摘要
在机电耦合系统中,常会附加半自由度的方程。为了求解与这类方程有关的强非线性振动系统,在单自由度复动频率法的基础上引入新的平衡规则,使其可应用于一个半自由度系统,得到Duffing振子强迫振动的渐近解和幅频响应关系。为进一步拓展该方法的使用范围,通过增加新的待定频率和动态频率,使复动频率法可用于分析两自由度强非线性振动系统,据此得到两自由度Duffing‑Van der Pol振子的渐近解。通过与多尺度法、数值解结果对比,证明了使用复动频率法研究多自由度强非线性振动问题的有效性。
Bursting oscillation is a fast-slow dynamic phenomenon widely existing in nature.These years,it has been a hot topic on nonlinear dynamics.It usually appears as the transition between large and small oscillations due to bifurcation points or unstable lim‑it cycles.According to different dynamic mechanisms,bursting oscillation can be divided into various modes such as‘point-point’mode and‘point-ring’mode.This paper focuses on a class of bistable composite laminates of nonlinear systems by parametric excitation and concerns the case where one parameter excitation frequency is an integer multiple of the other.The parameter excitation is regarded as a slow variable parameter,so the fast and slow subsystems of the multi-frequency parameter excitation system are obtained based on the fast-slow analysis method and the bifurcation behavior of the fast subsystem is analyzed.In the bifurcation analysis,the Hopf and fold bifurcation conditions of the fast subsystem with single mode and double mode bifurcation points are investigated.Exploiting double parameter bifurcation sets,phase portraits,time history curves and the overlap of transformed phase portraits with equilibrium branches,the mechanism and dynamic behavior of bursting oscillation with different parameters are studied.It is observed that the bursting oscillation phenomenon with different parameters may be independent of the pitchfork bifurcation points.
作者
张琪昌
杨阳
王炜
郝淑英
ZHANG Qi-chang;YANG Yang;WANG Wei;HAO Shu-ying(School of Mechanical Engineering,Tianjin University,Tianjin 300072,China;Tianjin Key Laboratory of Nonlinear Dynamics and Control,Tianjin 300072,China;School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2023年第3期606-611,共6页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(12072234)。
关键词
强非线性振动
渐近解
复动频率法
一个半自由度
两自由度
strong nonlinear vibration
asymptotic solution
complex dynamic frequency method
one and a half degrees of freedom
two degrees of freedom
