摘要
拓展了范式方法 ,使其可以研究强非线性振动问题。创新之处在于改进了 Nayfeh关于响应频率的选取 ,根据振动过程中基频的变化选取响应的频率。采用本文所提出的方法 ,无论是周期解的稳定性 ,还是渐近解都可以较容易地获得。作为算例 ,用本文提出的方法计算了一般具有平方、立方项强非线性系统的范式及其渐近解、定常解 。
The normal form method is extended to study the strongly non-linear vibration problems.A new selection of the response frequency is proposed. According to it the frequency is determined allowing for the change of the fundamental frequency during vibration rather than by natural frequency suggested by Nayfeh. With the present method both the stability of the periodic solutions and the asymptotic expressions for the periodic solutions can be obtained easily. The results obtained by the method presented coincide very well with the results obtained by numerical integration for the Duffing-Van der Pol-Rayleigh oscillator.
出处
《振动工程学报》
EI
CSCD
2000年第3期481-486,共6页
Journal of Vibration Engineering
基金
国家自然科学基金重大基金资助项目! (编号 :19990 5 10 )
国家重点基础研究专项经费资助项目! (编号 :G19980 2 0 316 )
关键词
非线性振动
强非线性
范式
渐近解
non-linear vibration
strong non-linear
normal form
asymptotic solution
