关于Duffing—van der Pol非线性振动系统的可视化分析

VISUALIZED EXPERIMENT TO REALIZE DUFFING-VAN DER POL NON-LINEAR VIBRATION SYSTEM

应用MATLAB软件研究了Duffing—van der Pol非线性振动系统的数学模型。利用该图形用户界面,可以实现Duffing—van der Pol振子数学模型的初始条件设定、任意参数组合和几何显示功率谱图、相平面轨迹图、Poincaré映射图、位移变化动态模拟图、相轨迹动态图和质量块振动模拟图,可以直观、快速、准确、形象地研究非线性振动出现的各种动力特征,可以全面实现Duffing—van der Pol振动系统的计算机可视化实验和研究。

Based on the mathematic model of Duffing -van der Pol non -linear vibration system, the MAT- LAB Graphic User Interface has been designed. With this interface, the setting of initial conditions, the combination of arbitrary parameters, the geometrical display of power spectrums, trochoid chart of phase portraits, Poincare mapping, analogous dynamic graph of displacements and the analogous vibration graph of mass blocks can be realized in an interactive way. The various dynamic characteristics of non - linear vibration can be attained quickly and accurately in a direct and vivid manner, which makes it possible to fully implement the visualized computer experiments and study of Dulling - van der Pol non - linear vibration system.