一类弱非线性振动方程的变分迭代算法  

ITERATION APPROACH FOR A KIND OF WEAK NONLINEAR OSCILLATION EQUATIONS

作　　者：王德强 何吉欢[2] 

机构地区：[1]山东省内燃机研究所 [2]上海大学,上海市应用数学和力学研究所200072

出　　处：《振动与冲击》1998年第4期35-38,共4页Journal of Vibration and Shock

基　　金：山东省自然科学基金资助项目

摘　　要：本文提出了一种求解非线性方程的迭代算法,这种方法是先给方程一个带待定函数的试函数作为初始近似解,然后用拉氏乘子法构造一个迭代公式,而拉氏乘子可用变分的概念最佳确定。应用这种方法不会出现长期项,其结果比传统的摄动方法要好得多。In the paper, an iteration method is proposed to solve analytically a kind of weak nonlinear oscillation equations. In this method, a trial-function with possible unknowns is used as initial approximation and a Lagrange multiplier is introduced to construct an iteration formula, correcting successively its initial approximation. The multiplier can be identified via the variation-al theory. Comparision between the novel techinque and perturbation methods has been made, revealing the new method is very effective and convenient.

关 键 词：非线性 变分迭代算法 DUFFING方程 

分 类 号：O322[理学—一般力学与力学基础] O241.82[理学—力学]