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

doi:10.1088/1674-1056/ab65b4

中国物理B ›› 2020, Vol. 29 ›› Issue (2): 20504-020504.doi: 10.1088/1674-1056/ab65b4

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

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

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)

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

收稿日期:2019-09-12 修回日期:2019-12-18 出版日期:2020-02-05 发布日期:2020-02-05
通讯作者: Hong Gao E-mail:1147254245@qq.com
基金资助:
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).

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

Received:2019-09-12 Revised:2019-12-18 Online:2020-02-05 Published:2020-02-05
Contact: Hong Gao E-mail:1147254245@qq.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: giant magnetostrictive actuator (GMA), nonlinear hysteresis, bifurcation, chaos

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.

Key words: giant magnetostrictive actuator (GMA), nonlinear hysteresis, bifurcation, chaos

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

闫洪波, 高鸿, 杨高炜, 郝宏波, 牛禹, 刘霈. Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator[J]. 中国物理B, 2020, 29(2): 20504-020504.

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[J]. Chin. Phys. B, 2020, 29(2): 20504-020504.

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

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

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