摘要
针对一类含不同约束的单自由度碰撞振动系统,建立了系统的Poincaré映射,进而推导出映射的雅可比矩阵.在多参数协同仿真方法的基础上,结合胞映射法研究了系统在间隙(b1,b2)参数平面内各类周期运动分布及共存的特点,总结了相邻周期运动之间的转迁规律.系统相邻周期运动之间主要通过擦边分岔和鞍结分岔实现转迁,转迁过程不可逆,在相邻周期运动间分布着多态共存区;在转迁过程中当系统出现倍周期分岔或边界激变时,相邻周期运动之间会经过由复杂周期运动组成的过渡区进行转迁.
For a single-degree-of-freedom vibro-impact system with different constraints on both sides,the Poincare map and its Jacobi matrix were constructed.The distribution and coexistence of various periodic motions in the(b1,b2)-parameter plane were studied with multi-parameter co-simulation and cell mapping method.The transition law between adjacent periodic motions was summarized.Adjacent periodic motions of the system transition mainly by grazing bifurcation and saddle-node bifurcation,polymorphic coexistence areas are distributed between the adjacent periodic motions because of the transition process is irreversible;when double-cycle bifurcation and boundary crisis occur,transition between the adjacent periodic motions will pass through a transition zone composed of complex periodic motions.
作者
丁杰
王超
丁旺才
李得洋
DING Jie;WANG Chao;DING Wangcai;LI Deyang(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;School of Material Science and Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2021年第1期6-11,共6页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(11962013,50675092)
兰州交通大学青年科学基金资助项目(2013019)。
关键词
碰撞振动系统
转迁规律
约束
分岔
多态共存
过渡区
vibro-impact system
transition law
constraint
bifurcation
polymorphic coexistence
transition zone
