Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

doi:10.1088/1674-1056/23/8/088201

Abstract The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF)-shaped memory alloy (SMA) composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF-SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF-SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the 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 system's reliability is improved through stochastic optimal control, and the first-passage time is delayed. A GMF-SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF-SMA composite plates.

Keywords: giant magnetostrictive film shape memory alloy composite cantilever plate stochastic Hopf bifurcation optimal control

Received: 04 September 2013
Revised: 05 January 2014
Accepted manuscript online:

PACS:	82.40.Bj	(Oscillations, chaos, and bifurcations)
	47.20.Ky	(Nonlinearity, bifurcation, and symmetry breaking)
	05.10.Gg	(Stochastic analysis methods)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272229 and 11302144), the Ph. D. Programs Foundation of the Ministry of Education of China (Grant No. 20120032120006), and the Tianjin Research Program of Application Foundation and Advanced Technology, China (Grant No. 13JCYBJC17900).

Corresponding Authors: Xu Jia
E-mail: xujiatju@163.com

Cite this article:

Zhu Zhi-Wen (竺致文), Zhang Qing-Xin (张庆昕), Xu Jia (许佳) Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation 2014 Chin. Phys. B 23 088201

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Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

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