达芬-谐波振子的改进解析逼近解  

IMPROVED ANALYTICAL APPROXIMATE SOLUTIONS OF THE DUFFING-HARMONIC OSCILLATOR

作　　者：李鹏松[1] 吴柏生[1] 

机构地区：[1]吉林大学数学学院力学与工程科学系,长春130012

出　　处：《振动与冲击》2004年第3期113-116,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金 (1 9972 0 2 3)资助项目

摘　　要：研究达芬 -谐波振子的解析逼近解。所谓达芬 -谐波振子是指当位移远小于 1时 ,系统可化为三次非线性振子 ,而当位移远大于 1时 ,该系统则化为线性谐波振子。通过将变形后的控制方程的线性化与谐波平衡法组合起来 ,我们建立了达芬 -谐波振子频率及周期解的改进解板逼近。改进的解析逼近在振幅的全部取值范围内 ,包括振幅趋于零及无穷的情况 。Analytical approximate solutions of the Duffing-harmonic oscillator are dealt with. For small displacement u, the oscillator is a Duffing-type cubic non-linear oscillator, while for large displacement u, the oscillator approximates to a linear harmonic oscillator. By combining the linearization of the rewritten governing equation with the method of harmonic balance, the improved analytical approximate expressions of the frequency and the corresponding periodic solutions of the oscillator are derived. The improved analytical approximations show excellent agreement with the exact solutions, and are valid for total range of oscillation amplitudes, including the two extreme cases of the oscillation amplitude approaching zero and infinity.

关 键 词：振子 逼近解 无穷 谐波平衡法 周期解 振幅 线性化 频率 控制方程 

分 类 号：TU674[建筑科学—建筑技术科学] O321[理学—一般力学与力学基础]