Stochastic bifurcation and optimal control of GMF-SMA composite plate subjected to in-plane stochastic excitation

Abstract

Stochastic bifurcation characteristics and optimal control of giant magnetostrictive film (GMF)-shape memory alloy (SMA) composite plate subjected to in-plane stochastic excitation were studied in this paper. Nonlinear difference item was introduced to interpret the hysteretic phenomena of both GMF and SMA, and then the nonlinear dynamic model of GMF-SMA composite plate subjected to in-plane stochastic excitation was developed. The stochastic stability of the system was analyzed, and the condition of stochastic Hopf bifurcation was discussed. The reliability function of the system was solved from backward Kolmogorov equation, and then the probability density of the first-passage time was obtained. Finally, the stochastic optimal control strategy was obtained in stochastic dynamic programming method. Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the reliability of the system is improved by stochastic optimal control, and the first-passage time is delayed. GMF-SMA composite plate combines the advantages of both GMF and SMA, and can reduce vibration through passive control and active control effectively. The results of this paper are helpful to application of GMF-SMA composite plate in engineering fields.