单自由度含干摩擦和弹性约束碰振系统周期运动的转迁及共存特征

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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。

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	李得洋1
	李孟2
	吴少培2
	李国芳2
	丁旺才2
	丁杰2

关键词 ：碰撞振动, 干摩擦, 分岔, 吸引子共存, 转迁特征

Abstract：The distribution, transition and coexistence characteristics of periodic motion in parameter and state plane of a single degree of freedom vibro-impact system with elastic constraints and dry friction are analyzed. Firstly, the connection conditions of each motion state (slip, stick and impact) of the system are given. A method of computing Floquet Matrix by disturbing response is presented. Secondly, the motion of the system is 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 are judged. Based on cell mapping and shooting method, the distribution and transition of stable and unstable periodic motion coexisting in high frequency region are analyzed. It is found that the bifurcation coexistence phenomenon occurs at the intersection of the boundary lines of adjacen t multi-state coexistence regions, where different or the same type of bifurcation occurs in the system in different initial states. Since clearance and dry friction widely exist in practical mechanical systems, the study of the dynamical properties of such systems is great significance for the design of the subsequent system parameters and the control of various dynamical behaviors.

Key words： Vibro-impact Dry friction Bifurcation Multiple coexistent attractor;Transition characteristics;

收稿日期: 2023-06-20 出版日期: 2024-05-28

引用本文:

李得洋1，李孟2，吴少培2，李国芳2，丁旺才2，丁杰2. 单自由度含干摩擦和弹性约束碰振系统周期运动的转迁及共存特征[J]. 振动与冲击, 2024, 43(10): 52-63.
LI Deyang1，LI Meng2，WU Shaopei2，LI Guofang2，DING Wangcai2，DING Jie2. Transition and coexistence characteristics of periodic motions of a single-degree-of-freedom vibro-impact system with dry friction. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(10): 52-63.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I10/52

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