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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. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic characteristics of Fe-Ga cantilever nanobeam subjected to stochastic excitation are studied in this paper where the nonlocal effect is considered. Nonlinear differential terms are introduced to explain the hysteretic phenomena of the Fe-Ga alloy's strain-magnetic field intensity curves, and the nonlinear dynamic model of Fe-Ga cantilever composite nanobeam subjected to stochastic excitation is developed. The system's nonlinear dynamic characteristics are discussed, and the optimal control strategy is proposed to enhance the system's reliability. Numerical simulations show that the nonlocal effect can influence the system's stochastic Hopf bifurcation; the boundary of the system's safe basin has fractal characteristics, the area of safe basin decreases when the intensity of the noise increases, and it increases again through stochastic optimal control. The results of this study are helpful for the application of Fe-Ga composite nanobeam in engineering fields. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic characteristics and optimal control of magnetic shape memory alloy (MSMA) cantilever beam subjected to axial stochastic excitation is studied in this paper. Nonlinear difference item is introduced to interpret the hysteretic phenomena of MSMA, and the nonlinear dynamic model of MSMA cantilever beam subjected to axial stochastic excitation is developed. The steady-state probability density function of the dynamic response of the system is obtained, and the conditions of stochastic Hopf bifurcation are analyzed. The reliability function of the system is solved, and then the probability density of the first-passage time is obtained. Finally, the optimal control strategy is proposed in stochastic dynamic programming method. Numerical simulations show that the stability of the trivial solution varies with bifurcation parameter, and stochastic Hopf bifurcation appears in the process; the reliability of the system is proved by stochastic optimal control, and the first-passage time is delayed. The results are helpful to engineering application of MSMA cantilever beam. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear dynamic characteristics and optimal control of giant magnetostrictive laminated plate (GMLP) subjected to in-plane stochastic excitation were studied. Von del Pol nonlinear item was introduced to interpret the hysteresis phenomenon of the strain-magnetic field intensity curve of giant magnetostrictive material, and the nonlinear dynamic model of GMLP subjected to in-plane stochastic excitation was developed. Local and global stochastic stabilities were analyzed according to largest Lyapunov exponent theory and singular boundary theory. The functions of steady-state probability density and joint probability density were obtained, and the condition of stochastic Hopf bifurcation was analyzed. The reliability function was solved from backward Kolmogorov equation, and the probability density of the first-passage time was obtained. Finally, the optimal control strategy was proposed in stochastic dynamic programming method. Numerical simulation shows that the stability of the solution varies with parameter, and stochastic Hopf bifurcation appears in the process; the reliability of the system was improved by optimal control, and the first-passage time was delayed. The result is helpful to engineering applications of GMLP. [ABSTRACT FROM AUTHOR]