弹性碰撞振动系统相邻周期运动的转迁规律分析  

The transition of adjacent periodic motion analysis about elastic collision vibration system

作　　者：杨康 吴少培 卫佳 李国芳[1] 丁旺才[1] YANG Kang;WU Shao pei;WEI Jia;LI Guo fang;DING Wang cai(School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《兰州交通大学学报》2023年第5期93-97,147,共6页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(12162020,12262017);甘肃省自然科学基金(21JR7RA311);甘肃省青年科技基金计划(21JR7RA328);兰州交通大学基础研究拔尖人才项目(2022JC14)。

摘　　要：针对弹性碰撞振动系统全局动力学的研究,稳定与不稳定周期运动的转迁规律是揭示系统的关注要点,通过建立系统动力学模型,并计算系统运动解析解表达式,利用改进胞映射法刻画不同Poincaré截面上系统的吸引域形状轮廓和细节特征,进一步揭示系统多态共存分布区域及其转迁形成机理。利用单自由度弹性碰撞振动系统验证该方法的有效性,得到系统不同周期运动的吸引子和吸引域共存的情况。多态共存区内系统受到鞍结分岔、擦边分岔和倍化分岔的诱导,出现不同形式周期运动的共存,包括稳定和不稳定周期运动。In the study of the global dynamics of elastic collision vibration systems,the transition laws of stable and unstable periodic motion is the key points to reveal the system's concern.By establishing a system dynamics model and calculating the system motion analytical solution expression,the improved cell mapping method is used to depict the shape contour and detail characteristics of the attraction domain of the system on different Poincarécross-sections,further revealing the coexistence distribution regions of the system's polymorphism and the formation mechanism of the transition.The effectiveness of this method was verified using a single degree of freedom elastic collision vibration system,and the coexistence of attractors and domains of attraction for different periodic motions of the system was obtained.The system within the polymorphic coexistence zone is induced by saddle node bifurcation,edge scraping bifurcation,and doubling bifurcation,resulting in the coexistence of different forms of periodic motion,including stable and unstable periodic motion.

关 键 词：弹性碰撞 胞映射 吸引子 吸引域 

分 类 号：O322[理学—一般力学与力学基础] O241[理学—力学]