含磁准零刚度隔振器的非常规分岔

Unconventional Bifurcation Research on Magnetic Quasi-zero-stiffness Isolator

通过并联具有负刚度特性的磁力弹簧与线性正刚度弹簧,设计了一种新型含磁准零刚度隔振器模型,并推导出其无量纲化动力学方程.运用分岔图、时间响应图、相平面图、最大Lyapunov指数图等揭示了该系统的复杂非线性簇发振荡形式,发现了一种新颖的非常规分岔行为,多次切分岔导致周期簇发振荡与混沌簇发振荡反复交替,周期簇发振荡反复出现跨临界分岔.此现象表明,这类含磁准零刚度隔振器的动力学分岔行为敏感依赖于系统参数,外激励频率的变化导致系统产生不同形式的簇发振荡现象.

By combining parallelly the negative stiffness magnetic springs with the linear positive stiffness springs,a novel magnetic quasi-zero-stiffness vibration isolation system was designed and its dimensionless dynamic equation was given.Using the bifurcation diagram,the time response diagram,the phase diagram and the largest-Lyapunov exponent diagram,the complex nonlinear bursting oscillation forms of the system are revealed,and a novel unconventional bifurcation behavior is found.The periodic bursting oscillation and chaotic bursting oscillation alternate repeatedly due to multiple tangent bifurcation.The periodic bursting oscillations repeatedly occur transcritical bifurcation.This phenomenon shows that the dynamical bifurcation behaviors of this novel magnetic quasi-zero-stiffness isolator are sensitive to the system parameters.The change of the external excitation frequency will cause the system to generate different forms of bursting oscillation.