多自由度非线性随机系统的响应与稳定性

响应与稳定性分析一直是随机动力学研究的热点, 发展预测随机响应及判定系统响应性态的方法具有重要的科学意义与广阔的应用前景. 本文综述了有关多自由度非线性随机系统的响应与稳定性的研究. 首先简介用于随机系统响应预测的Fokker-Planck-Kolmogorov方程法、随机平均法、等效线性化法、等效非线性系统法和Monte Carlo模拟法, 评述其优缺点, 进而讨论了多自由度非线性随机系统响应的精确平稳解、近似瞬态解的研究现状. 然后介绍了随机系统稳定性分析的两类方法, 即Lyapunov函数法及Lyapunov指数法,并综述了多自由度非线性随机系统稳定性分析的研究现状. 最后给出几点发展建议.     

强非线性振动系统的渐近解法

本文推广文[1]中方法于求解广泛一类强非线性振动系统,导出了适于近似定性分析和定量计算的简便公式。作为例子研究了修正的Vander Pol振子,最后给出数字Poincaré映射结果,从近似定性分析和定量计算两方面证明了本文求得的方法的有效性。     

裂纹转子振动的瞬态分量研究

利用定性分析、多尺度法和数值模拟三种方法对裂纹转子振动的特点进行了研究，着重讨论了瞬态分量的构成及其特性．研究结果表明瞬态振动分量是一个比较理想的，可以用于裂纹早期检测的特征，同时也证明了多尺度法是研究带有突变参数的参数激振系统的有效方法．     

长江宜都河段茶店崩岸机理与防治研究

崩岸是长江汛期大堤最严重险情。 1998年长江特大洪水后期 ,宜都河段茶店岸坡崩岸直接威胁长江大堤安全。本文分析了长江宜都河段的环境地质条件 ,宜都河段河流地质作用的基本特征。系统研究了茶店崩岸的形成机制及稳定性分析 ,最后提出了岸坡崩岸防治措施。     

一类种群动力学传染病模型的定性分析

本文对一类种群动力学传染病模型，运用定性分析方法，分析了奇点和拓扑结构，论证了正平衡点是全局稳定的，并得出该系统不存在极限环的结论，为研究该传染病的发生、流行、传播机制，及控制消灭该传染病提供了充分的理论依据。     

一类种群动力学传染病模型的定性分析

本文对一类种群动力学传染病模型，运用定性分析方法，分析了奇点的拓扑结构，论证了正平衡点是全局稳定的，并得出该系统不存在板限环的结论．为研究该传染病的发生、流行、传播机制，及控制消灭该传染病提供了充分的理论依据．     

有常数出生率的传染病模型的定性分析

本文对有常数出生率的传染病模型，运用定性分析方法，分析了唯一正平衡点的拓扑结构．运用Liapunov第二方法，论证了正平衡点的稳定性．并运用DuLac函数法，得出该系统不存在极限环的结论。进而为研究该传染病的发生流行，传播及成为地方病等提供了充分的理论依据。     

食饵种群无密度制约的第Ⅱ类功能反应捕食系统的拓扑结构分析

本文对食饵种群无密度制约的第Ⅱ类功能反应捕食系统作了完整的拓扑结构分析，发现了在任何条件下，食饵种群的数量都有增至无穷大的可能，这说明模型的合理性比对模型的定性分析更重要。     

智能梁结构鲁棒PID控制及其时滞稳定性分析

研究了智能梁结构振动的鲁棒PID控制器的设计问题,考虑结构模态阻尼比及模态频率的不确定性,同时结合PID控制、保成本控制和H∞控制的优点,提出了一种鲁棒PID控制的设计方法,将PID控制器的参数整定问题转化为线性矩阵不等式凸优化问题的求解.考虑到实际系统中存在的时滞因素,对设计出的鲁棒PID控制系统进行了时滞稳定性分析,得出了使系统稳定的最大时滞量.最后,给出的数值算例说明了文中方法的可行性和有效性.     

电流变“Smart”轴承动态特性分析

本文采用作者提出的二次规划法为基础的双线性流变有限元方法分析了电流变“Ｓｍａｒｔ”轴承的动态特性,给出了在不同偏心率下轴承油膜八项动态特性系数随电压改变的曲线。通过对轴承－转子系统的稳定性分析,发现若加大油膜电压将会提高轴承的稳定性     

Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems

In this paper, we present the design, modelling and experimental validation of a novel experimental cam-follower rig for the analysis of bifurcations and chaos in piecewise-smooth dynamical systems with impacts. Experimental results are presented for a cam-follower system characterized by a radial cam and a flat-faced follower. Under variation of the cam rotational speed, the follower is observed to detach from the cam and then show the emergence of periodic impacting behaviour characterized by many impacts and chattering. Further variations of the cam speed cause the sudden transition to seemingly aperiodic behaviour. These results are compared with the numerical simulation of a mathematical model of the system which shows the same qualitative behaviour. Excellent quantitative agreement is found between the numerical and experimental results.     

Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array

In this paper, the three-dimensional (3-D) non-linear dynamics of a cantilevered pipe conveying fluid, constrained by arrays of four springs attached at a point along its length is investigated. In the theoretical analysis, the 3-D equations are discretized via Galerkin's technique. The resulting coupled non-linear differential equations are solved numerically using a finite difference method. The dynamic behaviour of the system is presented in the form of bifurcation diagrams, along with phase-plane plots, time-histories, PSD plots, and Poincaré maps for five different spring configurations. Interesting dynamical phenomena, such as 2-D or 3-D flutter, divergence, quasiperiodic and chaotic motions, have been observed with increasing flow velocity. Experiments were performed for the cases studied theoretically, and good qualitative and quantitative agreement was observed. The experimental behaviour is illustrated by video clips (electronic annexes). The effect of the number of beam modes in the Galerkin discretization on accuracy of the results and on convergence of the numerical solutions is discussed.     

Dynamics of cantilevered pipes conveying fluid. Part 3: Three-dimensional dynamics in the presence of an end-mass

In this part, the last in a three-part study, the three-dimensional (3-D) dynamics of a cantilevered pipe conveying fluid is explored when an additional “point” mass is attached at the free end. For a typical case, the dynamical behaviour of this system is presented in the form of a bifurcation diagram, along with the time traces, phase-plane plots, PSD plots and Poincaré maps, showing planar periodic, quasiperiodic and chaotic oscillations, followed by 3-D quasiperiodic and chaotic motions. The effect on the results of the number of beam modes used in the Galerkin solution scheme is studied in some detail. The theoretical results are then compared with the results of a set of experiments done previously and good qualitative and quantitative agreement is observed.     

Piercing a liquid surface with an elastic rod: Buckling under capillary forces

When a thin elastic structure comes in contact with a liquid interface, capillary forces can be large enough to induce elastic deformations. This effect becomes particularly relevant at small scales where capillary forces are predominant, for example in microsystems (micro-electro-mechanical systems or microfluidic devices) under humid environments. In order to explore the interaction between capillarity and elasticity, we have developed a macroscopic model system in which an initially immersed vertical elastic rod is raised through a horizontal liquid surface. We follow a combined approach of experiments, theory and numerical simulations to study this system. In spite of its apparent simplicity, our experiment reveals a complex phase diagram, involving large hysteretic behaviour. We employ Kirchhoff equations for thin elastic rods and use path-following methods from which we obtain a variety of equilibrium states and associated transitions that are in excellent qualitative and quantitative agreement with those observed experimentally.     

On the interpretation of data from Converging Flow Rheometers

A reappraisal of data obtained from a Converging Flow Rheometer (CFR) is presented, together with new results for a specific polymer solution.Particular emphasis is placed on the interpretation of the experimental pressure data in terms of a planar extensional viscosity. It is suggested that previous interpretations, while yielding viscosity levels that appear reasonable, nevertheless fail to give the qualitative behaviour that might be expected on the basis of predictions from well accepted constitutive models. This, in the authors' opinions, arises because certain fluids, i.e. those that are highly tension-thickening, cease to flow in accordance with the assumed kinematics at high flow rates.By adapting a recently proposed approximate analysis for flow through a contraction it is shown that better qualitative behaviour, for the planar extensional viscosity, can be obtained from the Converging Flow Rheometer.     

ASYMPTOTIC ANALYSIS OF STABILITY PROBLEM OF PLANE POISEUILLE FLOW FOR HIGH REYNOLDS NUMBER

A study of the stabifity of plane Poiseuille flow at higher Reynolds number is made. Within a "triple-deck" structural framework, the qualitative behaviour of the eigenvalue of Orr-Sommerfeld equation is analytically obtained. The corresponding eigenfunction is formulated approximately.     

“Horseshoe chaos” in the space-independent double sine-Gordon system

For the driven, damped space-independent double sine-Gordon equation threshold curves for horseshoe chaos of the Smale type are derived by the Melnikov technique. Different qualitative behaviour of the solutions is found in different regions of parameter space.     

LINEAR AND NONLINEAR DYNAMICS OF CANTILEVERED CYLINDERS IN AXIAL FLOW. PART 1: PHYSICAL DYNAMICS

This paper is the first in a three-part study of the dynamics of cantilevered cylinders in axial flow. After an extensive literature review, the physical dynamics of the system is examined; specifically (a) the experimental behaviour of elastomer cylinders in water flow, and (b) the energy transfer mechanisms, discussed from a work–energy perspective without solving the equations of motion. In general, the system loses stability by divergence and, as the flow velocity is increased, it is subject to second- and third-mode flutter, provided that the free end is well-streamlined; if, however, the free end is blunt, these instabilities do not occur. Oscillations are generally three-dimensional (orbital). The experimental observations are in good qualitative agreement with those expected from the energy transfer analysis, and in reasonably good quantitative agreement with solutions of the linearized equation of motion (obtained from Part 3 of this study). For some shapes of the free-end, resonances are observed with a fairly constant Strouhal number.     

Damping of mesh-induced errors in Free-Lagrange simulations of Richtmyer-Meshkov instability

Mesh-induced errors at material interfaces are identified as a source of unphysical behaviour in Lagrangian numerical simulations of Richtmyer-Meshkov instability. The mesh geometry introduces interface perturbations with wavelengths of the same order as the mesh resolution. When a shock propagates through the interface, these perturbations can grow, severely contaminating the predicted interface development. Here an algorithm is presented which damps small-scale interface perturbations. A body force is applied at the interface which depends upon the disturbance amplitude and growth rate, and which resembles surface tension. Using this technique, qualitative improvements are obtained in Free-Lagrange simulations of single-mode Richtmyer-Meshkov instability. Growth rate behaviour and the evolution of the instability are seen to agree well with previously published results. Received 9 March 2000 / Accepted 30 May 2000     

分离流动物理特性研究进展

分离流问题的研究在当前流体力学中占有十分重要的地位。它不仅具有重要的理论意义并且具有广泛的应用价值。本文着重评述三维分离流中的基本物理特性和它的流动结构。重点讨论了三维定常分离的两种模式及其判别准则;在三维分离流中应用奇点拓扑理论的定性分析;按照流动的物理特性对三维分离的分类;分离面的物理特性。最后简单介绍了目前在研究湍流边界层分离方面的进展。