非线性Zener模型的求解及多态共存机理研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (12) : 51-58.

论文

俞力洋，黄然，丁旺才，吴少培，李国芳

作者信息 +

Solution and polymorphic coexistence mechanism study of a nonlinear Zener model

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

Author information +

文章历史 +

摘要

非线性Zener模型可准确反映中低频范围内橡胶隔振系统的力学特性，受系统准对称特性和迟滞特性的影响，系统会存在分岔、混沌、多态共存等复杂非线性动力学行为。采用复数变量法和谐波平衡法求解了系统的瞬态响应与稳态响应，并分别与数值结果及UM软件仿真结果进行对比，研究了系统在叉式分岔、鞍结分岔、倍周期分岔和边界激变诱导下多态共存的形成机理及周期运动转迁规律。结果表明：系统在主共振区附近鞍结分岔的诱导下形成一对自对称周期运动的共存；在叉式分岔诱导下产生一对反对称周期运动的共存；在叉式分岔后鞍结分岔的诱导下系统产生两对反对称周期运动的共存；系统叉式分岔与逆叉式分岔构造出“ 多态域"，在“ 多态域"中，系统有一对反对称周期倍化序列的共存及一对反对称混沌运动的共存。

Abstract

Nonlinear Zener model can accurately reflect the mechanical properties of rubber vibration isolation system in the mid-low frequency range. Due to the quasi-symmetry and hysteresis characteristics of the system, the system will have complex nonlinear dynamic behaviors such as bifurcation, chaos and polymorphism coexistence. In this paper, the complex variable method and harmonic balance method are used to solve the transient response and steady-state response of the system. The numerical results and UM software simulation results are compared. The formation mechanism and periodic motion transition law of multi-state coexistence of the system induced by fork bifurcation, saddle-node bifurcation, period doubling bifurcation and boundary crisis are studied. The results show that the system forms the coexistence of a pair of self-symmetric periodic motions induced by-node bifurcation near the main resonance region. A pair of anti-symmetric periodic motions coexist in the system induced by fork bifurcation. Under the induction of saddle-node bifurcation after fork bifurcation, the system generates the coexistence of two anti-symmetric periodic motions. The fork bifurcation and inverse fork bifurcation of the system construct the ‘ polymorphic domain’. In the ‘ polymorphic domain’, the system has the coexistence of a pair of antisymmetric periodic doubling sequences and a pair of anti-symmetric chaotic motions.

导出引用

俞力洋，黄然，丁旺才，吴少培，李国芳. 非线性Zener模型的求解及多态共存机理研究[J]. 振动与冲击, 2022, 41(12): 51-58

YU Liyang，HUANG Ran，DING Wangcai，WU Shaopei，LI Guofang. Solution and polymorphic coexistence mechanism study of a nonlinear Zener model[J]. Journal of Vibration and Shock, 2022, 41(12): 51-58

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