用胞变换法分析分段线性系统周期运动稳定性

Stability of Periodic Motion of Systems with Piece-Wise Linearity Using Cell Mapping Method

本文首先简单介绍了胞变换法,并提出了加工绘图数据的一种算法,这种算法节省机时和存贮绘图数据所需的空间,使绘制各种吸引域图形成为可能。然后利用胞变换法对具有分段线性非线性特征的弹簧摇床的全局性态进行了分析研究,并用计算机模拟出该系统存在的各种周期运动的时间历程曲线及相应的周期运动的吸引域。论文分析了弹簧摇床五种阻尼参数下全局性态,得出了该类系统周期运动稳定性和阻尼之间的关系。

In this paper at first the cell mapping method is introduced briefly and drawing data processing method is presented.The method saves a large quantity of time and storage of computer and makes drawing the domains of attraction possible.Then global behaviour of,a nonlinear system with piece-wise linearity is analysed by cell mapping method and the time-history curves of the various periodic motions in this system are simulated by computer.The influence of damping in the system on the stability of the periodic motions is found by means of analysing global behaviour for five damping parameters.