振动台上冲击消振器垂直双面冲击运动研究

本文对固定在简谐振动台面上的冲击消振器垂直双面冲击运动进行了理论与实验研究。     

垂直冲击消振系统简谐激励响应及稳定性分析

运用迭代映射及其稳定性分析原理,研究了垂直冲击消振系统的简谐激励响应及其周期响应的稳定性．首先建立了稳定周期响应的参数区域边界方程,分析了稳定周期运动向混沌转变的一般规律．然后以典型的二阶主振系为例,得到了几个对消振效果影响较大的稳态周期响应区域的详细数值结果,讨论了稳态周期响应区域及附近的消振效果．     

线性碰振系统周期解擦边分岔的一类映射分析方法

擦边分岔是碰振机械系统的一种重要分岔行为. 以固定相位面作为Poincaré截面, 建立了线性碰振系统单碰周期$n$运动的Poincaré映射. 通过分析该映射,得到了系统 发生擦边分岔的条件和分岔方程,并以单自由度碰振系统为实例验证了分析结果的正确性. 该方法不仅可以计算线性碰振系统擦边分岔的参数值,还可以计算系统的任意周 期$n$解的分岔参数值.     

一类双面冲击振子对称型周期运动的稳定性与分岔

本文研究了一类双面冲击振子对称型周期ｎ－２运动的存在性、稳定性与分岔问题。结果表明该模型存在鞍结分岔、倍化分岔等分岔现象，并且与其它带弹性的双面振子具有不同的特点。     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

具有裂纹-碰摩耦合故障转子-轴承系统的动力学研究

以非线性动力学和转子动力学理论为基础，分析了带有碰摩和裂纹耦合故障的弹性转子系统的复杂运动，在考虑轴承油膜力的同时构造了含有裂纹和碰摩故障转子系统的动力学模型。针对短轴承油膜力和碰摩-裂纹转子系统的强非线性特点，采用Runge-Kutta法对该系统由碰摩和裂纹耦合故障导致的非线性动力学行为进行了数值仿真研究，发现该类碰摩转子系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象，该研究结果为转子-轴承系统故障诊断、动态设计和安全运行提供理论参考。     

具有单侧刚性约束的两自由度振动系统在强共振条件下的拟周 …

采用理论分析和数值仿真相结合的方法,研究了一类两自由度碰撞振动系统在一种强共振条件下的Ｈｏｐｆ分叉问题,分析并证实了碰撞振动系统在此共振条件下可由稳定的周期１－１振动分叉为不稳定的周期３－３振动,讨论了亚谐振动向混沌运动的演化过程。     

一类冲击振动系统在强共振条件下的亚谐分叉与Hopf分叉

通过理论分析和数值仿真,研究了一类二维冲击振动系统在一种强共振条件下的Hopf分叉与亚谐分叉。分析并证实了该类系统在此共振条件下可由稳定的周期1 1振动分叉为周期4 4振动或概周期振动,讨论了亚谐振动和概周期振动向混沌运动的演化过程。     

Steady state motions of shallow arch under periodic force with 1∶2 internal resonance on the plane of physical parameters

The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1∶2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to the types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end. Project supported by National Natural Science Foundation and National Youth Science Foundation of China     

Symmetry, cusp bifurcation and chaos of an impact oscillator between two rigid sides

Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered.The theory of bifurcations of the fixed point is applied to such model,and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincarémap.The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation.While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences,and bring about two antisymmetric chaotic attractors subse- quently.If the symmetric system is transformed into asymmetric one,bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.     

Double impact periodic orbits for an inverted pendulum

There exist many types of possible periodic orbits that impact at the walls for the inverted pendulum impacting between two rigid walls. Previous studies only focused on single impact periodic orbits and symmetric periodic orbits that bounce back and forth between the two walls. They respectively correspond to Types I and II orbits in the Chow, Shaw and Rand classification. In this paper we discuss two types of double impact periodic orbits that have not been studied before. The equations need to be solved for double impact orbits are transcendental and it is very hard to see the structure of the solutions. Consequently the analysis of double impact orbits is much more difficult than that of Types I and II orbits. A combination of analytical and numerical methods is employed to investigate the existence, stability and bifurcations of these orbits. Grazing bifurcations, which do not present for Types I and II orbits, are also observed.     

Quasi-periodic and chaotic behaviour of a two-degree-of-freedom impact system in a strong resonance case

A two-degree-of-freedom system contacting a single stop is considered. Quasi-periodic and chaotic behavior of the system in a strong resonance case is investigated by theoretical analysis and numerical simulation This work was supported by the National Natural Science Foundation of China(19672052).     

周期激励浅拱分岔研究

研究了一阶和二阶模态在１：２内共振条件下浅拱的复杂动力学行为，指出当周期激励浅拱具有初始静变形时，系统的一阶模态和二阶模态会产生内共振，系统两共振模态之间会产生相互作用，系统的能量会在其低阶和高阶模态之间相互传递，对称破缺后的Ｈｏｐｆ分岔解会通过一系列的倍化周期分岔导致混沌，在混沌域中还会发现稳定的周期解窗口．     

惯性式冲击振动落砂机周期倍化分岔的反控制

在不改变惯性式冲击振动落砂机系统平衡解结构的前提下,考虑碰撞振动系统的Poincaré映射的隐式特点以及经典的映射周期倍化分岔临界准则给反控制带来的困难,基于不直接依赖于特征值计算的周期倍化分岔显式临界准则,研究了落砂机系统周期倍化分岔的反控制.论文首先对落砂机系统施加线性反馈控制,得到受控闭环系统的Poincaré映射,并应用不直接依赖于特征值计算的周期倍化分岔显式临界准则,获得了系统发生周期倍化分岔的控制参数区域.然后应用中心流形-正则形方法分析了周期倍化分岔的稳定性.最终采用数值仿真验证了在任意指定的系统参数点通过控制能产生稳定的周期倍化分岔解.     

Impact phenomena of rotor-casing dynamical systems

Rubbing and impacting between a rotor and adjacent motion-constraining structures is a serious malfunction in rotating machinery. A shaver rotor-casing system with clearance and mass imbalance is modelled with two second-order ordinary differential equations and inelastic impact conditions. The dynamics is investigated analytically, as well as by numerical simulation. A Lyapunov exponent technique is developed to characterize the topologically different behavior as the parameters are varied. The dry friction coefficient and the eccentricity of the rotor imbalance were chosen to be the two variable parameters, the effect of which on the system dynamics is illustrated through phase plots, bifurcation diagrams, as well as Poincaré maps. The results demonstrate the existence of both rubbing and impacting behavior. Depending on values of the parameters, rubbing motion in both the clockwise and counter-clockwise directions may occur. Within the impact regime, the impact behavior could be periodic, quasi-periodic or chaotic, as confirmed by the calculation of Lyapunov exponents.