Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(11): 110504    DOI: 10.1088/1674-1056/ace822
GENERAL Prev   Next  

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 College of Artificial Intelligence, Nankai University, Tianjin 300350, China;
2 Silo AI, Helsinki 00100, Finland
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

[1] Chen P, Luo Z and Tasoglu S 2014 Adv. Mater. 26 5936
[2] Fujita Y, Ishihara S, Nakashima Y, et al. 2021 Appl. Mech. 2 16
[3] Monterosso M E, Futrega K, Lott W B, Vela I, Williams E D and Doran M R 2021 Sci. Rep. 11 5118
[4] Tmaa B, Ga A, Frt A, Dias M M G, Domingues R R, de Carvalho M, de Castro Fonseca M, Rodrigues V K T, Leme A F P and Figueira A C M 2022 SLAS Discovery 27 167
[5] Khademhosseini A, May M H and Sefton M V 2005 Tissue Engineering Part A 11 17971806
[6] Dai H, Xia B and Yu D 2021 Appl. Phys. Lett. 119 11601
[7] Am A, Nai A, Vmf A, et al. 2021 Colloids and Surfaces A: Physicochemical and Engineering Aspects 621 126550
[8] Snezhko A and Aranson I S 2011 Nat. Mater. 10 698
[9] Luo Y, Feng R, Li X and Liu D 2019 Eur. J. Phys. 40 065001
[10] Tuan P H, Wen C P, Chiang P Y and Yu Y T 2015 J. Acoust. Soc. Am. 137 2113
[11] Zhou L and Chen F 2021 Math. Comput. Simul. 192 1
[12] Gendelman O, Kravetc P and Rachinskii D 2019 Chaos 29 113116
[13] Licsko G and Csernak G 2012 IEEE International Conference on Nonlinear Science and Complexity IEEE 121
[14] Li S, Wu H, Zhou X, et al. 2021 Int. J. Nonlinear Mech. 133 103720
[15] Norris A 2004 J. Acoust. Soc. Am. 116 2544
[16] Meleshenko P A, Semenov M E and Klinskikh A F,2020 Nonlinear Dyn. 101 2523
[17] Boudjema R 2022 Int. J. Theor. Phys. 61 1
[18] Alliluev A D and Makarov D V 2022 Biomicrofluidics Journal of Russian Laser Research 43 71
[19] Kruglov V P, Krylosova D A, Sataev I R, Krylosova D A, Sataev I R, Seleznev E P and Stankevich N V 2021 Chaos 31 073118
[20] Vaidyanathan S and Volos C 2015 Arch. Control Sci. 25 333
[21] Jia I, Shi W, Wang L, et al. 2020 Chaos, Solitons and Fractals 133 109635
[22] Cang S J, Li Y, Kang Z J and Wang Z H 2020 Chaos 30 033103
[23] Singh J P, Rajagopal K and Roy B K 2020 Int. J. Bifur. Chaos 31 2130048
[24] Zhang K J, Chen M S, Wang Y, Tian H G and Wang Z 2021 Complexity 3 1
[25] Han N and Lu P P 2009 Chin. Phys. B 29 110502
[26] Pelino V and Maimone F 2009 Chaos, Solitons and Fractals 64 67
[27] Yang Y and Qi G 2018 Chaos, Solitons and Fractals 108 187
[28] Tlelo-Cuautle E, Gerardo D L F L, Pham V T, et al. 2017 Nonlinear Dyn. 89 1129
[29] Bahi J M, Fang X, Guyeux C, et al. 2013 Appl. Math. Inform. Sci. 7 2175
[30] Ding P, Feng X and Wu C 2020 Chin. Phys. B 29 108202
[31] Vaidyanathan T and Volos C 2015 Archives of Control Sciences 25 1
[32] Luo S, Ma H, Li F, et al. 2022 Nonlinear Dyn. 108 97
[33] Din Q, Ishaque W, Iqbal M A, et al. 2021 Journal of Vibration and Control 3 107754632110340
[34] Makouo L, Tsafack K, Tingue M M, et al. 2021 International Journal of Robotics and Automation 1 19
[35] Hu J H 2016 Appl. Phys. 6 114
[36] Tuan P H, Tung J C, Liang H C, Chiang P Y, Huang K F and Chen Y F 2015 Europhys. Lett. 116 64004
[37] Song Q H, Shi J H, Liu Z H, et al. 2016 Int. J. Mech. Sci. 117 16
[38] Taher G, Ali N, Hamed A and Majid Z 2016 Journal of the Brazilian Society of Mechanical Sciences and Engineering 38 403
[39] Jiao X D, Tao J, Sun H and Sun Q L 2022 Sustainability 14 14900
[1] Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system
Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(1): 010501.
[2] Control of chaos in Frenkel-Kontorova model using reinforcement learning
You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[3] A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation
En-Zeng Dong(董恩增), Rong-Hao Li(李荣昊), and Sheng-Zhi Du(杜升之). Chin. Phys. B, 2021, 30(2): 020505.
[4] Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system
Fei Gao(高飞), Wen-Qin Li(李文琴), Heng-Qing Tong(童恒庆), Xi-Ling Li(李喜玲). Chin. Phys. B, 2019, 28(9): 090501.
[5] The electric field and frequency responses of giant electrorheological fluids
Hanqing Zhao(赵汉青), Rong Shen(沈容), Kunquan Lu(陆坤权). Chin. Phys. B, 2018, 27(7): 078301.
[6] Frequency response range of terahertz pulse coherent detection based on THz-induced time-resolved luminescence quenching
Man Zhang(张曼), Zhen-Gang Yang(杨振刚), Jin-Song Liu(刘劲松), Ke-Jia Wang(王可嘉), Jiao-Li Gong(龚姣丽), Sheng-Lie Wang(汪盛烈). Chin. Phys. B, 2018, 27(6): 060204.
[7] Coordinated chaos control of urban expressway based on synchronization of complex networks
Ming-bao Pang(庞明宝), Yu-man Huang(黄玉满). Chin. Phys. B, 2018, 27(11): 118902.
[8] Parrondo's paradox for chaos control and anticontrol of fractional-order systems
Marius-F Danca, Wallace K S Tang. Chin. Phys. B, 2016, 25(1): 010505.
[9] Control of fractional chaotic and hyperchaotic systems based on a fractional order controller
Li Tian-Zeng (李天增), Wang Yu (王瑜), Luo Mao-Kang (罗懋康). Chin. Phys. B, 2014, 23(8): 080501.
[10] Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity
Yin Jiu-Li (殷久利), Zhao Liu-Wei (赵刘威), Tian Li-Xin (田立新). Chin. Phys. B, 2014, 23(2): 020204.
[11] Complex dynamical behavior and chaos control for fractional-order Lorenz-like system
Li Rui-Hong (李瑞红), Chen Wei-Sheng (陈为胜). Chin. Phys. B, 2013, 22(4): 040503.
[12] Chaos detection and control in a typical power system
Hossein Gholizadeh, Amir Hassannia, Azita Azarfar. Chin. Phys. B, 2013, 22(1): 010503.
[13] Control of fractional chaotic system based on fractional-order resistor–capacitor filter
Zhang Lu (张路), Deng Ke (邓科), Luo Mao-Kang (罗懋康). Chin. Phys. B, 2012, 21(9): 090505.
[14] Cascade adaptive control of uncertain unified chaotic systems
Wei Wei(魏伟), Li Dong-Hai(李东海), and Wang Jing(王京). Chin. Phys. B, 2011, 20(4): 040510.
[15] Controlling chaos in power system based on finite-time stability theory
Zhao Hui(赵辉), Ma Ya-Jun(马亚军), Liu Si-Jia(刘思佳), Gao Shi-Gen(高士根), and Zhong Dan(钟丹) . Chin. Phys. B, 2011, 20(12): 120501.
No Suggested Reading articles found!