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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ying Sun & Jingyi Liu & Junhua Zhang & Aiwen Wang & Fei Mao, 2022. "Chaos of the Six-Dimensional Non-Autonomous System for the Circular Mesh Antenna," Mathematics, MDPI, vol. 10(23), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4454-:d:984242
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