周期激励下van der Pol-Rayleigh系统的簇发振动及其机理  

Bursting oscillation and its mechanism of van der Pol-Rayleigh system under periodic excitation

作　　者：唐建花 李向红 申永军[2,3] TANG Jian-hua;LI Xiang-hong;SHEN Yong-jun(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Department of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao Uniuersity,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043 [2]石家庄铁道大学机械工程学院,河北石家庄050043 [3]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,河北石家庄050043

出　　处：《振动工程学报》2019年第6期1067-1076,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11672191,11772206);河北省高校百名人才支持计划(SLRC2017053)

摘　　要：研究了慢变周期激励下van der Pol-Rayleigh系统的振动响应及其产生机理。利用快慢分析法,揭示了簇发振动的产生机理,并讨论了激励幅值对系统响应的影响。研究发现,两个Hopf分岔导致不同吸引子之间的转迁是产生双Hopf簇发的主要原因。慢变过程与快变过程共同影响系统响应,并且两者之间存在有趣的博弈现象:当激励幅值较小时,快变过程稳定吸引子对系统起着主导作用;激励幅值较大时,慢变过程对系统响应的影响更明显,并从系统响应的频率成分和分岔机理两方面详细解释了这一博弈现象。同时,在周期簇发振动中,系统存在激发态滞后行为,利用匹配渐近展开法分析了滞后机理,并计算出了有转折点情况下激发态滞后的近似时间。The vibration response and generation mechanism of van der Pol-Rayleigh system under slowly periodic excitation are studied in this paper.The generation mechanism of bursting vibration is revealed by using the slow-fast method,and the influence of excitation amplitude on the system response is discussed.It is found that the two Hopf bifurcations leading the system to switch between different attractors.It is the main reason for the double-Hopf bursting.Both the slow and fast subsystem affect the system response simultaneously,and there is an interesting game phenomenon between them.When the amplitude is small,the stable attractor of fast subsystem plays a leading role in the system.If the excitation amplitude is large,the slow subsystem has more obvious influence on the system response.This game phenomenon is explained in detail based on the frequency components and bifurcation mechanism of the system response.The hysteresis behavior of spiking state exists in periodic bursting vibration.The hysteresis mechanism is analyzed by using the matching asymptotic expansion method,and the approximate hysteresis time of the spiking states in the case of turning point is calculated.

关 键 词：非线性振动 簇发 滞后 分岔 快慢系统 

分 类 号：O322[理学—一般力学与力学基础]