Nonlinear Dynamic Characteristics and Control of Giant Magnetostrictive Ultrasonic Transducer

  • F. Liu
  • Z. W. Zhu
  • H. Sheng
  • J. XuEmail author
Original Paper


The nonlinear dynamic characteristics of giant magnetostrictive ultrasonic transducer (GMUT) are researched in this paper, and the optimal control strategy is proposed. New nonlinear differential terms are introduced to explain the hysteretic phenomena of giant magnetostrictive materials (GMM), and the nonlinear dynamic model of a giant magnetostrictive ultrasonic transducer subjected to harmonic magnetic field and stochastic disturbance is developed. The system’s nonlinear dynamic responses are discussed, and the optimal control strategy is proposed to improve the system’s accuracy. Numerical simulation and experiment results show that there are abundant nonlinear dynamic behaviors in the system; the stability of the system varies with the parameters, which causes stochastic bifurcation; the system’s accuracy is improved through stochastic optimal control. The results of this study are helpful for the application of giant magnetostrictive ultrasonic transducer in engineering fields.


Giant magnetostrictive ultrasonic transducer (GMUT) Hysteretic nonlinearity Stochastic Hopf bifurcation Optimal control 


Funding Information

The authors gratefully acknowledge the support of the Natural Science Foundation of China (NSFC) through Grant Nos. 11872266 and 51875396, Chinese Aviation Science Foundation through Grant No. 2016ZA48001, and the Tianjin Research Program of Application Foundation and Advanced Technology through Grant No. 16JCYBJC18800.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringTianjin UniversityTianjinPeople’s Republic of China
  2. 2.Tianjin Key Laboratory of Nonlinear Dynamics and ControlTianjinPeople’s Republic of China

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