摘要
非线性问题研究是当今工程应用研究的热点问题之一,常规方法有多尺度法、积分法、平均法、同伦摄动法等。但常规方法所能解决的非线性问题仍然十分有限。本文应用线化和校正法,研究了Duffing方程的非线性振动,分别求出了Duffing方程非线性振动周期的精确解和近似解,利用Maple9.0绘图分别作出了Duffing方程周期、绝对误差和相对误差随参数k的变化曲线。所得结论为Duffing方程周期随参数k的增加而减小,相对误差随参数k的增加而增加;Duffing方程周期近似解与精确解比较,具有简单实用、精度高、相对误差低等优点。该方法在求解非线性振动中具有较强的理论价值和实用价值。
The nonlinear problems are frequently found in practical engineering. Among the common methods applied for these problems are the multiple scale method, the integral calculus method, the average method, and the homotopy method, but they have very limited capability in real applications. The nonlinear oscillations of the Duffing equations are studied by means of the method of linearization and correction, and the approximate solutions are compared with the exact solutions. With Maple 9.0, the curves of the period, the absolute error and the relative error are plotted against the parameter . It is concluded that the period decreases and the relative error increases with the increase of parameter ; as compared to the exact solution, the approximate solution is simple, with high accuracy and lower relative error. So the method of linearization and correction is very useful in solving problems of nonlinear oscillations.
出处
《科技导报》
CAS
CSCD
北大核心
2009年第23期66-69,共4页
Science & Technology Review
基金
广东揭阳学院2006年院级重点科研项目(JYCKZ0604)
关键词
非线性振动
DUFFING方程
近似解
线化和校正法
nonlinear oscillations
Duffing equations
approximate solution
linearization and correction method
