一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学

发布时间：2018-03-07 12:55

本文选题：碰撞振动系统　切入点：对称不动点　出处：《力学学报》2016年01期 　论文类型：期刊论文

【摘要】：考虑一类具有对称性的三自由度碰撞振动系统.系统的庞加莱映射在一定条件下存在对称不动点,对应于系统的对称周期运动.根据对称性导出庞加莱映射P是另外一个隐式虚拟映射Q的二次迭代.推导了庞加莱映射对称不动点的解析表达式.根据映射不动点的稳定性及分岔理论,映射P的对称不动点发生内伊马克沙克-音叉(Neimark--Saker-pitchfork)分岔对应于映射Q发生内伊马克沙克-倍化(Neimark--Sakerflip)分岔.利用隐式虚拟映射Q,通过对范式作两参数开折分析,研究了映射P的对称不动点在内伊马克沙克-音叉分岔点附近的局部动力学行为.碰撞振动系统在这个余维二分岔点附近的局部动力学行为可能表现为投影后的庞加莱截面上的单一对称不动点、一对共轭不动点、单一对称拟周期吸引子以及一对共轭拟周期吸引子.数值模拟得到了内伊马克沙克-音叉分岔点附近的各种可能情况.内伊马克沙克-分岔和音叉分岔互相作用可能产生新的结果:对称不动点虽然首先分岔为两个共轭不动点,但是这两个共轭不动点是不稳定的,最终收敛到同一个对称拟周期吸引子.
[Abstract]:In this paper, we consider a class of symmetric collisional vibration systems with three degrees of freedom. The Poincare map of the system has symmetric fixed points under certain conditions. According to symmetry, the Poincare map P is a quadratic iteration of another implicit virtual map Q, and the analytic expression of symmetric fixed point of Poincare map is derived. According to the mapping fixed point, we derive the analytic expression of the symmetric fixed point of the Poincare map. Point stability and bifurcation theory, The symmetric fixed point of the mapping P is corresponding to the Neimark-Saker-Pitchfork bifurcation of the mapping Q. By using the implicit virtual mapping Qs, the paper makes a two-parameter analysis of the normal form, which is called "Neimark-Sakerflipk" bifurcation. The local dynamical behavior of symmetric fixed point of mapping P near the Naymak shake-tuning fork bifurcation point is studied. The local dynamical behavior of the collisional vibration system near this codimensional two-bifurcation point may be shown as projective. The single symmetric fixed point on the Poincare section, A pair of conjugate fixed points, A single symmetric quasi periodic attractor and a pair of conjugate quasi periodic attractors are numerically simulated. Various possible conditions near the Naymak shake-tuning fork bifurcation point are obtained by numerical simulation. The interaction between Naymak shake-bifurcation and tuning fork bifurcation. It is possible to produce new results: symmetric fixed points, although the first bifurcation is two conjugate fixed points, But these two conjugate fixed points are unstable and converge to the same symmetric quasiperiodic attractor.
【作者单位】：西南交通大学力学与工程学院应用力学与结构安全四川省重点实验室;
【基金】：国家自然科学基金资助项目(11272268,11172246)
【分类号】：O313

【共引文献】