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VanderPol_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·
A new parameter transformation α=α(ε,nω 0/m,ω 1) was defined for extending the applicable range of the modified Lindstedt_Poincaré 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 Van der Pol_Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.
出处
《应用数学和力学》
CSCD
北大核心
2000年第10期1039-1045,共7页
Applied Mathematics and Mechanics
