区间参数结构振动问题的矩阵摄动法

当结构的参数具有不确定性时，结构的固有频率也将具有某种程度的不确定性．本文讨论了区间参数结构的振动问题，将区间参数结构的特征值问题归结为两个不同的特征值问题来求解．提出了求解区间参数结构振动问题的矩阵摄动方法．数值运算结果表明，本文所提出方法具有运算量小，结果精度高等优点．     

地下结构和岩土介质弹塑性耦合分析的摄动半解析法*

本文研究了一个用于物理非线性相互作用分析的有效的数值方法。结构和介质耦合分析的弹塑性问题可用摄动法转化为几个线性问题,然后对相应的线性问题分别用有限条和有限层法分析地下结构和岩土介质以达到简化计算的目的。这种方法用了两次半解析技术——摄动和半解析解函数——将三维非线性耦合问题化为一维的数值问题。此外,本法是半解析法结合解析的摄动法应用于非线性问题的新进展,同时也是近年来发展的摄动数值法的一个分支。     

统计能量分析中参数不确定性分析

统计能量分析方法是计算结构高频振动噪声的有效方法之一，内损耗因子和耦合损耗因子是其中重要的参数但不易测量，测量误差通常比较大，导致计算得到的子系统振动能量和真实值之间存在偏差.为解决上述问题，该文采用了4种不同的区间分析方法:区间矩阵摄动法、基于区间变量特性法、仿射算法和仿射逆矩阵法，从理论上计算了统计能量分析子系统的振动能量区间，该区间结果充分考虑了内损耗因子和耦合损耗因子的测量误差对计算结果的影响，对传统的统计能量分析理论进行了完善.然后，通过算例比较了每种方法所求子系统总能量区间的优劣.     

基于积分二次约束混合摄动系统的摄动界

讨论正向通道为线性不确定系统,反馈通道为非线性动态不确定系统组成的不确定混合摄动系统的摄动界问题。假定其线性部分的参数不确定由区间摄动模式描述,非线性部分的动态不确定由积分二次约束(IQC)描述。用Minkowski泛函出给出区间摄动模式下的摄动界的定义,并给出参数空间中混合摄动模式下系统摄动界的估计式。根据双凸函数和凹凸函数的特性把混合摄动系统的无穷稳定检验问题转化为顶点检验和一维检验问题。最后给出例子。     

接触表面中多场耦合方程的边界层特征解

介绍由约束场和受重力影响的对流扰动耦合而成的衰减平衡向量场动力学方程的渐近求解.为分析实验室内微观与自然界中宏观现象的正则和奇异扰动问题.运用复合尺度方法进行Fourier调和分析、尺度变化,并引进新的参数,将一个复杂的三维约束耦合动力学方程降维投影并转化成复空间里一维的边界层问题.通过渐近摄动分析,给出多场耦合中扰动问题的特征函数边界层解法,在例2中对流场扰动问题分析,得出从指数振荡解过渡到代数解的转点.进一步分析计算非线性特征值问题并做了渐近摄动分析,最后给出多场耦合中扰动问题的特征值边界层解法.最后,特征关系式的各参数表明其在接触表面中对动力衰变的关键影响.     

矩阵DA的特征值及在系统稳定性分析中的应用

本文分析了矩阵ＤＡ的特征值，并提出了一种新的矩阵稳定性问题：Ｄ－－稳定性和块Ｄ－－稳定性．这里Ｄ是一个正对角阵，Ａ是给定的矩阵．应用劳斯判据及李雅普诺夫方法等，详细地分析了此类稳定性问题，提出了一些易于验证的结果，可用于分析多变量奇异摄动系统稳定问题．     

用摄动配置方法求解含时薛定谔方程

将摄动配置方法应用到含时薛定谔方程,在计算实现的基础上结合摄动配置的特征提出了一类新的数值积分方法,并给出了一个2级2阶和一个3级4阶的辛摄动配置方法对含时薛定谔方程的数值算例.为了检验新的数值积分方法,我们还给出了与两个辛摄动配置格式在理论上等价的辛龙格-库塔方法以及同阶的非辛方法的数值模拟.展示了一些数值结果,并给出了一些分析.     

摄动初参数法解轴对称壳几何非线性问题

作者在文[7]中提出轴对称壳任意大挠度问题的一阶微分方程组和以载荷变量为尺度的变特征无量纲化方法。在此基础上,本文选取挠角非线性偏差的加权均方根作摄动参数,给出该问题的无量纲摄动微分方程组。从而把非线性问题转化为n个线性问题来解决。本文采用数值积分的初参数方法对摄动后的各阶线性问题进行了计算。摄动结果与实验[4]相符合。     

区间有限元方法及其在抗滑稳定性分析中的应用

通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题,给出了保证区间计算获得足够精度的计算方法;提出了基于单元的子区间摄动有限元计算方法,并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式．结合工程实例,基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围,为更合理地估计和评价结构的抗滑稳定性提供一定的依据．     

一维粘弹性波动方程弹性系数的识别方法

本文就一维粘弹性波动方程弹性系数的求解问题，给出了一个新的求解方法．通过对算法进行分析可知，该方法具有较小的计算量，并且具较好的数值稳定性．数值模拟表明了该方法的可行性及有效性．     

A new method of performance sensitivity analysis for non-Markovian queueing networks

The paper develops a new method of calculating and estimating the sensitivities of a class of performance measures with respect to a parameter of the service or interarrival time distributions in queueing networks. The distribution functions may be of a general form. The study is based on perturbation analysis of queueing networks. A new concept, the realization factor of a perturbation, is introduced for the network studied. The properties of realization factors are discussed, and a set of linear differential equations specifying the realization factors are derived. The sensitivity of the steady-state performance with respect to a parameter can be expressed in a simple form using realization factors. Based on this, the sensitivity can be estimated by applying a perturbation analysis algorithm to a sample path of the system. We show that the derivative of the performance measure with respect to a parameter based on a single sample path converges with probability one to the derivative of the steady-state performance as the length of the sample path goes to infinity. The results provide a new analytical method of calculating performance sensitivities and justifies the application of perturbation analysis algorithms to non-Markovian queueing networks.     

A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term

In this paper, a numerical method based on finite difference scheme and Shishkin mesh for singularly perturbed two second order weakly coupled system of ordinary differential equations with discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.     

基于Lanczos方法的结构动力学灵敏度分析

利用数学理论得到结构动力学重特征值的灵敏度表达式,从而解决了奇异性问题.然后,为降低计算工作量,基于Lanczos方法得到降阶的结构系统,从而得到降阶的灵敏度分析近似解.用一个算例证明的方法正确性.     

Calculation of the spectral dependence of the Anderson localization criterion in a one-dimensional system with correlated diagonal disorder

We consider the problem of calculating the Anderson criterion for a one-dimensional disordered chain with correlated disorder. We solve this problem by the perturbation method with the inverse correlation length as the small parameter. We show that in a correlated system, the degree of localization not only naturally decreases but its spectral dependence also differs significantly from the spectral dependence in uncorrelated chains. The calculations are based on the method for constructing joint statistics of Green’s functions, which was previously used to analyze uncorrelated one-dimensional systems. We illustrate the theoretical calculations with a numerical experiment.     

Damping of the free oscillations of a neutral buoyancy sphere in a viscous stratified fluid

A technique is developed for calculating the oscillations of balanced spheres at neutral buoyancy levels based on the linearization of the equations of the mechanics of a viscous, continuously stratified fluid. A self-consistent system of integro-differential equations is obtained and analysed using perturbation theory methods. The results of calculations of the displacements of the centres of the spheres are reduced to a form which a permits direct comparison with a laboratory experiment and they agree with the data of measurements. A comparison is made with calculations of the free oscillations of a sphere in an ideal fluid.     

A fast algorithm for solving Toeplitz penta-diagonal systems

In this paper a fast algorithm for solving a large system with a symmetric Toeplitz penta-diagonal coefficient matrix is presented. This efficient method is based on the idea of a system perturbation followed by corrections and is competitive with standard methods. The error analysis is also given.     

Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods

A generalization and extension of a finite difference method for calculating numerical solutions of the two dimensional shallow water system of equations is investigated. A previously developed non-oscillatory relaxation scheme is generalized as to included problems with source terms in two dimensions, with emphasis given to the bed topography, resulting to a class of methods of first- and second-order in space and time. The methods are based on classical relaxation models combined with TVD Runge–Kutta time stepping mechanisms where neither Riemann solvers nor characteristic decompositions are needed. Numerical results are presented for several test problems with or without the source term present. The wetting and drying process is also considered. The presented schemes are verified by comparing the results with documented ones.     

Optimal system and approximate solutions of nonlinear dissipative media

In this paper, the problem of approximate symmetries of a class of nonlinear wave equations with a small nonlinear dissipation has been investigated. In order to compute the first-order approximate symmetry, we have applied the method that was proposed by Valenti basically based on the expansion of the dependent variables in perturbation series but removing the drawback of the impossibility to work in hierarchy in calculating symmetries. The algebraic structure of the approximate symmetries is discussed, an optimal system of one-dimensional subalgebras is defined and constructed, and, finally, some invariant solutions corresponding to the resulted symmetries are obtained.     

Intelligent control of chaos using linear feedback controller and neural network identifier

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network.     

Sensitivity analysis for variational inequalities

Sensitivity analysis results for variational inequalities are presented which give conditions for existence and equations for calculating the derivatives of solution variables with respect to perturbation parameters. The perturbations are of both the variational inequality function and the feasible region. Results for the special case of nonlinear complementarity are also presented. A numerical example demonstrates the results for variational inequalities.The author is indebted to A. V. Fiacco for many valuable suggestions and comments. This work was supported in part by funding from the Economic Regulatory Administration, US Department of Energy, under Contract No. W31109ENG38.