谷值电流控制反激变换器的非线性现象

为了选取DC-DC变换器的参数,建立了谷值电流控制反激变换器动力学方程和离散映射模型,利用分岔图和庞加莱映射,研究了其复杂的非线性动力学行为,并对基于谷值参考电流和输入直流电压变化的稳定性和分岔特性进行了分析.通过Matlab/Simulink平台构造了相应的时域仿真模型,得到了谷值电流控制反激变换器的时域波形和相轨图.研究结果表明,谷值电流控制反激变换器存在非线性动力学行为,变换器随着电路参数的变化,从稳定状态经过倍周期分岔和边界碰撞分岔进入混沌状态.     

货车系统的非线性动力学分析

阐述了车辆系统的线性、非线性和实际临界速度的概念,建立了具有３１个自由度的非线性货车系统数学模型,考虑了系统中的干摩擦力和轮轨相互作用关系等非线性因素。应用数值方法研究了货车系统的蛇行稳定性特性,包括货车系统中的极限环、准周期解以及混沌运动。     

一类非线性车辆跟驰模型的稳定性与分岔特性

针对一类常用的非线性车辆跟驰模型,本文运用时滞动力系统理论,分析了由3辆车组成的系统的稳定性及其Hopf分岔特性,得到了系统参数平面上的稳定域范围,以及不同的系统时滞量（驾驶员反映时间）和不同的安全间距对系统稳定域的影响,揭示了非线性车辆跟驰模型中存在的复杂动力学现象。通过数值仿真验证了理论分析和计算的结果,并判明了系统经历的Hopf分岔是亚临界的。理论分析的结果可推广到由任意辆车组成的车队。     

长江口南北港分汊口河段护滩限流工程效果分析

作为长江口南北港分汊口治理工程的重要组成部分之一,新浏河沙护滩及南沙头通道限流潜堤工程是长江口深水航道上延的基础性工程,也是南北港分汊口河势控制的关键工程。根据现场水沙测验和地形监测资料,从治理工程实施前后汊道分流比、河床冲淤变化、航道条件以及工程结构稳定性等因素入手,初步分析了新浏河沙护滩及南沙头通道限流潜堤工程的实施效果。结果表明,工程实施效果显著,南北港分汊口河段局部河势向不利方向发展的态势基本得到遏制,宝山南、北水道航道条件明显改善,整治建筑物结构安全稳定,总体达到了预期的治理目标,有利地保障了10.5 m深水航道稳定运行,同时也为长江口12.5 m深水航道向上延伸创造了良好条件。     

一类具有食物偏好的三种群生物模型的动力学分析

利用Kolmogorov定理和Lyapunov稳定性定理对一种带有食物偏好的生物种群模型的稳定性进行了分析,得到了平衡点和极限环稳定的充分条件.而后利用分岔图、Poincaré映射图及相图等数值方法研究了系统复杂的动力学行为,发现了系统经由两种非常规周期倍化分岔——"混沌泡"和"周期泡",进入混沌的道路.最后,利用Floquet理论数值验证了系统的倍周期分岔行为.     

A nonlinear model of bicycle shimmy

This paper presents a nonlinear model accurately describing, both qualitatively and quantitatively, the onset and dynamics of bicycle shimmy. Methods of nonlinear dynamics, such as numerical continuation and bifurcation analysis, show that the model exhibits two stable periodic motions found experimentally in on-road tests: the weave and wobble (or shimmy) mode. The modelling results are compared with experimental data collected by riding a racing bicycle downhill at high speeds with hands on the handlebar. The model predicts with surprising accuracy the amplitudes and frequencies of the oscillations, the longitudinal velocity at which they occur, as well as the substantial independence of wobble frequency and amplitude from the forward speed. The lateral acceleration of the upper tube of the frame near the steering axis reaches 5–10?g, both in the model and in the data. The analysis shows that wobble onset and amplitude is particularly sensitive to changes in the torsional stiffness of the frame and strongly depends on tyre lateral force and aligning torque at the wheel–road contact point. It also allows to quantify the additional viscous rotary damping that should be added to the steering assembly to prevent wobble.     

含Josephson结电路的混沌形成过程

用数值模拟方法研究了含Josephson结电路的动力学行为.根据电路模型和基尔霍夫定律建立系统的动力学方程,求出系统的平衡点,利用系统的相平面图、分岔图和Lyapunov指数图分析系统的混沌形成过程.为在此系统中避免混沌提供了直接的线索,为Josephson结器件稳定工作提供了有价值的参考.     

单自由度碰撞振动系统的稳定性分析

通过数值仿真研究了一类具有双侧刚性约束的单自由度碰撞振动系统对称周期运动经叉式分岔、倍化分岔、“擦边”奇异性向混沌转迁的全局分岔过程,及其在混沌区域的“磕碰”行为.对其分岔与混沌行为的研究为工业实际中含间隙机械系统和冲击振动系统的优化设计提供了理论依据.     

Numerical prediction of the surf-riding threshold of a ship in stern quartering waves in the light of bifurcation theory

In order to develop design and operational criteria to be used at the International Maritime Organization (IMO), critical conditions for broaching are explored in the light of bifurcation analysis. Since surf-riding, which is a prerequisite to broaching, can be regarded as a heteroclinic bifurcation, one of global bifurcations, of a surge-sway-yaw-roll model in quartering waves, the relevant bifurcation condition is formulated with a rigorous mathematical background. Then an efficient numerical solution procedure suitable for tracing the surf-riding threshold hypersurface is presented with successful examples. This deals with all state and control variables in parallel, and excludes backward time integration and an orthogonal condition in the iteration process. The bifurcation conditions identified were compared with the results from a direct numerical simulation in the time domain. As a result, it was confirmed that the heteroclinic bifurcation provides a boundary between motions periodically overtaken by waves and nonperiodic motions such as surf-riding and broaching.     

双层非线性隔振系统混沌特性分析

以双层非线性隔振系统为对象，建立两自由度非线性隔振系统的动力学模型，研究在不同激励条件下的动力学特性和隔振效果。分析激励幅值一定的条件下系统响应随激励频率的全局分岔变化规律及其非线性动力学特征，采用优势频率处的能量衰减评估隔振系统对强线谱的隔离效果。计算结果表明，处于混沌状态时优势频率处的线谱强度降低了25.9 dB，验证混沌隔振方法能有效降低结构噪声中的线谱成分。