Nonlinear Dynamic Characteristics Of GMF-SMA Composite Structure Subjected To Stochastic Excitation

In this paper, non- linear differential items are introduced to interpret the hysteretic phenomena of giant magnetostrictive material(GMM) and the shape memory alloy(SMA) based on the experimental data, and the effect of the magnetic field frequency on the hysteresis curves has been considered according to multi- field coupled nonlinear theory. The partial least squares regression methods have been used to obtain the relationships among strain, magnetic field intensity and frequency. Similarly, the relationships among strain, stress and temperature of SMA have been discussed.Then, the dynamic models of GMM-SMA simply-supported beam, cantilever beam and cantilever plate subjected to stochastic excitation have been developed. Based on stochastic dynamics theory, the dynamics characteristics of the system have been discussed. The local stability of the system has been determined by the largest Lyapunov exponent. The global stability of system has been obtained by singular boundary theory. Stochastic Hopf bifurcation has been discussed and the stability of the system are improved by adjusting the system's parameters.Finally, the probability density of first-passage time and reliability of the system have been solved from FPK equation, and the optimal control strategy is proposed by the stochastic dynamic programming method. Numerical simulation and experimental results show that the stability of the system varies with bifurcation parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of safe basin decreases with the increase in noise intensity, and the boundary of safe basin becomes fractal; the reliability of the system is improved through chaotic control, the first-passage time is delayed, and the area of safe basin increases. The results obtained in this research are helpful for engineering applications of GMF-SMA composite structure.