Affiliations: [a] Deparment of Mechanics, Tianjin University, Tianjin,
China | [b] Tianjin Key Laboratory of Nonlinear Dynamics and Chaos
Control, Tianjin, China | Université Laval, Canada | Tohoku University, Japan
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.
