周期激励浅拱的全局分岔

Global bifurcation of shallow arch with periodic excitation

考虑1∶1内共振下周期激励浅拱的全局分岔,首先用平均法得到其平均系统,在此基础上运用规范型理论得到其约化系统,系统的特征方程出现非半单的两个零根和一对纯虚根的余维三情况 运用Kovacic和Wiggins的全局扰动方法,给出系统异宿轨道的分岔方式及其转迁集,作出相图。

The global bifurcations of a shallow arch with 1∶1 internal resonance are investigated. Based on the averaged equations of the system and by applying the normal form theory, the simplified system is obtained. The characteristic equation has two zeros and a pair of pure imaginary eigenvalues. Based on the global perturbation methods developed by Kovacic and Wiggins, the heteroclinic bifurcation, transition boundary and different phase portraits according to different regions are further obtained so as to have a better understanding of global behavior of the system.