激励力幅值对非线性能量阱系统全局分岔特性的影响研究  

Research on the influence of excitation amplitude on global bifurcation characteristics of nonlinear energy sink system

作　　者：李爽[1] 楼京俊[2] 柴凯 刘树勇[1] LI Shuang;LOU Jing-jun;CHAI kai;LIU Shu-yong(College of Power Engineering,Naval University of Engineering,Wuhan 430033,China;College of Naval Architecture and Ocean,Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学动力工程学院,武汉430033 [2]海军工程大学舰船与海洋学院,武汉430033

出　　处：《船舶力学》2021年第4期479-488,共10页Journal of Ship Mechanics

基　　金：国家自然科学基金项目(51509253,51579242,51679245);湖北省自然科学基金项目(2018CFB182)。

摘　　要：本文在质量比为小参数条件下,研究了简谐激励力幅值变化对非线性能量阱系统全局分岔特性的影响。首先,建立了简谐激励力作用下单自由度非线性能量阱吸振系统动力学模型,并运用复变量平均法推导了系统1:1:1主共振响应的慢变方程;然后通过多尺度法分别在慢变与快变两个时间尺度上研究了对系统慢不变流形以及全局分岔特性;最后,结合相轨迹法仿真了系统平衡点个数和吸引子类型随激励力幅值的演变过程。研究结果表明:非线性能量阱阻尼比小于1/√3时,系统才会存在跳跃现象;随着激励力幅值的增加,系统可能出现周期吸引子与折奇点两类平衡点共存、亚临界分岔、Hopf分岔等复杂的非线性动力学行为,系统相轨迹也会发生明显的改变。Under the condition that the system mass ratio is small,the influence of harmonic excitation force amplitude on the global bifurcation characteristics of nonlinear energy sink(NES)system was investigated in this paper.Firstly,the dynamic model of single-degree-of freedom nonlinear energy sink vibration absorption system was established,after that the reduced slow flow equations of the system 1:1:1 primary resonance response was derived by complexification-averaging approach.Then,the multi-scale method was used to investigate the slow invariant manifold and global bifurcation characteristics of the system on slow and fast time scales separately.Finally,the evolution of equilibrium points with the amplitude of the harmonic excitation force was simulated by phase trajectory method.The results show that the nonlinear jumping phenomenon only exists in the system when the nonlinear energy sink damping ratio is less than 1/√3.With the increase of excitation force amplitude,the two kinds of equilibrium points of periodic attractor and folded singularities may coexist in the system.Besides,the system could exhibit complicated nonlinear dynamic behaviors,such as subcritical bifurcation and Hopf bifurcation.Also,the phase trajectories will change significantly.

关 键 词：非线性能量阱 慢不变流形 全局分岔 周期吸引子 折奇点 激励力幅值 

分 类 号：O328[理学—一般力学与力学基础]