【作者】 皇甫玉高；

【导师】 李群宏；

【作者基本信息】 广西大学 ， 应用数学， 2008， 硕士

【摘要】 本文研究了一类弹性悬臂梁碰振系统的擦边分岔。首先利用数值仿真的方法研究了悬臂梁碰撞系统的擦边分岔,进而利用Nordmark不连续映射方法具体推导了擦边周期轨道附近的局部不连续映射,给出了局部不连续映射的解析表达式,并用数值方法进行了模拟。主要内容如下:第一、讨论了一类悬臂梁碰振系统的擦边周期运动。首先得到了该系统两种不同的擦边分岔:周期一到周期二;周期一到混沌。且得到了一组共存吸引子:一个周期一和两个混沌吸引子共存。第二、对悬臂梁系统进行了推广,得到了一类具有相似结构的更一般动力系统的局部不连续映射的解析范式。并利用导出的局部不连续映射的范式得到了该悬臂梁系统的局部不连续映射,并利用局部不连续映射对该系统的擦边分岔行为进行了研究,所得的结果与数值仿真该系统的结果相一致。更多还原

【Abstract】 In this dissertation, periodic grazing motions in a cantilever beam system are studied. By method of numerical simulations, two cases of grazing bifurcations are given. And on the basis of Nordmark’s discontinuity mapping method, a local-discontinuity-mapping near the grazing trajectory is established. Then the mapping is used to analyze the grazing bifurcations. Also the numerical simulations are used to verify the theoretical results.Firstly, the grazing periodic motions in this cantilever beam system with one constrain are discussed. At the beginning, two cases of grazing bifurcations are obtained: one is from period one motion to period two motion, the other is from period one motion to chaos. And, in our analysis, a group of co-existence attractors is found, i.e. a period one attractor and two chaos attractors.Secondly, a normal form of discontinuity mapping of a piecewise smooth dynamic system which is the generalization of the above cantilever beam system is given. And the derived normal form is used to give out the local discontinuity mapping of the cantilever beam system discussed previously, by this means, the grazing bifurcation of the cantilever beam system is studied. It is shown that the results of numerical simulation about the system agree with that of local discontinuity mapping.更多还原