一类单自由度滞后—自激振动系统的分叉

本文研究了一类单自由度滞后—自激振动系统的分叉。用平均法求出了系统的稳态分叉解,克服了中心流形法要求非线性函数光滑的这一限制。本文提出了转迁极限点集的概念,并利用奇异性理论方法,研究了参数空间不同区域内系统分叉图的拓扑结构,揭示了一些新的分叉模式,最后用数值积分法验证了本文的部分结果。

Bifurcations of a Certain One-Degree-of-Freedom Hysteretic Self-Excited Vibrational System

This paper presents the analysis of the bifurcation in a certain one DOFhysterestie self-excited vibrational system By using of the averaging method,thesteady-state bifurcation solution are obtained,and overcome the barrier in centremanifold method,i.e.the nonlinear terms must be smooth.the concept oftransition limit point set is introduced.Following the singularity theory method,the various bifurcation diagrams in parameter space and verify some of the resultsare got by numerical integral.