一类附加斜弹簧支撑的悬臂梁碰撞系统的全局动力学  

Global dynamics for an impacting system of cantilever beam supported by oblique springs

作　　者：张绎沣 徐慧东 张建文 ZHANG Yi‑feng;XU Hui‑dong;ZHANG Jian‑wen(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China;College of Mechanical and Vehicle Engineering,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024 [2]太原理工大学机械与运载工程学院,山西太原030024

出　　处：《振动工程学报》2024年第8期1308-1319,共12页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11872264)。

摘　　要：本文研究了双侧非对称刚性约束下附加斜弹簧支撑的悬臂梁碰撞系统的次谐分岔和混沌的全局动力学。由于斜弹簧支撑结构的刚度项为超越函数,给解析研究系统混沌和次谐分岔造成很大的困难。本文近似拟合了该系统的刚度项,并对比分析了近似系统和原系统的同宿轨道及其内部的次谐轨道。将Melnikov方法发展应用于非光滑的碰撞悬臂梁系统,给出了发生同宿混沌和次谐分岔的阀值条件。利用光滑流形的特征乘子结合碰撞函数分析了碰撞次谐轨道的稳定性,并分析了次谐分岔与混沌的关系。基于阀值条件研究了阻尼、激励频率、激励幅值以及碰撞恢复系数对混沌和次谐分岔的影响,进一步验证了理论分析的正确性。In this paper,the global dynamics of chaos and subharmonic bifurcation of an impacting system of cantilever beam supported by oblique springs under bilateral asymmetric rigid constraints are studied.It is difficult to study analytically the chaos and subharmonic bifurcation of the system because the stiffness term of the oblique spring support structure is a transcendental function.To do this,the stiffness term of the system is fitted by the approximation method,and the homoclinic orbit and its internal orbits of the approximate system are compared with the orbits of the original system.The threshold conditions for homoclinic chaos and subharmonic bifurcation are presented by applying the Melnikov method to the non-smooth impacting cantilever beam system.Moreover,the stability of the impacting subharmonic orbit is analyzed by combining characteristic multipliers of smooth manifolds with impact function,and the relationship between subharmonic bifurcation and chaos is analyzed.The effects of damping,excitation frequency,excitation amplitude and impact coefficient of restitution on chaos and subharmonic bifurcation are studied based on threshold conditions,which further verify the theoretical analysis.

关 键 词：非线性振动 碰撞悬臂梁 同宿混沌 次谐分岔 MELNIKOV方法 

分 类 号：O322[理学—一般力学与力学基础]