横向补给系统高架索的稳定性与分岔研究

考虑集中质量对系统动力学行为的影响,建立了横向补给系统高架索振动的理论模型.利用Galerkin方法和多尺度方法对动力学方程进行渐近分析.通过对系统Jacobi矩阵特征值的讨论,分析了系统的稳定性.根据系统渐近解的消除永年项条件,得到了系统的振幅分岔方程.借助Mathematica软件,对系统的局部分岔行为进行研究,得到了系统的转迁集以及相应的局部分岔图,研究表明横向补给系统高架索的振动中存在的多种分岔现象.

The study of stability and bifurcation of highline cable of alongside replenishment system

A theoretical model of transverse vibration of highline cable of alongside replenishment system was established, which considers the influence of the concentrated loading. The partial differential equation was asymptotically analysed by Galerkin method and muti-scale method. The bifurcation equation of system with higher order nonlinear terms was obtained by the solvability condition of eliminating the secular terms. Local bifurcation behavior of highline cable was studied with the software Mathematica. Bifurcation models and transition sets of system were obtained. The result shows that there are many kinds of bifurcation behaviors in highline cable of alongside replenishment system.