一类非线性振动周期与周期解的解析逼近  

Analytical Approximations to Period and Periodic Solution for a Class of Nonlinear Oscillators

作　　者：周显波[1] 李鹏松[2] 吴柏生[2] 

机构地区：[1]空军长春飞行学院力学教研室,长春130022 [2]吉林大学数学科学学院,长春130012

出　　处：《吉林大学学报（理学版）》2002年第4期350-354,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:19972023);教育部优秀青年教师基金;高等学校骨干教师基金.

摘　　要：研究具有奇非线性单自由度保守系统的非线性振动。将控制方程的线性化与调和平衡法组合起来,建立周期及周期解的解析逼近公式.这些公式既适用于小振幅又适用于大振幅情况.举例说明提出方法的有效性.This paper deals with the nonlinear oscillations of conservative singledegreeoffreedom systems with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we have established analytical approximate formulas for the period and the periodic solution. These formulas are valid for oscillations with small as well as large amplitude. It is illustrated by one example that the proposed formulas can give very satisfactory approximate results.

关 键 词：振动周期 解析逼近 非线性振动 周期解 线性化 调和平衡 奇非线性单自由度保守系统 

分 类 号：O322[理学—一般力学与力学基础]