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

doi:10.1088/1674-1056/ace822

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.

Keywords: thin plate oscillator conservative chaos Bubnov-Galerkin method frequency response chaos control

Received: 22 June 2023
Revised: 13 July 2023
Accepted manuscript online: 18 July 2023

PACS:

05.45.-a

(Nonlinear dynamics and chaos)

Fund: 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.

Corresponding Authors: Hao Sun, Qinglin Sun
E-mail: sunh@nankai.edu.cn;qlsun@nankai.edu.cn

Cite this article:

Xiaodong Jiao(焦晓东), Xinyu Wang(王新宇), Jin Tao(陶金), Hao Sun(孙昊) Qinglin Sun(孙青林), and Zengqiang Chen(陈增强) Dynamic modelling and chaos control for a thin plate oscillator using Bubnov-Galerkin integral method 2023 Chin. Phys. B 32 110504

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

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