非线性系统分谐波振荡的两种分析方法

Two Methods lor the Analysis of Subharmonic Oscillations in Nonlinear Systems

本文提出了分析高阶非线性系统分谐波振荡的一种符号算法和一种图解法。这两种分析方法均适用于非线性函数为f(x)=ax-bx^3的情况,而图解法也适于f(x)为五次多项式的情况,且可用来确定多解系统的全部周期解。文末给出一个具有6个解的例子。

A symbolic algorithm and a graphical method are presented for analyzing sub-harmonic oscillations in nonlinear high-order systems.The two approaches are appliable to the systems with a nonlinear function f(x)=ax-bx3.The graphical method is useful for analyzing the systems with a five-order polynomial nonlinearity and for obtaining the multiple solutions of a nonlinear system.An example with six solutions is also given.