非线性奇异振子的解析逼近解

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 104-106.

论文

非线性奇异振子的解析逼近解

孙维鹏吴柏生

作者信息 +

Analytical Approximate Solutions to a Nonlinear Singular Oscillator

Sun Wei-peng, Wu Bai-sheng

Author information +

文章历史 +

摘要

利用修正的牛顿-谐波平衡法建立了非线性奇异振子的解析逼近周期和周期解．通过改写控制方程和选取简单、合适的校正项对牛顿-谐波平衡法进行了修正.构造的两个解析逼近周期和周期解不仅在振幅和参数全部取值范围内有效且能快速地收敛到精确解；两个逼近周期与精确周期的百分比误差分别低于0.92%和0.09%，后者比已有结果精度高。

Abstract

A modified Newton-harmonic balance method is used to construct analytical approximate periods and periodic solutions to the singular oscillator describing certain phenomena in plasma physics. The Newton-harmonic balance method is modified by rewriting the original control equation and selecting the simple and suitable correction terms. Two new analytical approximate solutions obtained in this paper are effective for the whole range of initial oscillation amplitudes and parameters, and they can rapidly converge to exact solution. The percentage errors between two new analytical approximate periods and the exact one are lower than 0.92% and 0.09%, respectively, and the latter is more accurate than the existing results.

导出引用

孙维鹏吴柏生. 非线性奇异振子的解析逼近解[J]. 振动与冲击, 2009, 28(6): 104-106

Sun Wei-peng; Wu Bai-sheng. Analytical Approximate Solutions to a Nonlinear Singular Oscillator[J]. Journal of Vibration and Shock, 2009, 28(6): 104-106

中图分类号： O322