噪声与振动控制

噪声与振动控制 ›› 2014, Vol. 34 ›› Issue (2): 28-33.DOI: 10.3969/j.issn.1006-1335.2014.02.007

• 2.振动理论与数值解法 • 上一篇    下一篇

非线性常微分方程高阶谐波平衡法傅里叶展开的简化

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  1. （ 1. 海军工程大学  动力工程学院，  武汉  430033；  2. 船舶振动噪声重点实验室，  武汉  430033 ）
  • 收稿日期:2013-07-10 修回日期:2013-08-29 出版日期:2014-04-18 发布日期:2014-04-18
  • 通讯作者: 唐元璋
  • 基金资助:

    国家自然科学基金资助项目;高等学校全国优秀博士学位论文作者专项资金资助项目

Simplification of Fourier Expansion in the High-order Harmonic Balance Method for Nonlinear Ordinary Differential Equations

  • Received:2013-07-10 Revised:2013-08-29 Online:2014-04-18 Published:2014-04-18

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摘要：

简化了一种求取非线性常微分方程高阶谐波解的近似解析计算方法。对平方和立方非线性项的傅里叶展开过程进行改进和简化，使计算过程变为两次矩阵运算即可完成展开过程，且两次矩阵运算过程一致，易于编程。以Duffing方程为算例，计算结果与数值方法一致，运算效率有所提高。

关键词: 振动与波, 非线性常微分方程, Duffing方程, 傅立叶展开, 谐波平衡法

Abstract:

A simplification computation method of the high-order harmonic solution of nonlinear ordinary differential equation was discussed. The Fourier coefficient expansion procedure of nonlinear ordinary differential equation with quadratic or cube term is improved and simplified. The procedure is composed of two steps of matrix operation with the same computation process so that the algorithm is easier to program than previous. Results for the Duffing equation show high-order harmonic solution in line with numerical solution but more efficient.

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