分数阶非线性隔振系统的超谐波共振与周期运动转迁规律分析  

Analysis of super-harmonic resonance and periodic motion transition laws of fractional order nonlinear vibration isolation system

作　　者：屈鸣鹤 吴少培 俞力洋 丁旺才[1] 李国芳[1] 黄然 QU Minghe;WU Shaopei;YU Liyang;DING Wangcai;LI Guofang;HUANG Ran(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》2023年第5期66-73,121,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11962013;11732014);甘肃省青年科技基金资助项目(21JR7RA335)。

摘　　要：针对具有非线性和黏弹性的隔振系统采用分数阶非线性Zener模型对其本构关系进行表征。将分数阶项等效成三角函数的形式,采用高阶谐波平衡法求解系统的稳态响应并结合多种方法对结果进行比较,数值模拟系统在低频区的动力学响应,采用Floquet理论对系统分岔类型进行判定,揭示了分数阶项对系统动力学响应的影响。研究结果表明,高次超谐波不仅存在跳跃现象且相邻次数超谐波转迁过程中存在周期运动多样性。数值模拟过程中还发现系统存在周期运动和混沌共存的现象,并总结了多态共存区域及其相邻区域的运动规律。Here, for vibration isolation system with nonlinearity and viscoelasticity, fractional order nonlinear Zener model was used to characterize the system’s constitutive relation. The fractional order term was equivalent to the form of trigonometric functions. The high-order harmonic balance method was used to solve steady-state response of the system and a variety of methods were used to compare their solving results. Dynamic responses of the system in low frequency domain were numerically simulated. Floquet theory was used to judge types of system bifurcations, and reveal effects of the fractional order term on dynamic responses of the system. The results showed that not only high order super-harmonic waves cause jump phenomena, but also in transition processes of adjacent order super-harmonic waves, the diversity of periodic motion exists;numerical simulation reveals periodic motion and chaos coexisting in the system, and motion laws of polymorphic coexistence regions and their adjacent regions being summarized.

关 键 词：非线性Zener模型 分数阶微分 超谐波共振 转迁规律 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.4