, which is decoupled introducing a set of normal parameters. The magnitude of the eigenvalues of the diffusivity matrix corresponds to the time scales for Darcy flow, diffusion of ionic constituents, and diffusion of electrical potential. The radial strain is very sensitive to the ionization.