单自由度含干摩擦碰撞振动系统周期运动转迁及共存特征  

Transition and coexistence characteristics of periodic motions of a single-degree-of-freedom vibro-impact system with dry friction

作　　者：李得洋 李孟 吴少培 李国芳[2] 丁旺才[2] 丁杰[2] LI Deyang;LI Meng;WU Shaopei;LI Guofang;DING Wangcai;DING Jie(School of Materials Science and Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学材料科学与工程学院,兰州730070 [2]兰州交通大学机电工程学院,兰州730070

出　　处：《振动与冲击》2024年第10期52-63,共12页Journal of Vibration and Shock

基　　金：国家自然科学基金(12162020,12262017);甘肃省青年科技基金计划(21JR7RA328);甘肃省自然科学基金项目(20JR5RA406)。

摘　　要：在参数平面和状态平面内,研究了一类单自由度含干摩擦和弹性约束碰撞振动系统周期运动的分布、转迁及共存特征。首先,给出了系统各运动状态(滑动、黏着及碰撞)的衔接条件,并利用响应微扰计算方法得到系统的Floquet矩阵。其次,由相轨线与黏着面的关系将系统在参数平面内的运动划分为六种类型,根据Floquet乘子和滑移分岔发生的几何条件判定相邻周期运动在转迁时的稳定性和分岔类型,并基于胞映射和打靶法分析稳定及不稳定周期运动共存及转迁特征。研究发现,在相邻的多态共存区边界线交点处,系统在不同初始状态下存在分岔共存现象。由于间隙和干摩擦广泛存在于实际机械系统中,研究此类系统的动力学特性,对后续系统参数的设计及各种动力学行为的控制具有重要的意义。The distribution,transition and coexistence characteristics of periodic motions in the parameter and state plane of a single degree of freedom vibro-impact system with elastic constraints and dry friction were analyzed.The connection conditions of each motion state(slip,stick and impact)of the system were given out.A method for computing the Floquet Matrix by disturbing response was presented.The motions of the system were divided into six types according to the relationship between the phase trajectory and the stick surface.By the Floquet multiplier and the geometric conditions of sliping bifurcation,the stability and bifurcation types of adjacent periodic motions in the parameter plane during transition were judged.Based on the cell mapping and shooting method,the distribution and transition of stable and unstable periodic motions coexisting in the high frequency region were analyzed.It is found that the bifurcation coexistence phenomenon occurs at the intersection of the boundary lines of adjacent multistate coexistence regions,where the different or identical type of bifurcation occurs in the system according to different initial states.Since clearance and dry friction widely exist in practical mechanical systems,the study of the dynamical properties of such systems is of great significance for the design of the subsequent system parameters and the control of various dynamical behaviors.

关 键 词：碰撞振动 干摩擦 分岔 吸引子共存 转迁特征 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3