Geodesic
Periodic solutions of nonlinear differential systems by the method of averaging
Applications of Mathematics, Tome 65 (2020) no. 4, pp. 511-542

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In many engineering problems, when studying the existence of periodic solutions to a nonlinear system with a small parameter via the local averaging theorem, it is necessary to verify some properties of the fundamental solution matrix to the corresponding linearized system along the periodic solution of the unperturbed system. But sometimes, it is difficult or it requires a lot of calculations. In this paper, a few simple and effective methods are introduced to investigate the existence of periodic solutions for a kind of small parametric systems. In order to prove the existence of periodic solutions by these ideas, we also introduce a forced autoparametric vibrating system and a generalized model of the tuned mass absorber with pendulum discussed by Brzeski, Perlikowski, and Kapitaniak. Then, we also propose an averaging method to study the existence of periodic solutions.
DOI : 10.21136/AM.2020.0006-19
Classification : 34C25, 34C29
Keywords: periodic solution; local averaging theorem; forced autoparametric vibrating system; tuned mass absorber 
@article{10_21136_AM_2020_0006_19,
     author = {Li, Zhanyong and Liu, Qihuai and Zhang, Kelei},
     title = {Periodic solutions of nonlinear differential systems by the method of averaging},
     journal = {Applications of Mathematics},
     pages = {511--542},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     doi = {10.21136/AM.2020.0006-19},
     mrnumber = {4134145},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0006-19/}
}
TY  - JOUR
AU  - Li, Zhanyong
AU  - Liu, Qihuai
AU  - Zhang, Kelei
TI  - Periodic solutions of nonlinear differential systems by the method of averaging
JO  - Applications of Mathematics
PY  - 2020
SP  - 511
EP  - 542
VL  - 65
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0006-19/
DO  - 10.21136/AM.2020.0006-19
LA  - en
ID  - 10_21136_AM_2020_0006_19
ER  - 
%0 Journal Article
%A Li, Zhanyong
%A Liu, Qihuai
%A Zhang, Kelei
%T Periodic solutions of nonlinear differential systems by the method of averaging
%J Applications of Mathematics
%D 2020
%P 511-542
%V 65
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0006-19/
%R 10.21136/AM.2020.0006-19
%G en
%F 10_21136_AM_2020_0006_19
Li, Zhanyong; Liu, Qihuai; Zhang, Kelei. Periodic solutions of nonlinear differential systems by the method of averaging. Applications of Mathematics, Tome 65 (2020) no. 4, pp. 511-542. doi: 10.21136/AM.2020.0006-19

Cité par Sources :