Nonlinear dynamic characteristics and control of Galfenol-Shape Memory Alloy composite plate subjected to stochastic excitation

Abstract

In this paper, the nonlinear dynamic characteristics and control of a Galfenol-shape memory alloy (SMA) composite plate under stochastic excitation are studied. New nonlinear differential terms are applied in the constitutive modeling of Galfenol alloy and SMA, and the nonlinear dynamic model of the composite system is developed. The drift coefficient and the diffusion coefficient are calculated to obtain the steady-state probability density function of the system, and finally the optimal control strategy is proposed to improve the effects of vibration reduction. Numerical simulation and experiments results show that the system has abundant nonlinear dynamic characteristics, including stochastic Hopf bifurcation and limit cycle bifurcation. The stochastic optimal control strategy can improve the effects of vibration reduction efficiently. These results are helpful for the application of Galfenol-SMA composite structures.