不对中联轴器 柔性转子系统非线性动力学行为

主要研究了在滑动轴承支承下转子间具有平行不对中故障的柔性联转子系统非线性动力学行为.首先,在考虑到联轴器的连接刚度后,基于两转子间运动的几何关系和位移约束条件推导了在非线性油膜力作用下平行不对中转子系统的动力学模型,理论分析表明该系统是一个含有时变系数和强非线性特征的11自由度非自治系统.然后采用数值方法重点分析了系统的非线性振动特性,例如,系统的轴心轨迹、频谱相应,Poincaré截面等.结果表明:在较低转速时,转子的涡动轨迹在较小的范围内作同步振荡;随着转速的提高,系统出现倍周期分叉现象,以及准周期、混沌运动等复杂的非线性动力学行为.最后讨论了联轴器的连接刚度对系统运动特性的影响.     

具时滞的非线性纵向飞行模型稳定性和分支分析

研究一类具有时滞的非线性飞行模型的稳定性和分支问题。首先考虑数据测量的时间延迟,给出了含时滞的大迎角纵向多项式飞行模型;然后应用泛函微分方程Hopf分支理论和中心流形等非线性方法给出了该模型稳定性和分支的解析分析,得到了由时滞引起的Hopf分支存在条件、分支点计算公式以及分支周期解的稳定性判别准则;最后利用所得结论进行了飞行实例分析,分析结果表明,数据测量延时可能会引起飞行稳定性的改变,而且延时超过一定临界值时将产生Hopf分支,出现纵向周期振荡,其结论具有实际参考意义。     

Exponential stabilisation of nonlinear parameter-varying systems with applications to conversion flight control of a tilt rotor aircraft

The exponential stabilisation problem of nonlinear parameter-varying (NPV) systems with input constraints is investigated. Unlike the existing NPV-related works, this paper directly addresses NPV models to conduct the stabilisation problem, without hiding nonlinearities or ignoring the time-varying nature. Existence conditions of a nonlinear time-varying (NTV) controller to render the uniformly exponential stability of an NPV system are given in terms of state-and-parameter-dependent linear matrix inequalities (SPLMIs). Specifically, a new controller structure and a novel Lyapunov functional are adopted such that the exact variation rates of the state and parameters can be incorporated into the SPLMIs. The generalised S-procedure is used to convexify the input constraints such that the resulting closed-loop system satisfies input constraints for any state starting from an admissible set. The derived SPLMIs can then be efficiently solved via sum-of-squares programming. The proposed approach is applied to the conversion flight control of a tilt rotor aircraft.     

动力吸振器对转子系统气流激振稳定性影响分析

针对气流激振引起离心压缩机转子振动失稳的问题,提出了采用动力吸振方法提高转子系统的稳定性.首先建立流体激励作用下转子 吸振系统动力学模型;其次采用Lyapunov理论研究附加吸振器后流体激励作用下转子系统的稳定性;分析了吸振器参数变化对转子系统稳定性的影响;最后采用数值方法进行验证.结果表明,动力吸振方法能够有效地提高转子系统失稳转速,吸振器固有频率和阻尼比对转子稳定性有较大的影响.     

基于Matlab工具箱的一类神经网络分叉分析与计算

根据非线性动力系统的Hopf分叉和环面分叉理论,应用Matlab环境下的非线性分叉分析工具箱,对简化的Wilson-Cowan神经网络系统模型中存在的复杂非线性现象进行分析计算,通过仿真验证计算结果,表明该方法用于高维非线性动力系统的分叉研究具有简单、便捷和精确的特点,能够满足一般非线性动力系统理论分析和仿真计算的要求.     

一类弦-梁耦合非线性振动系统的动力学数值模拟研究

本文研究了一类具有参数激励和外激励弦-梁耦合非线性系统.首先,运用多尺度法分析弦-梁耦合非线性系统的响应,求得系统平均方程.其次,基于求得的方程,以系统的阻尼系数作为分叉参数,并对系统平衡点的稳定性进行分析,得到平衡点的分叉曲线.为了验证理论预测的正确性数值模拟了不同分叉参数下的相空间轨线.利用四阶龙格库塔方法验证了弦-梁耦合非线性系统混沌运动的存在性,从数值模拟看出系统存在单倍周期运动、多倍周期运动和混沌运动.     

一类非线性金融系统的数值研究

利用数值模拟的方法研究了一类非线性金融系统的动力学行为.建立了由生产、资金、股份、劳动力四个部分构成的一类非线性金融系统的动力学模型.首先运用四维微分方程来描述由利率、投资需求、价格指数和平均利润率构成的四个状态变量随时间的变化,然后将金融系统简化为四维自治微分方程组.通过对四维自治微分方程组进行数值模拟发现了非线性金融系统的动力学特性,从数值模拟获得的三维相图反映了金融系统的非线性特性.从数值模拟结果发现,在特定的条件下非线性金融系统存在周期运动和混沌运动.除此之外,还观察到参数的改变对四维自治金融系统的非线性特性有着显著的影响.     

Stability analysis of a control system with nonlinear input uncertainty based on disturbance observer

In disturbance observer (DO)‐based control, control input attenuates a disturbance using observer output. Thus, the input may not achieve the attenuation if the input term includes uncertainty. Therefore, in order to correctly suppress the disturbance, it is essential to consider the uncertainty existing in the input term, and thus this article focuses on a nonlinear uncertainty in the input term. This article analyzes the stability and robustness of a DO‐based nonlinear control system with both the disturbance and the input uncertainty. We address the case that the disturbance and the uncertainty depend on time and states of a controlled system. The disturbance and the uncertainty are gathered in an integrated disturbance, and the integrated disturbance depends on many variables: the states, the control input, and the time. Therefore, a norm estimations for the disturbance and a time variation of the disturbance is difficult without knowledge of the state trajectory. Hence, a slope‐restriction for the disturbance is used for the stability analysis. Based on the mathematical analysis, we show input‐to‐state stability conditions due to extend the application class of the DO‐based controller to a control system with the disturbance and the nonlinear input uncertainty. The analytical results are verified by numerical simulations.     

一类具有时滞和非线性发生率的SIRS传染病模型稳定性与Hopf分岔分析

研究了一类具有时滞及非线性特性发生率的SIRS传染病模型,首先利用特征值理论分析了无病平衡点和地方病平衡点的局部稳定性;并以时滞τ作为分岔参数,分析了模型的Hopf分岔行为,运用中心流形定理和规范型理论给出了分岔方向及分岔周期解稳定性的计算公式;最后,数值模拟验证了理论分析结果.     

规范形Qi系统的Hopf分岔分析及控制

文章研究了一个Qi系统的Hopf分岔控制问题.根据计算的极限环曲率系数,判定原系统的Hopf分岔类型,并采用washout滤波器控制该系统的分岔行为.首先讨论了控制器的线性增益对Hopf分岔点位置的影响,然后引入规范形计算方法,求出受控系统的Hopf分岔规范形.分析了规范形中系数对控制参数的选择原则所产生之影响,以及对Hopf分岔类型及极限环幅值的影响.理论和仿真结果表明,控制器的线性增益能使原系统的Hopf分岔点延迟或消失,而非线性增益能则改变极限环的稳定性和极限环幅值的大小.最后把washout滤波器和线性控制器的控制效果作了对比,发现washout滤波器比之线性控制器具有一定的优势.     

悬臂梁限位器非线性动力学效应实验分析

针对具有限位器的悬臂梁系统设计了一个实验装置,通过实验分析限位器对悬臂梁系统非线性动力学行为的影响规律,展示了跳跃、多稳态以及它们之间的转换等实验现象.本文还分析了限位器宽度和高度对悬臂梁非线性幅频响应的影响规律,同时揭示了限位器宽度和高度对悬臂梁与限位器接触的一般规律.在实验中还发现了随外激励频率的变化,系统的运动从周期变为混沌再到跳跃的现象,同时给出了时间历程图与频谱分析图,并解释了这种现象.本文的研究体现了非光滑系统的丰富的非线性动力学现象.     

Deriving a discrete approximate solution for a nonlinear dynamic system of two-phase soil media

A discrete approximate generalized solution is derived for a nonlinear differential model of the dynamics of two-phase soil media and its convergence is estimated for the corresponding generalized solution in the space W ₂ ¹ (Ω). Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 69–80, July–August 2009     

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

This paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete‐time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete‐time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

基于胞参考点映射法对转子/定子碰摩响应的全局分析

利用胞参考点映射法对两自由度(四维)分段光滑的转子/定子碰摩模型的全局响应特性进行了计算,着重对解析分析得到的碰摩系统典型的吸引子共存现象进行了验证,确定了相应吸引子的吸引域.此外,通过计算转子/定子碰摩系统全局特性随系统参数变化的演化特点,考察了吸引子与其吸引域边界对参数变化的敏感性,讨论了其对实际转子/定子碰摩系统...     

A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations

In this article, we study some fundamental results concerning the convergence of the Adomian decomposition method (ADM) for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Under certain conditions, we obtain upper estimates for the norm of solutions of this system. We also obtain results about the error estimates for the approximate solutions by the ADM and discuss their applications.