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Shock and Vibration
Volume 2015 (2015), Article ID 523723, 10 pages
Research Article

Nonlinear Dynamic Characteristics and Optimal Control of SMA Composite Wings Subjected to Stochastic Excitation

1Department of Mechanics, Tianjin University, Tianjin 300072, China
2Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, China

Received 31 May 2015; Revised 23 June 2015; Accepted 25 June 2015

Academic Editor: Nerio Tullini

Copyright © 2015 Zhi-Wen Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A kind of high-aspect-ratio shape memory alloy (SMA) composite wing is proposed to reduce the wing’s fluttering. The nonlinear dynamic characteristics and optimal control of the SMA composite wings subjected to in-plane stochastic excitation are investigated where the great bending under the flight loads is considered. The stochastic stability of the system is analyzed, and the system’s response is obtained. The conditions of stochastic Hopf bifurcation are determined, and the probability density of the first-passage time is obtained. Finally, the optimal control strategy is proposed. Numerical simulation shows that the stability of the system varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the reliability of the system is improved through optimal control, and the first-passage time is delayed. Finally, the effects of the control strategy are proved by experiments. The results of this paper are helpful for engineering applications of SMA.