一类多自由度非线性振动系统的多频摄动法

A Multiple-Frequency Perturbation Approach of Many Degrees Freedom Non-Linear Vibration Systems

本文把Lindstedt的频率展开思想推广到高维系统,并通过引进自变量的非线性变换,给出一类多自由度非线性自治系统内共振锁相周期解的多频摄动法。最后给出该法的若干应用。

This paper extends the idea of Lindstedt's frequencies expansion into the non-linear autonomous sys-tems with many degrees of freedom and describes a multiple-frequency perturbation approach of the phase-locked periodic solutions for the case of the internal resonance by way of the non-linear trasformation ofthe independent variable.Finally,two application examples of the present method are given.