Abstract: In this paper, using the interpolation perturbation method, the author seeks to soive the initial problems of the weakly non-linear damped vibration.We transform the original differential equation into that of the interpolation function, Thus, we obatain the value of the interpotation function, and it is easy to obtain the original unknown function.There are calculating examples, which show that the results of this paper are quite near to the corresponding results obtained by using the m ultiple scales method^[2].

Key words: weakly nonlinear vibration, damping, interpolation, singular perturbation

摘要： 用插值摄动法^[1]求解有阻尼的弱非线性振动问题引入插值函数,把原微分方程变换成为关于插值函数的微分方程.求得插值函数后(用平均法),极易求得原来的未知函数(振体的位置坐标).算例表明,本文结构与多重尺度法的相应结果十分接近.

关键词: 弱非线性振动, 阻尼, 插值, 奇异摄动法