Chaos of the Six-Dimensional Non-Autonomous System for the Circular Mesh Antenna

Ying Sun (), Jingyi Liu, Junhua Zhang, Aiwen Wang and Fei Mao
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Ying Sun: School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Jingyi Liu: School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Junhua Zhang: College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, China
Aiwen Wang: School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Fei Mao: Beijing Zhongpuda Technology Company Ltd., Beijing 100015, China

Mathematics, 2022, vol. 10, issue 23, 1-25

Abstract: In the process of aerospace service, circular mesh antennas generate large nonlinear vibrations under an alternating thermal load. In this paper, the Smale horseshoe and Shilnikov-type multi-pulse chaotic motions of the six-dimensional non-autonomous system for circular mesh antennas are first investigated. The Poincare map is generalized and applied to the six-dimensional non-autonomous system to analyze the existence of Smale horseshoe chaos. Based on the topological horseshoe theory, the three-dimensional solid torus structure is mapped into a logarithmic spiral structure, and the original structure appears to expand in two directions and contract in one direction. There exists chaos in the sense of a Smale horseshoe. The nonlinear equations of the circular mesh antenna under the conditions of the unperturbed and perturbed situations are analyzed, respectively. For the perturbation analysis of the six-dimensional non-autonomous system, the energy difference function is calculated. The transverse zero point of the energy difference function satisfies the non-degenerate conditions, which indicates that the system exists Shilnikov-type multi-pulse chaotic motions. In summary, the researches have verified the existence of chaotic motion in the six-dimensional non-autonomous system for the circular mesh antenna.

Keywords: circular mesh antenna; Smale horseshoe; the Poincare map; multi-pulse chaotic motion; the extended energy phase method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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