含间隙多约束碰撞振动系统稳定性分析  

Stability Analysis of Impact Vibration Systems with Multiple Constraints and Clearances

作　　者：王超 丁旺才[1] 李得洋 丁杰[1] WANG Chao;DING Wangcai;LI Deyang;DING Jie(School of Mechanical and Electrical Engineering,Lanzhou Jiaotong University,Lanzhou730070,China;School of Materials Science and Engineering,Lanzhou Jiaotong University,Lanzhou730070,China)

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

出　　处：《噪声与振动控制》2022年第1期14-19,共6页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(11962013);甘肃省青年科技基金计划资助项目(21JR7RA328)。

摘　　要：针对一类单自由度含间隙多约束碰撞振动系统,通过在碰撞面处建立系统的Poincaré映射,推导系统的Jacobi矩阵,将连续动力系统转换为离散动力系统,并利用Gram-Schmidt正交化和范式归一化计算得到系统的Lyapunov指数谱。通过数值模拟,计算系统混沌吸引子与周期吸引子的收敛序列,结合系统相图、单参分岔图及Lyapunov指数谱,分析系统周期运动稳定性及各类分岔现象,通过控制系统参数双向变化发现相邻周期运动间存在的周期共存现象,验证该计算方法的有效性和正确性,研究成果可为后续针对该系统的混沌判断及混沌控制提供理论依据。A sort of single-DOF multi-constraint impact vibration systems with gaps is studied.The Poincarémapping in the impact surface is established and the system’s Jacobi matrix is derived.By transforming the continuous dynamic system into a discrete dynamic system and using Gram-Schmidt orthogonalization and paradigm Normalization,the Lyapunov exponent spectrum of the system is obtained.Through numerical simulation,the convergent sequence of the chaotic attractor and periodic attractor of the system is calculated.Combining the phase diagram,single-parameter bifurcation diagram and Lyapunov exponential spectrum of the system,the stability of the periodic motion of the system and various bifurcation phenomena are analyzed.Through the double-way change of the control system parameters,the phenomenon of periodic coexistence between adjacent periodic motions is found,which verifies the validity and correctness of the calculation method.This research provides a theoretical basis for the subsequent chaos judgment and chaos control of the system.

关 键 词：振动与波 碰撞振动 LYAPUNOV指数 混沌 分岔 稳定性 

分 类 号：O322[理学—一般力学与力学基础]