限幅型非光滑吸振器模型的稳定性与周期运动研究  

Stability and Periodic Motions for a Non-Smooth Vibration Absorber Model with Limited Amplitude

作　　者：郭子玉 李静[1] 朱绍涛 张伟[1,4] Guo Ziyu;Li Jing;Zhu Shaotao;Zhang Wei(School of Mathematics,Statistics and Mechanics,Beijing University of Technology,Beijing 100124,China;School of Materials Science and Engineering,Tsinghua University,Beijing 100084,China;Faculty of Information Technology,Beijing University of Technology,Beijing 100124,China;School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China)

机构地区：[1]北京工业大学数学统计学与力学学院,北京100124 [2]清华大学材料学院,北京100084 [3]北京工业大学信息学部,北京100124 [4]广西大学土木建筑工程学院,南宁530004

出　　处：《动力学与控制学报》2024年第5期8-15,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12272011);国家重点研发计划(2022YFB3806000)。

摘　　要：本文研究具有分段光滑特性的限幅型吸振器模型的稳定性与周期运动.建立一类限幅型非光滑吸振器的动力学模型,探讨模型容许平衡点的存在性,通过Liénard-Chipart稳定性准则,分析容许平衡点的稳定性.通过参数变换,将限幅型吸振器模型转化为具有两个切换流形的四维分段光滑系统.通过计算系统首次积分,获得四维含参分段光滑动力系统在其未扰系统存在一族周期轨条件下的Melnikov函数.探讨不同参数条件下系统周期轨的存在性及个数,并利用数值模拟方法给出其相图构型,验证理论结果的正确性.研究结果表明不同的间隙参数影响系统周期轨个数及相对位置.In this paper,the stability and periodic motions for a limited vibration absorber model with the piecewise smooth property are studied.The dynamic model of a kind of limited vibration absorber is established.The existence of the admissible equilibrium point of the model is discussed,and the stability of the admissible equilibrium point is analyzed by Liénard-Chipart stability criterion.With the aid of pa-rameter transformations,the vibration absorber model with limited amplitude is transformed into a four-dimensional piecewise smooth system with two switching manifolds.By the first integrals of the system,the Melnikov function of the four-dimensional parametric piecewise smooth dynamic system under the condition that the unperturbed system has a family of periodic orbits is obtained.The existence and number of periodic orbits of the system under different parameter conditions are discussed,and the phase diagram configuration is given by numerical simulation method to verify the correctness of the theoretical results.The results show that different clearance parameters affect the number and relative positions of periodic orbits.

关 键 词：非光滑吸振器 高维分段光滑系统 稳定性 周期运动 MELNIKOV方法 

分 类 号：O322[理学—一般力学与力学基础]