一种改进的KBM法求解非线性振动方程

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摘要经典KBM法可以较好地解决含有小参数的非线性振动方程的求解问题，但这个小参数很大程度限制了经典KBM法的应用。本文将经典KBM法中频率表达式的基本方程进行平方修正，使得该方法的求解范围不受小参数的限制；应用改进后的方法求解Duffing方程，并在计算中对振动系统的频率方程进行简化，求得方程的二次近似解和频率解分别与其它方法的解进行对比，验证了本文改进的KBM法的可行性，且证实其计算结果的精度较其它方法高。

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	王磊佳
	张鹄志
	胡辉
	祝明桥

关键词 ：非线性振动, KBM法, 改进的KBM法, Duffing方程

Abstract：The classical KBM method can be used to solve nonlinear vibration equations with small parameters, but these small parameters greatly restrict the application of the classical KBM method. Here, the square modification was done for the basic equation of frequency expression in the classical KBM method so that the solving range of the method could not be restrained by small parameters. The improved KBM method was used to solve Duffing equation. In calculation, the frequency equation of the vibration system was simplified. The equation’s quadratic approximate solution and frequency solution were compared with solutions of other methods. It was shown that the feasibility of the improved KBM method is verified; the accuracy of its calculation results is higher than that of other methods.

Key words： non-linear vibration Krylov-Bogoliubov-Mitropolsky method improve KBM method Duffing equation

收稿日期: 2017-06-30 出版日期: 2018-06-28

引用本文:

王磊佳,张鹄志,胡辉,祝明桥. 一种改进的KBM法求解非线性振动方程[J]. 振动与冲击, 2018, 37(13): 165-170.
WANG Leijia，ZHANG Huzhi，HU Hui，ZHU Mingqiao. An improved KBM method for solving nonlinear vibration equations. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(13): 165-170.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I13/165

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