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.     

随机干扰对两自由度碰撞振动系统的倍化分岔的影响

针对一类含单侧刚性约束的两自由度碰振系统确定Poincaré映射截面,用四阶Runge-Kutta法数值仿真了系统的倍化分岔及其向混沌的转迁过程,并讨论了随机干扰对系统倍化分岔的影响.结果表明:该系统周期运动经倍化分岔向混沌转迁的途径中,包含了倍化序列、Neimark-Sacker分岔、擦边分岔,随机干扰会导致周期运动由确定的单线扩散为带状,当确定系统的多周期运动相轨线距离较近时,可能会因为随机干扰导致的扩散而重叠,随机干扰还会造成擦边运动的提前.     

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。     

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.     

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.     

汽油机燃烧循环变动的分岔特征

对16种不同工况下的汽油机示功图进行了测量,以缸内峰值压力的试验数据为基础,应用符号时间序列分析方法,得到了汽油机燃烧循环变动的分岔特性,同时获得了汽油机燃烧循环变动随转速与负荷的变化规律。     

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.     

Kopel系统的分岔研究

应用中心流形定理和分岔理论,证明Kopel系统会发生跨临界分岔和叉式分岔.运用数值方法证明了当临界平衡点失稳时,系统中Neimark-Sacker分岔的存在,即从平衡点处会分岔出稳定的极限环.应用Matlab进行了数值模拟,数值模拟的结果与理论分析一致,而且数值分析展示了更为丰富的动力行为.     

直齿圆柱齿轮副动力学特性分析

利用拉格朗日方程建立了含间隙直齿圆柱齿轮副的动力学模型,通过齿轮轮齿弹性变形的原理数值计算建立了时变刚度的数学模型.利用4~5阶Runge-Kutta数值积分法对系统进行了数值求解.结合Poincaré映射图、相图、FFT频谱图、系统分岔图分析了系统随激励频率和阻尼变化时的动力学行为,发现了其稳定周期运动和倍周期运动及混沌运动.通过齿轮冲击模型数值计算,找出了不同初值情况下的冲击状态.     

非对称连拱隧道设计技术研究

由于我国城市交通量急剧增加,城市交通需求旺盛,为了减少道路建设对区域规划的破坏及既有建筑的影响,城市隧道工程成为新的发展趋势。以重庆市渝中连接隧道为依托,介绍城市非对称连拱隧道结构设计的控制性因素和技术,为类似工程的设计施工提供借鉴。