Open AccessBifurcation of Periodic Solutions and Its Maximum Number in a Circular Mesh Antenna System with 1:2 Internal Resonance
Author(s) -
Lishuang Jiang,
Jing Li,
Wei Zhang
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1622/1/012003
Subject(s) - bifurcation , displacement (psychology) , antenna (radio) , nonlinear system , mathematics , vibration , resonance (particle physics) , mathematical analysis , control theory (sociology) , topology (electrical circuits) , physics , control (management) , computer science , telecommunications , acoustics , combinatorics , psychology , particle physics , quantum mechanics , artificial intelligence , psychotherapist
In this paper, we study the bifurcation of periodic solutions for a four-dimensional deployable circular mesh antenna system. The tools for proving these results are the averaging theory and Brouwer degree theory. Based on constructing displacement maps, we study the bifurcation of the periodic solutions of linear center, and to discuss the maximum number of periodic solutions in certain parameter control conditions. The results in this paper are helpful to the study of nonlinear dynamic characteristics and vibration control of deployable circular mesh antenna model.