Nonlinear Dynamic Characteristics and Optimal Control of Giant Magnetostrictive Laminated Plate Subjected to In-plane Stochastic Excitation

Abstract

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.