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.

Received: 12 September 2019
Revised: 18 December 2019
Accepted manuscript online:

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

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