Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(2): 020504    DOI: 10.1088/1674-1056/ab65b4
GENERAL Prev   Next  

Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator

Hong-Bo Yan(闫洪波)1, Hong Gao(高鸿)1, Gao-Wei Yang(杨高炜)1, Hong-Bo Hao(郝宏波)2, Yu Niu(牛禹)1, Pei Liu(刘霈)1
1 College of Mechanical Engineering, Inner Mongolia University of Science&Technology, Baotou 014010, China;
2 Baotou Research Institute of Rare Earths, State Key Laboratory of Bayan Obo Rare Earth Resource Researches and Comprehensive Utilization, Baotou 014030, China
Abstract  Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator (GMA). Therefore, in the present study we intend to investigate the influences of the system damping coefficient, system stiffness coefficient, disc spring cubic stiffness factor, and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA. In this regard, the nonlinear piezomagnetic equation, Jiles-Atherton hysteresis model, quadratic domain rotation model, and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA. Moreover, the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system. Then, the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed. Finally, the fourth-order Runge-Kutta method is used to obtain the time domain waveform, phase portrait and Poincaré mapping diagrams of the system. Subsequently, the obtained three graphs are analyzed. The obtained results show that when the system output is stable, the variation range of each parameter can be determined. Moreover, the stability interval of system damping coefficient, system stiffness coefficient, and the coefficient of the cubic stiffness term of the disc spring are obtained. Furthermore, the stability interval of the exciting force and the excitation frequency are determined.
Keywords:  giant magnetostrictive actuator (GMA)      nonlinear hysteresis      bifurcation      chaos  
Received:  12 September 2019      Revised:  18 December 2019      Published:  05 February 2020
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
Fund: Project supported by the Science Fund from the Ministry of Science and Technology of China (Grant No. 2017M010660) and the Major Project of the Inner Mongolia Autonomous Region, China (Grant No. 2018ZD10).
Corresponding Authors:  Hong Gao     E-mail:  1147254245@qq.com

Cite this article: 

Hong-Bo Yan(闫洪波), Hong Gao(高鸿), Gao-Wei Yang(杨高炜), Hong-Bo Hao(郝宏波), Yu Niu(牛禹), Pei Liu(刘霈) Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator 2020 Chin. Phys. B 29 020504

[1] Li Y S, Zhu Y C, Wu H T, Niu S Y and Tian Y S 2018 Int. J. Appl. Electromagnet. Mech. 57 439
[2] Yang Z S, He Z B, Yang F B, Rong C and Cui X H 2018 Int. J. Appl. Electromagnet. Mech. 57 439
[3] Zhu Y and Li Y 2014 Smart Mater. Structures. 23 115001
[4] Braghin F, Cinquemani S and Resta F 2012 Sens. Actuators A: Physical. 180 67
[5] Yang Y, Yang B and Niu M 2018 Nonlinear Dyn. 92 1109
[6] Ting Z, Bin T Y, Hong G L and Guang M 2013 Sens. Actuators A: Physical. 190 96
[7] Kotaro M, Tadashi H and Shigekazu I 2018 Materials 11 581
[8] Fang Z W, Zhang Y W, Li X, Ding H, Chen L Q 2017 J. Sound Vibration 391 35
[9] Yan B, Zhang C and Li L 2017 Smart Mater. Structures 26 05LT02
[10] Xue G M, Zhang P L, He Z B, Li B and Rong C 2017 Smart Mater. Structures 26 05LT02
[11] Xue G M, Zhang P L, He Z B, Li D W, Huang Y J and Zhang L 2019 Sens. Actuators A: Physical 287 150
[12] Liu H F, Zhao J J, Wang W G, Yang G Z and Gao Z J 2016 Chin. J. Sens. & Actuators 29 1797
[13] Zhou J T, He Z B, Rong C and Xue G M 2019 Sens. Actuators A: Physical 287 150
[14] Xue G M, Zhang P L, He Z B, Li D W, Yang Z S and Zhao Z L 2016 Mater. & Design. 95 501
[15] Liu Y G, Gao X H and Li Y L 2016 Sens. Actuators A: Physical 250 7
[16] Gao X H and Liu Y G 2018 Nonlinear Dyn. 92 793
[17] Xue G M, Zhang P L, Li X Y, He Z B, Wang H G, Li Y N, Rong C, Zeng W and Li B 2018 Sens. Actuators A: Physical 273 159
[18] Nealis J M and Smith R C 2003 Proc. SPIE. 221
[19] Han F, Wang Z J, Fan H and Gong T 2015 Chin. Phys. Lett. 32 040502
[20] Wang L, Tan J B and Liu Y T 2005 J. Phys.: Conf. Ser. 13 446
[21] Oates W S, Smith R C and Smith R C 2016 Smart Mater. Structures 25 085036
[22] Liu P, Mao J Q, Liu Q S and Zhou K M 2013 Control Theory & Applications 30 148
[23] Zhou H M, Li M H, Li X H and Zhang D G 2016 Smart Mater. Structures 25 085036
[24] Tan X B and Baras J S 2004 Autom. 40 1469
[25] Zhu Y C, Yang X L and Wereley N M 2016 Smart Mater. Structures 25 085030
[26] Liu H F, Wang H Y, Wang J and Shan G K 2016 Opt. Precision Engineering 24 1128
[27] Zeng H Q, Leng J and Asundi A K 2015 Chin. Phys. Lett. 32 050501
[28] Liu B, Hu W P, Zou X, Ding Y J and Qian S Y 2019 Acta Phys. Sin. 68 028702 (in Chinese)
[29] He J H and Sun C 2019 J. Math. Chem. 57 01063
[30] He J H 2019 Int. J. Numer. Methods Heat Fluid Flow
[31] He J H 2019 Int. J. Numer. Methods Heat Fluid Flow
[32] Li L L and Xue C X 2019 Acta Phys. Sin. 68 010501 (in Chinese)
[33] Peng R R 2019 Appl. Math. Mech. 40 1122
[34] Zhang Q F, Huang C Q, Yao J, Li Y and Yan X 2019 Acta Phys. Sin. 68 164 (in Chinese)
[35] Xia G H, Fang F, Chen T and Wang J G 2019 Chin. J. Appl. Mech.
[36] Wu L M and Cao S Q 2019 J. Mech. Eng. 55 92
[37] Zeng H Q 2009 Trans. Chin. Soc. For Agricultural Machinery 40 185
[38] Sun H G, Yuan H Q, He W and Li D 2007 Chin. J. Appl. Mech. 24 486
[39] Yuan H Q, Li H, Zhou S W and Bang C 2002 J. Northeastern University (Natural Science) 404–409
[40] Liu B, Zhao H X, Hou D X and Liu H R 2014 Acta Phys. Sin. 63 074501 (in Chinese)
[41] Ogunjo S T and Fuwape I A 2019 arXiv preprint arXiv: 08584
[42] Liu B, Zhao H X and Hou D X 2014 Acta Phys. Sin. 63 174502 (in Chinese)
[43] Ji Q B, Zhou Y, Yang Z Q and Meng X Y 2015 Chin. Phys. Lett. 32 050501
[44] Cao B F, Li P, Li X Q, Zhang X Q, Ning W S, Liang R, Li X, Hu M and Zheng Y 2019 Chin. Phys. B 28 040201
[45] Shi L J and Wen Z S 2019 Chin. Phys. B 28 040201
[46] Chen J Y, Min F H, Jin Q S and Ye B M 2019 Chin. Phys. B 28 020503
[47] Alamodi O A, Sun K H, Ai W, Chen C and Peng D 2019 Chin. Phys. B 28 020503
[48] Yu X C, Ren Z Z and Zhang X 2019 Chin. Phys. B 28 020504
[49] Cao S Y, Wang B W, Yan R G, Huang W M and Wen L 2007 IEEE Trans. Magn. 43 3467
[50] Anderson P I, Moses A J, Stanbury H J and Standury H J 2007 IEEE Trans. Magn. 43 3467
[51] Jiles D C and Atherton D L 1984 J. Appl. Phys. 55 2115
[52] Hamimid M, Mimoune S M and Feliachi M 2017 Int. J. Numer. Modell.: Electronic Networks, Devices and Fields 30 e2225
[53] Ren Z F, Yao S W and He J H 2019 J. Low Freq. Noise Vib. Active Control 38 1708
[1] Dynamics and coherence resonance in a thermosensitive neuron driven by photocurrent
Ying Xu(徐莹), Minghua Liu(刘明华), Zhigang Zhu(朱志刚), Jun Ma(马军). Chin. Phys. B, 2020, 29(9): 098704.
[2] Quantum to classical transition induced by a classically small influence
Wen-Lei Zhao(赵文垒), Quanlin Jie(揭泉林). Chin. Phys. B, 2020, 29(8): 080302.
[3] Generating mechanism of pathological beta oscillations in STN-GPe circuit model: A bifurcation study
Jing-Jing Wang(王静静), Yang Yao(姚洋), Zhi-Wei Gao(高志伟), Xiao-Li Li(李小俚), Jun-Song Wang(王俊松). Chin. Phys. B, 2020, 29(5): 058701.
[4] Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control
Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Chin. Phys. B, 2020, 29(5): 050504.
[5] The second Hopf bifurcation in lid-driven square cavity
Tao Wang(王涛), Tiegang Liu(刘铁钢), Zheng Wang(王正). Chin. Phys. B, 2020, 29(3): 030503.
[6] Chaotic dynamics of complex trajectory and its quantum signature
Wen-Lei Zhao(赵文垒), Pengkai Gong(巩膨恺), Jiaozi Wang(王骄子), and Qian Wang(王骞). Chin. Phys. B, 2020, 29(12): 120302.
[7] Nonlinear dynamics in non-volatile locally-active memristor for periodic and chaotic oscillations
Wen-Yu Gu(谷文玉), Guang-Yi Wang(王光义), Yu-Jiao Dong(董玉姣), Jia-Jie Ying(应佳捷). Chin. Phys. B, 2020, 29(11): 110503.
[8] Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation
Ming Song(宋明), Beidan Wang(王贝丹), Jun Cao(曹军). Chin. Phys. B, 2020, 29(10): 100206.
[9] 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.
[10] Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation
Li-Juan Shi(师利娟), Zhen-Shu Wen(温振庶). Chin. Phys. B, 2019, 28(4): 040201.
[11] Dynamical stable-jump-stable-jump picture in a non-periodically driven quantum relativistic kicked rotor system
Hsincheng Yu(于心澄), Zhongzhou Ren(任中洲), Xin Zhang(张欣). Chin. Phys. B, 2019, 28(2): 020504.
[12] Design new chaotic maps based on dimension expansion
Abdulaziz O A Alamodi, Kehui Sun(孙克辉), Wei Ai(艾维), Chen Chen(陈晨), Dong Peng(彭冬). Chin. Phys. B, 2019, 28(2): 020503.
[13] Enhancing von Neumann entropy by chaos in spin-orbit entanglement
Chen-Rong Liu(刘郴荣), Pei Yu(喻佩), Xian-Zhang Chen(陈宪章), Hong-Ya Xu(徐洪亚), Liang Huang(黄亮), Ying-Cheng Lai(来颖诚). Chin. Phys. B, 2019, 28(10): 100501.
[14] Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
Runzu Zhang(张润祖), Weihua Zhang(张为华), Barbara Dietz, Guozhi Chai(柴国志), Liang Huang(黄亮). Chin. Phys. B, 2019, 28(10): 100502.
[15] Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts
Deli Wang(王德莉), Wei Xu(徐伟), Xudong Gu(谷旭东). Chin. Phys. B, 2019, 28(1): 010203.
No Suggested Reading articles found!