一类弱非线性振动系统的摄动求解

Perturbation method for solving a class of weakly nonlinear oscillation system

主要讨论了一类带有小参数的弱非线性振动系统,利用一种新的摄动技巧求得了带小扰动参数的Duffing方程的渐近解,将所得的渐近解和用Lindstedt Poinca啨方法得到的一级近似解相比较,结果表明该渐近解精度较高 最后对问题的这两种渐近解进行数值模拟,进一步表明了该方法所得到的渐近解具有较好的精确度。

A class of perturbed weakly nonlinear system is discussed. The asymptotic solution for perturbed Duffing equation is solved by using a new perturbation technique. The solution is compared with the first-order asymptotic solution which is obtained by Lindstedt-Poincaré technique. It shows that the solution is very precise. Numerical simulations for the two classes of asymptotic solutions are carried out. The conditions for the initial amplitude and perturbation parameters under which the two classes of solutions are approximate, are elucidated.