中国物理B ›› 2023, Vol. 32 ›› Issue (11): 110504-110504.doi: 10.1088/1674-1056/ace822

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Dynamic modelling and chaos control for a thin plate oscillator using Bubnov-Galerkin integral method

Xiaodong Jiao(焦晓东)1, Xinyu Wang(王新宇)1, Jin Tao(陶金)2, Hao Sun(孙昊)1,† Qinglin Sun(孙青林)1,‡, and Zengqiang Chen(陈增强)1   

  1. 1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
    2 Silo AI, Helsinki 00100, Finland
  • 收稿日期:2023-06-22 修回日期:2023-07-13 接受日期:2023-07-18 出版日期:2023-10-16 发布日期:2023-11-07
  • 通讯作者: Hao Sun, Qinglin Sun E-mail:sunh@nankai.edu.cn;qlsun@nankai.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61973172, 62003177,62103204, 62003175, and 61973175), the Joint Fund of the Ministry of Education for Equipment Pre-research (Grant No. 8091B022133), and General Terminal IC Interdisciplinary Science Center of Nankai University.

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov-Galerkin integral method

Xiaodong Jiao(焦晓东)1, Xinyu Wang(王新宇)1, Jin Tao(陶金)2, Hao Sun(孙昊)1,† Qinglin Sun(孙青林)1,‡, and Zengqiang Chen(陈增强)1   

  1. 1 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
    2 Silo AI, Helsinki 00100, Finland
  • Received:2023-06-22 Revised:2023-07-13 Accepted:2023-07-18 Online:2023-10-16 Published:2023-11-07
  • Contact: Hao Sun, Qinglin Sun E-mail:sunh@nankai.edu.cn;qlsun@nankai.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61973172, 62003177,62103204, 62003175, and 61973175), the Joint Fund of the Ministry of Education for Equipment Pre-research (Grant No. 8091B022133), and General Terminal IC Interdisciplinary Science Center of Nankai University.

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摘要： The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov-Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably, the reaction force of the thin plate vibration system is defined as f = α|w|, resembling Hooke's law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude-frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude-frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system's states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.

关键词: thin plate oscillator, conservative chaos, Bubnov-Galerkin method, frequency response, chaos control

Abstract: The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov-Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably, the reaction force of the thin plate vibration system is defined as f = α|w|, resembling Hooke's law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude-frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude-frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system's states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.

Key words: thin plate oscillator, conservative chaos, Bubnov-Galerkin method, frequency response, chaos control

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a