非线性传送带系统的复杂分岔

Complex bifurcations in a nonlinear system of moving belt

讨论了一类单自由度非线性传送带系统.首先通过分段光滑动力系统理论得出系统滑动区域的解析分析和平衡点存在性条件;其次利用数值方法,对系统几种类型的周期轨道进行单参数和双参数延拓,得到系统的余维一滑动分岔曲线和若干余维二滑动分岔点,以及系统在参数空间中的全局分岔图.通过对系统分岔行为的研究,反映出传送带速度和摩擦力振幅对系统动力学行为有较大影响,揭示了非线性传送带系统的复杂动力学现象.

bstract A kind of one-degree-of-freedom nonlinear moving belt system is considered. The analytical research of sliding region and existence conditions of equilibrium are first derived by the theory of piecewise-smooth dynamical system. Then, using numerical method, one- or two-parameter continuation of several types of periodic orbits of the system is calculated. We obtain codimension-1 sliding bifurcation curves, codimension-2 sliding bifurcation points, and global bifurcation diagram in parameter space for the system. The investigation of bifurcation behavior shows that the speed of moving belt and amplitude of friction have a great influence on dynamic behavior, and reveals the complex nonlinear dynamic phenomenon of the moving belt system.