窄带随机噪声作用下非线性系统的响应

研究了Duffing振子在窄带随机噪声激励下的主共振响应和稳定性问题.用多尺度法分离了系统的快变项,讨论了系统的阻尼项、随机项等对系统响应的影响.在一定条件下,系统具有两个均方响应值.数值模拟表明方法是有效的.     

谐和与随机噪声联合作用下Duffing振子的双峰稳态密度

研究Duffing振子在谐和与随机噪声联合作用下系统响应的双峰稳态概率密度问题．用多尺度法分离了系统的快变项,得到了系统慢变项满足的随机微分方程．用线性化方法求出了双峰稳态概率密度的表达式．数值模拟表明提出的方法是有效的．     

谐和与随机噪声联合作用下的粘弹系统

研究了粘弹系统在谐和与随机噪声联合作用下的响应和稳定性问题.用谐波平衡法和随机平均法分析了系统在确定性谐和激励和随机激励联合作用下的响应,讨论了粘弹项、随机扰动项对系统响应的影响.结果表明,在一定条件下,系统具有两个均方响应值和跳跃现象.数值模拟表明,谐波平衡法与随机平均法相结合的研究方法是有效的.     

非对称碰撞约束下形状记忆合金梁的随机响应与分岔

形状记忆合金(SMA)是二十一世纪具有形状记忆效应的新型智能材料.针对具有非对称约束的SMA梁,本文构造了碰撞振动系统.在无碰撞和有碰撞两种情况下,利用随机平均法给出了近似解析结果.数值模拟作为验证解析结果的工具.结果表明,系统能量的概率响应曲线具有非光滑特性.当约束位置发生变化时,系统会出现随机P分岔和D分岔.     

弹性约束浅拱的非线性动力响应与分岔分析

浅拱采用竖向、转动方向弹性约束时,自振频率和模态与理想的铰支/固结边界存在差异,不同约束刚度将改变外激励下的非线性响应及各种分岔产生的参数域．由浅拱基本假定建立无量纲动力学方程, 采用在频率和模态中考虑约束刚度大小的方法,通过Galerkin全离散和多尺度摄动分析导出极坐标、直角坐标形式的平均方程, 其中方程系数与约束刚度一一对应．用数值方法分析了周期激励下竖向弹性约束系统最低两阶模态之间1∶2内共振时的动力行为, 所得结果与有限元的对比以及平均方程系数的收敛性证明了所采用方法是可行的．随着激励幅值、频率的变化存在若干分岔点,分岔发生时的参数分布与约束刚度值有关,在由分岔点连接的不稳定区或共振区附近,存在一系列稳态解、周期解、准周期解和混沌解窗口,且随参数的变化可观测到倍周期分岔．     

谐和随机噪声联合作用下Van der PolDuffing振子的参数主共振

研究了Van der Pol－Duffing振子在谐和与随机噪声联合激励下的参数主共振响应和稳定性问题。用多尺度法分离了系统的快变项，并求出了系统的最大Liapunov指数和稳态概率密度函数，还分析了失稳、分 叉和跳跃现象，讨论了系统的阻尼项、非线性项、随机项和确定性参激强度等参数对系统响应的影响。数值模拟表明所提出的方法是有效的。     

一类准零刚度隔振器的分段非线性动力学特性研究

建立了一类带有滚轮装置的准零刚度隔振系统的分段非线性动力学模型,利用平均法对系统在基础激励下的动力学特性进行了理论分析,得到了系统主共振响应的一次近似解析解.利用数值方法对动力学方程求解,验证了平均法求解此类分段非线性动力学问题的有效性.进一步,讨论了激励幅值、阻尼对系统响应的影响,利用位移传递率评估了隔振系统的隔振性能.结果表明,激励幅值和阻尼对系统响应具有显著影响:激励幅值较小时,该准零刚度隔振系统的隔振性能明显优于相应的线性系统;而随激励幅值增大时,其隔振性能变差,但最多与线性系统相当,而不会变得更差,此特征优于传统准零刚度隔振系统.     

小曲率粘弹性索非线性随机稳定性分析

基于Kelvin粘弹性材料本构模型,研究小曲率粘弹性索在窄带随机激励作用下的非线性随机稳定性及均方响应。首先建立小曲率粘弹性索数学模型;然后提出一种确定粘弹性索均方响应及概率渐近稳定性方法;给出了系统均方稳定对激励带宽、幅值、中心频率等要求;给出系统的稳定区域;最后讨论了材料粘性、波速比及介质阻尼对系统不稳定区域的影响。     

调制白噪声激励下的单自由度强非线性系统的近似瞬态响应概率密度

研究调制白噪声激励下,包含弱非线性阻尼及强非线性刚度的单自由度系统的近似瞬态响应概率密度．应用基于广义谐和函数的随机平均法,导出关于幅值瞬态概率密度的平均Fokker－Planck－Kolmogorov 方程．该方程的解可近似表示为适当的正交基函数的级数和,其中系数是随时间变化的．应用Galerkin方法,这些系数可由一阶线性微分方程组解得,从而可得幅值响应的瞬态概率密度的半解析表达式及系统状态响应的瞬态概率密度和幅值的统计矩．以受调制白噪声激励的van der Pol-Duffing振子为例验证其求解过程,并讨论了线性阻尼系数及非线性刚度系数等系统参数对系统响应的影响．     

面内平动黏弹性板非线性振动的内-外联合共振

研究了同时存在受迫共振和1∶3内共振时的面内平动黏弹性板的横向非线性振动问题．板的黏弹性材料用Kelvin本构关系描述．基于系统的运动方程和四边简支的边界条件,对偏微分方程应用直接多尺度法建立了联合共振时的可解性条件．应用Routh-Hurvitz判据对系统幅频响应的稳定性进行了判别．给出了黏弹性系数、面内平动速度和激励幅值3个参数对幅频响应的影响．最后,应用微分求积数值方法验证了近似解析方法的结论.     

三维浮式结构的流固耦合动力特性分析

对于采用位移-压力有限元格式从流固耦合系统导出的大型非对称矩阵特征值问题,构造出了一种新格式的迭代Arnoldi方法进行非对称特征值分析来获得浮式结构的动力特性．该迭代格式在克服零频的移频技术中,可以高效地计算出Arnoldi向量．实例分析结果表明,流固耦合作用对水上大型薄壁浮式结构动力特性具有重要影响．     

Analysis of a self-scaling quasi-Newton method

We study the self-scaling BFGS method of Oren and Luenberger (1974) for solving unconstrained optimization problems. For general convex functions, we prove that the method is globally convergent with inexact line searches. We also show that the directions generated by the self-scaling BFGS method approach Newton's direction asymptotically. This would ensure superlinear convergence if, in addition, the search directions were well-scaled, but we show that this is not always the case. We find that the method has a major drawback: to achieve superlinear convergence it may be necessary to evaluate the function twice per iteration, even very near the solution. An example is constructed to show that the step-sizes required to achieve a superlinear rate converge to 2 and 0.5 alternately.This work was supported by National Science Foundation Grant CCR-9101359, and by the Department of Energy Grant DE-FG02-87ER25047.This work was performed while the author was visiting Northwestern University.     

A new polynomial time method for a linear complementarity problem

The purpose of this paper is to present a new polynomial time method for a linear complementarity problem with a positive semi-definite matrix. The method follows a sequence of points. If we generate the sequence on a path, we can construct a path following method, and if we generate the sequence based on a potential function, we can construct a potential reduction method. The method has the advantage that it requires at most iterations for any initial feasible point whose components lie between 2^–O(L) and 2^O(L).Research was supported in part by Grant-in-Aids for Encouragement of Young Scientists (63730014) and for General Scientific Research (63490010) of The Ministry of Education, Science and Culture.     

An a posteriori error estimate for a first-kind integral equation

In this paper we present a new a posteriori error estimate for the boundary element method applied to an integral equation of the first kind. The estimate is local and sharp for quasi-uniform meshes and so improves earlier work of ours. The mesh-dependence of the constants is analyzed and shown to be weaker than expected from our previous work. Besides the Galerkin boundary element method, the collocation method and the qualocation method are considered. A numerical example is given involving an adaptive feedback algorithm.

     

A Locally Conservative Eulerian-Lagrangian Finite Difference Method for a Parabolic Equation

The object of this paper is to define a finite difference analogue of a locally conservative Eulerian—Lagrangian method based on mixed finite elements and to prove its convergence. The method is appropriate for convection-dominated diffusive processes; here, it will be considered in the case of a semilinear parabolic equation in a single space variable.This revised version was published online in October 2005 with corrections to the Cover Date.     

Convergence analysis of a finite volume method via a new nonconforming finite element method

The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213–231, 1998     

一维抛物型方程一种新的边值问题的解法

在建立目标一维热红外温度模型时,提出了热传导方程的一个新的边值问题;通过比较,选择了GE差分格式,求解方程,并进行了稳定性分析;采用虚拟网格点法处理边界条件,得出了GE格式的完整形式;计算实例表明,分组显示方法更适合此类边值问题的实际计算.     

Optimal control in a macroeconomic problem

The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.     

On the Galerkin Method Based on a Particular Class of Scaling Functions

The aim of this paper is to provide a large class of scaling functions for which the convergence analysis for the Galerkin method developed in [9] is applicable, whereas in that paper the only scaling functions considered for practical applications are B-splines and a few of the orthonormal Daubechies scaling functions. The functions considered here, were recently introduced in [12] where it was proved that they satisfy many properties making them interesting for the applications. In particular, here we show that the use of these functions has some advantages with respect to other basis functions.     

Implementation of a continuation method for normal maps

This paper presents an implementation of a nonsmooth continuation method of which the idea was originally put forward by Alexander et al. We show how the method can be computationally implemented and present numerical results for variational inequality problems in up to 96 variables. The research reported here was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAH04-95-1-0149, and by the National Science Foundation under grant number CCR-9109345. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the sponsoring agencies or the U.S. Government.