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

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (5) : 66-73.

论文

屈鸣鹤，吴少培，俞力洋，丁旺才，李国芳，黄然

作者信息 +

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

QU Minghe, WU Shaopei, YU Liyang, DING Wangcai, LI Guofang, HUANG Ran

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文章历史 +

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。

Abstract

The fractional nonlinear Zener model is used to describe the nonlinear and viscoelastic constitutive relation of the vibration isolation system. The fractional-order derivative term was made equivalent to a term in the form of trigonometric function, the steady-state response of the system was solved by high-order harmonic balance method, and the results were compared with a variety of methods. The dynamic response of the system in the low frequency region was obtained by using numerically simulation. The bifurcation type of the system was determined by Floquet theory and the influence of fractional order term on dynamic response was revealed. The results show that there is a jump phenomenon in high-order super-harmonics, and periodic motion diversity in the process of adjacent-order super-harmonic transfer. Additionally, it is found that the periodic motion and chaos coexist in the system, and the transition laws of the polymorphic coexistence region and its adjacent regions was summarized explicitly.

导出引用

屈鸣鹤，吴少培，俞力洋，丁旺才，李国芳，黄然. 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[J]. 振动与冲击, 2023, 42(5): 66-73

QU Minghe, WU Shaopei, YU Liyang, DING Wangcai, LI Guofang, HUANG Ran. Analysis of super-harmonic resonance and periodic motion transition laws of fractional order nonlinear vibration isolation system[J]. Journal of Vibration and Shock, 2023, 42(5): 66-73

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