Approximate analytical solution in slow-fast system based on modified multi-scale method
Approximate analytical solution in slow-fast system based on modified multi-scale method
复制标题
基于改进多尺度方法的慢-快系统近似解析解
DOI：
10.1007/s10483-020-2598-9
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发表时间：
2020-03
期刊：
影响因子：
--
通讯作者：
Yongjun Shen
中科院分区：
文献类型：
--
作者：
Xionghong Li;Jianhua Tang;Yanli Wang;Yongjun Shen
提出了一种简单而精确的修正多尺度法（MMSM），用于求解强迫简谐激励下双时间尺度非线性振子的近似解析解。该方法依赖于经典的多尺度方法（MSM）和变参数方法。在强迫激励为常数的条件下，基于传统的MSM模型，可以很容易地得到简化系统的近似解析解。然后，将谐振激励替换为恒定激励后，就可以建立受强迫谐振激励下振子的解。为了验证所提出的分析方法的正确性和精确性，研究了受慢周期激励的双尺度货车der Pol系统，该系统呈现出丰富的动力学现象，如尖峰（SP）、尖峰-静止（SP-QS）和静止（QS）响应.用该方法给出了三种响应的近似解析表达式，结果表明，该方法的精度高于经典的MSM方法，优于谐波平衡法。特别是当激励频率远小于系统固有频率时，用本方法得到的结果在定量和定性上都比传统方法得到的结果好得多。
A simple, yet accurate modified multi-scale method (MMSM) for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed. This method depends on the classical multi-scale method (MSM) and the method of variation of parameters. Assuming that the forced excitation is a constant, one could easily obtain the approximate analytical solution of the simplified system based on the traditional MSM. Then, this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation. To certify the correctness and precision of the proposed analytical method, the van der Pol system with two scales subject to slowly periodic excitation is investigated; this system presents rich dynamical phenomena such as spiking (SP), spiking-quiescence (SP-QS), and quiescence (QS) responses. The approximate analytical expressions of the three types of responses are given by the MMSM, and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method (HBM). The results obtained by the present method are considerably better than those obtained by traditional methods, quantitatively and qualitatively, particularly when the excitation frequency is far less than the natural frequency of the system.
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DOI：
10.1137/100811726
发表时间：
2010-10
期刊：
SIAM J. Appl. Dyn. Syst.
影响因子：
--
作者：
Guillaume Lajoie;E. Shea-Brown
通讯作者：
Guillaume Lajoie;E. Shea-Brown
DOI：
10.1137/s1111111102404738
发表时间：
2003
期刊：
SIAM J. Appl. Dyn. Syst.
影响因子：
--
作者：
J. Guckenheimer;Kathleen A. Hoffman;Warren Weckesser
通讯作者：
J. Guckenheimer;Kathleen A. Hoffman;Warren Weckesser
影响因子：
4.7
作者：
A. Papangelo;M. Ciavarella
通讯作者：
A. Papangelo;M. Ciavarella
影响因子：
15.1
作者：
E. Lashina;N. Chumakova;G. Chumakov;A. Boronin
通讯作者：
E. Lashina;N. Chumakova;G. Chumakov;A. Boronin
DOI：
10.5860/choice.32-6286
发表时间：
1995
期刊：
--
影响因子：
--
作者：
Ali H. Nayfeh;Balakumar Balachandran
通讯作者：
Ali H. Nayfeh;Balakumar Balachandran