摘要
应用同伦分析方法(HAM)解决强非线性多自由度系统在谐波激振力下的主共振问题.同伦分析方法的有效性独立于所考虑的方程中是否含有的小参数.同伦分析方法提供了一个简单的方法,通过一个辅助参数h-来调节和控制级数解的收敛区域.两个具体算例表明,同伦分析方法得出的结果与修正Linstedt-Poincaré法、增量谐波平衡法的解决方案得出的结果相吻合.
The homotopy analysis method （HAM） was presented for the primary resonance of multi-degree-of-freedom system with strongly non-linearity excited by harmonic forces. The vao lidity of the HAM is independent of whether or not there are small parameters in the considered equation. The HAM has provided a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h. Two examples were presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincare method and the incremental harmonic balance method.
出处
《应用数学和力学》
CSCD
北大核心
2010年第10期1229-1238,共10页
Applied Mathematics and Mechanics
基金
中央高校基本科研业务费专项资金资助项目(90405009)
关键词
同伦分析法
主共振
强非线性
级数解
多自由度
homotopy analysis method
primary resonance
strongly non-linearity
series solution
multi-degree-of-freedom
