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

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Zhi-Wen Zhu ◽  
Xin-Miao Li ◽  
Jia Xu
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Dynamic Characteristics ◽  
Control Strategy ◽  
First Passage Time ◽  
Passage Time ◽  
Stochastic Excitation ◽  
First Passage ◽  
Nonlinear Dynamic Characteristics ◽  
Stochastic Hopf Bifurcation

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.

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

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1547-1554
Author(s):  
Xiao-Huan Li ◽  
Fang Liu ◽  
Jia Xu ◽  
Zhi-Wen Zhu
Keyword(s):  
Optimal Control ◽  
Dynamic Characteristics ◽  
Control Strategy ◽  
Nonlinear Dynamic ◽  
Composite Plate ◽  
Vibration Reduction ◽  
Stochastic Excitation ◽  
Optimal Control Strategy ◽  
Nonlinear Dynamic Characteristics ◽  
And Control

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.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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