基于多尺度法的分段线性-非线性振子的解析解  

Analytical Solution of Segmented Linear-nonlinear Oscillators Based on Multiscale Method

作　　者：赵毅康 袁满玉 陈小刚[1] 崔继峰[1] ZHAO Yikang;YUAN Manyu;CHEN Xiaogang;CUI Jifeng(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《内蒙古农业大学学报（自然科学版）》2023年第3期65-72,共8页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：国家自然科学基金项目(12062018,12172333);内蒙古自治区自然科学基金项目(2020MS01015);内蒙古自治区高等学校青年科技英才支持计划资助项目(NJYT22075);内蒙古自治区直属高校基本科研业务费项目(JY20220063,JY20220331,ZTY2023014)。

摘　　要：以一个正弦波激励的分段线性-非线性振子为研究对象,分段振子的线性部分可以直接求出其精确解。基于多尺度法,得到了该分段振子的非线性部分的解析近似解,通过与数值解的比较,发现解析近似解与数值解十分吻合。此外,还研究了阻尼项及非线性项的系数对振子动力学行为的影响。A segmented linear-nonlinear oscillator excited by a sinusoidal wave was studied in this paper,and the linear part of the segmented oscillator could be directly solved.Based on the multiscale method,the analytical approximation of the nonlinear part of the segmented oscillator was obtained,and the analytical approximation was found to be in good agreement with the numerical solution.In addition,the effects of the damping term and the coefficients of the nonlinear term on the dynamic behavior of the oscillator were also investigated.

关 键 词：分段振子 多尺度法 解析近似解 数值验证 

分 类 号：O194[理学—数学]