含间隙双频激励碰撞振动系统的动力学分析  

Dynamics Analysis of Vibro-impact System with Double-frequency Excitation and Clearance

作　　者：马康州 卫佳 吴少培 MA Kangzhou;WEI Jia;WU Shaopei(Lanzhou Jiaotong University,Lanzhou Gansu 730070,China)

机构地区：[1]兰州交通大学,甘肃兰州730070

出　　处：《甘肃科技纵横》2024年第5期45-51,共7页Scientific & Technical Information of Gansu

基　　金：甘肃省科技计划项目“碰撞振动系统RBF神经网络智能优化控制研究”(21JR7RA311);甘肃省科技计划项目“碰撞和摩擦振动系统的多稳态动力学及其智能控制研究”(23JRRA1697)。

摘　　要：文章研究了一类单自由度双频激励碰撞振动系统的动力学模型,建立了2个在不同频率正弦激励作用下的碰撞振动运动微分方程,给出了含间隙系统双频激励下Poincaré映射的建立方法,推导出该映射的Jacobian矩阵,从而得到相应的特征值。同时,研究了单个频率变化时对周期运动的影响,以及在一定的频率比下不同间隙和频率对周期分布的影响。进一步利用特征值研究了系统随频率变化出现的周期运动、分岔、擦边以及混沌现象,通过Poincaré映射图和相图对分岔点处的特性进行了分析。The paper mainly studies a kind of single-degree impacting dynamical model with double-frequency excitation,establishes the equation of vibro-impact with double-frequency.The Poincarémap of system is estab-lished to deduce the Jacobian matrix and the corresponding eigenvalues.It also studies the influence of the single-frequency change to periodic motion.And under a certain ratio of frequency,it studies the influence of frequency and clearance to the periodic distribution.The paper further uses the eigenvalues to study the phenomenon of peri-odic motion,bifurcation,rubbing edge and chaotic motion,and analyzes the characteristics of the bifurcation points through the Poincare map diagram and the phase diagram.

关 键 词：双频激励 碰撞振动 POINCARÉ映射 擦边 混沌 

分 类 号：O322[理学—一般力学与力学基础]