含预紧弹簧碰撞系统的两参数动力学  

Two-parameter dynamics of an impact oscillator with a pre-compressed spring

作　　者：吕小红[1] 王继培 张锦涛 L Xiaohong;WANG Jipei;ZHANG Jintao(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]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4期12-19,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(12062008);甘肃省科技计划项目(20YF8WA043;21JR11RA063);中央引导地方科技发展资金项目(22ZY1QA005)。

摘　　要：考虑含预紧弹簧机械碰撞系统,构建由光滑流映射和不连续映射复合的Poincaré映射,给出Floquet乘子计算的数值方法。数值仿真系统在两参数平面的周期吸引子模式及其参数域,应用延拓打靶法和胞映射法研究周期1吸引子的分岔特征以及不连续擦边分岔、擦边和周期倍化诱导的分岔、亚临界周期倍化分岔和激变等不连续分岔行为,揭示迟滞域和亚谐包含域的形成机理。不连续擦边分岔在相邻1-m与1-(m+1)吸引子的转迁过程中产生迟滞域和亚谐包含域。然而,当预压量等于0时,擦边诱导的鞍结和周期倍化分岔分别产生迟滞域和亚谐包含域。研究结果能够为工程实际含预紧弹簧机械碰撞系统的参数设计与优化提供参考。A mechanical impact oscillator with a pre-compressed spring was considered.The Poincarémap composed of a smooth flow map and a discontinuous map was constructed,and a numerical calculation method of Floquet multipliers was given.The periodic attractor patterns and their parameter regions of the system in the two-parameter plane were obtained by numerical simulation.The bifurcation characteristics of period-1 attractors and the discontinuous bifurcation behaviors,such as discontinuous grazing bifurcation,bifurcations induced by grazing and period-doubling,subcritical period-doubling bifurcation and crisis,were studied by applying a continuation shooting method and a cell mapping method,and the formation mechanism of hysteresis and subharmonic inclusions regions was revealed.In the transition between adjacent 1-m and 1-(m+1)attractors,the hysteresis and subharmonic inclusions regions were created by discontinuous grazing bifurcations.However,they were respectively created by grazing induced saddle-node and period-doubling bifurcations as the pre-compression is equal to 0.The results can provide guidance for the parameter design and optimization of mechanical impact system with a pre-compressed spring.

关 键 词：非光滑系统 数值延拓 两参数动力学 周期吸引子 分岔 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]