一类双稳态复合材料层合板的簇发振荡现象分析

Analysis of bursting oscillation in a class of bistable composite laminates

针对一类参数激励下的双稳态复合材料层合板非线性系统,考虑了一个参数激励频率是另一个的整数倍的情形,并将参数激励视为慢变参数,利用“快慢分析方法”得到了多频参数激励系统的快子系统和慢子系统,分析了快子系统的分岔行为。在平衡点分岔分析中,分析出单模和双模平衡点下快子系统的Hopf和fold分岔条件;利用双参数分岔集,相图、时间历程曲线图、转换相图与平衡分支的叠加图,分析了不同参数下簇发振荡的产生机理及其动力学行为,观察到不同的参数条件下其簇发振荡现象可能与叉形分岔点无关。

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.