Abstract: In this paper,using the interpolation perturbation method,the authors seek to solve two classes of weakly nonlinear oscillations.The one is the nonlinear free oscillation of conservative system.The other is the parametric oscillation.For the former,since we transform the problem to solve differentiation into that to solve algebraic equation,the calculating process is very simple.For the latter,since we transform the problem to seek to solve the second order differential equation into that of twice integrations,the calculating process is also simple.There are calculating examples which show that the results of the paper is reliable.

摘要： 用插值摄动法[1] 求解两类弱非线性振动问题 .其一是保守系统的非线性自由振动 ;其二是参数振动 .前者由于把求解微分方程的问题转化成为求解二次代数方程 ,计算过程十分简单 ;后者由于把一个二阶微分方程的求解转化成为两次积分问题 ,也使计算过程简化 .有算例、算例表明 ,本文结果是可靠的

关键词: 插值摄动法, 参数激励, 保守系统, 非线性, 自由振动, 多尺度法