强Van der Pol振子的谐波与修正算法

大学物理 ›› 2009, Vol. 28 ›› Issue (3): 4-4.

强Van der Pol振子的谐波与修正算法

国忠金[1] 梁以德[2] 马晓燕[1]

[1]泰山学院数学与系统科学系,山东泰安271021 [2]香港城市大学建筑工程系,香港九龙

出版日期:2009-03-25 发布日期:2009-03-20

Harmonic wave and correction algorithm for forced Van der Pol oscillator

Online:2009-03-25 Published:2009-03-20

摘要/Abstract

摘要： 引入谐波平衡近似解的符号运算与同伦延拓法，获得了强Van der Pol振子的解析近似极限环与稳定响应．为提高其近似精度，给出了谐波解的修正算法，并与数值模拟比较．结果表明，该算法非常精确可靠，是研究强非线性动力学系统的有效分析方法．

关键词: 谐波平衡, 同伦延拓法, 修正算法, 极限环

Abstract: The sign algorithm of the harmonic balance approximate solutions and homotopy continuation method are introduced to get the analytic limit cycle and steady state response of the forced Van der Pol oscillator. In order to enhance precision,a correction algorithm is proposed. The approximate solution presented here is compared with numerical simulation. It is shown that the algorithm is very accurate, reliable and also an effective way of analyzing strong nonlinear systems.

Key words: harmonic balance, homotopy continuation method, correction algorithm, limit cycle

中图分类号:

N941

国忠金[] 梁以德[] 马晓燕[]. 强Van der Pol振子的谐波与修正算法[J]. 大学物理, 2009, 28(3): 4-4.