## 留言板

 引用本文: 唐驾时. 求强非线性系统次谐共振解的MLP方法[J]. 应用数学和力学, 2000, 21(10): 1039-1045.
TANG Jia-shi. The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1039-1045.
 Citation: TANG Jia-shi. The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1039-1045.

• 中图分类号: O322

## The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems

• 摘要: 定义了一个新的参数变换α=α(ε,nω0/m,ω1),扩展了改进的LP方法的应用范围,使该方法能够求强非线性系统的次谐共振解.研究了Duffing方程的1/3亚谐和3次超谐共振解以及Vander Pol-Mathieu方程1/2亚谐共振解,这些例子说明近似解和数值解相当吻合.
•  [1] 徐兆.非线性力学中一种新的渐近方法[J].力学学 报,1985,17(3):266-271. [2] Cheung Y K,Chen S H,Lau S L.A modified Lindstedt-Poincaré meth od for certain strongly nonlinear oscillators[J].Int J Non-Linear Mechanic s,1991,26(3,4):367-378. [3] 李骊.强非线性系统的频闪法[J].力学学报,1990,22(4):402-412. [4] Jones S E.Remarks on the perturbation process for certain conservative systems[J].Int J Non～Linear Mechanics,1978,13(1):125-136. [5] Chen S H,Cheung Y K.A modified Lindstedt-Poincaré method for a strongly non-linear two degree of freedom system[J].Journal of Sound and Vibration,1996,193(4):751-762. [6] Chen S H,Cheung Y K.A modified Lindstedt-Poincaré method for a strongly nonlinear system with quadratic and cubic nonlinearities[J].Shock and Vibration,1996,3(4):279-285.
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##### 出版历程
• 收稿日期:  1999-09-17
• 修回日期:  2000-04-15
• 刊出日期:  2000-10-15

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