分析强非线性振动系统周期解的一种方法

A Method for Analysing periodic Solutions of Strongly Nonlinar Oscillators

本文提出了分析强非线性拟保守系统+g(x)=μf(x,) 0<μ≤1周期解的一种方法,它是 Lindstedt—Poincaré方法的推广,用此法可以确定极限环的振幅和周期。作为实例,确定了修正的 van der Pol 振子的极限环振幅;研究了立方强非线性保守系统的 Duffing 方程,并给出了一阶近似周期解。

A method is presented for analysing periodic solutions of the strongly nonlinear quasi-conservative system +g(x)=μf(x,) 0<μ≤1 It is an extension of the method of Lindstedt-Poincare.Using this method,the amplitudes and periods of the limit cycles of the above system can be determined.As examples,the amplitude of the limit cycle of modified van der Pol equation and a first approximation of thc periodic solution of the strongly nonlinear Duffing equation are investigated.