求强非线性系统次谐共振解的MLP方法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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

Department of Engineering Mechanics, Hunan University, Changsha 410082, P. R. China

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.
- 强非线性系统 /
- 次谐共振 /
- 参数变换
Abstract: A new parameter transformation α=α(ε,nω₀/m,ω₁) was defined for extending the applicable range of the modified Lindstedt-Poincar method. It is suitable for determining subharmonic and ultraharmonic resonance solutions of strongly nonlinear systems. The 1/3 subharmonic and 3 ultraharmonic resonance solutions of the Duffing equation and the 1/2 subharmonic resonance solution of the Vander Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.
- strongly nonlinear system /
- subharmonic and ultraharmonic resonance /
- parameter transformation

[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.