图的Laplacian特征值

本文研究了连通图的Laplacian特征值,利用图的Laplacian矩阵的特征多项式的行列式表示式,对存在两个不同顶点,但有相同邻集的一类图,得到了一个Laplacian特征值,并给出了它的应用.     

Error analysis of symplectic Lanczos method for Hamiltonian eigenvalue problem

A rounding error analysis for the symplectic Lanczos method is given to solve the large-scale sparse Hamiltonian eigenvalue problem. If no breakdown occurs in the method, then it can be shown that the Hamiltonian structure preserving requirement does not destroy the essential feature of the nonsymmetric Lanczos algorithm. The relationship between the loss of J-orthogonality among the symplectic Lanczos vectors and the convergence of the Ritz values in the symmetric Lanczos algorithm is discussed. It is demonstrated that under certain assumptions the computed J-orthogonal Lanczos vectors lose the J-orthogonality when some Ritz values begin to converge. Our analysis closely follows the recent works of Bai and Fabbender. Selected from Journal of Mathematical Research and Exposition, 2004, 24(1): 91–106     

改进Guyan～递推减缩技术

本文基于广义逆技术和逐级逼近思想,既建立了精度显著提高的改进Guyan减缩法,又提出了“物理型”近似减缩技术方面精度最好的准动态k级速推减缩公式,然而这些方法的执行时间却与其它“同一级”方法大抵相同．因此说,本方为工程界提供了至今综合效果最好的一类准动态模型减缩技术。     

电磁共振腔辛有限元法

将电磁场的基本方程导向了对偶方程形式。给出了推导电磁场有限元所需相应的对偶变量变分原理。为了有限元列式的保辛，交分原理被积函数可导向对于对偶变量为对称的形式。交分原理的边界积分项对于相邻单元互相抵消。对偶变量有限元推导可避免所谓的C1连续性问题。采用对偶变量离散分析了共振腔本征值问题，离散后再消去一类变量可导出普通的广义本征值问题而求解。算例表明了对偶变量有限元分析的有效性。     

结构动力学修改重分析方法的发展

结构动力学修改重分析技术是结构／机械振动控制和动态特性设计与优化的重要理论工具，本文简要述评了一些主要的高效重分析计算方法的研究发展概况，其中侧重于摄动分析方法。最后简单介绍了这些重分析方法的若干重要应用领域。     

Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach

The Dafermos regularization of a system of n hyperbolic conservation laws in one space dimension has, near a Riemann solution consisting of n Lax shock waves, a self-similar solution u = u _ε(X/T). In Lin and Schecter (2003, SIAM J. Math. Anal. 35, 884–921) it is shown that the linearized Dafermos operator at such a solution may have two kinds of eigenvalues: fast eigenvalues of order 1/ε and slow eigenvalues of order one. The fast eigenvalues represent motion in an initial time layer, where near the shock waves solutions quickly converge to traveling-wave-like motion. The slow eigenvalues represent motion after the initial time layer, where motion between the shock waves is dominant. In this paper we use tools from dynamical systems and singular perturbation theory to study the slow eigenvalues. We show how to construct asymptotic expansions of eigenvalue-eigenfunction pairs to any order in ε. We also prove the existence of true eigenvalue-eigenfunction pairs near the asymptotic expansions.     

一种有效的广义特征值分析方法

提出了一种适合于自适应有限元分析中求解广义特征值问题的多重网格方法．这种方法充分利用了初始网格下的结果，通过插值或最小二乘拟合技术来得到网格变化后的新的近似特征向量，然后由多重网格迭代过程实现对结构广义特征值问题的求解．在多重网格迭代的光滑步中，选择了收敛梯度法以提高其收敛率；在粗网格校正步中，则导出了一种近似求解特征向量误差的方程．这种方法将网格离散过程和数值求解过程很好地相结合，建立了一个网格细分后广义特征值问题的快速重分析方法，与传统有限元方法相比较，具有计算简便、计算量少等特点，可以作为结构动力问题自适应有限元分析的一种十分有效的工具．     

线性哈密顿系统的本征摄动法

利用哈密顿算子辛自共轭的特点讨论了保守哈密顿体系的摄动问题,给出了哈密顿矩阵的本征值与本征向量的二阶摄动分析方法。即当系统在哈密顿框架下进行较小修改时,不重复求解大型哈密顿矩阵的本征问题,只需在原系统的模态参数基础上进行模态分析即可,这种矩阵摄动法给出了修改后矩阵的二阶本征值和本征向量,为一般线性保守体系的本征摄动求解提出了一个新方法。     

Effects of damping on brake squeal coalescence patterns – application on a finite element model

Brake squeal is referred to, in most publications, as a flutter instability triggered by a mode coupling phenomenon. A lot of clues tend to prove that damping would be a key parameter in brake squeal modelling. This study aims at investigating the effects of damping on coalescence patterns, that is to say on the way the modes couple. A finite element model of the whole brake corner has been used to compute the brake modal behaviour. Then a complex eigenvalue analysis has been undertaken to assess the brake stability as a function of the friction coefficient. Different kinds of damping spreading over the modes have been studied. Two main effects have been noticed: a shifting effect and a smoothing effect. The first one always stabilize the brake, whereas this is not the case of the second one. The combination of the two effects may make the brake more unstable depending on the spreading of the additionnal damping.