Nonlinear Dynamic Characteristics of Giant Magnetostrictive Nanofilm-SMA Composite Beam in Axial Stochastic Excitation

2013 ◽  
Vol 284-287 ◽  
pp. 173-177
Author(s):  
Zhi Wen Zhu ◽  
Wei Guo ◽  
Jia Xu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Composite Beam ◽  
Stochastic Bifurcation ◽  
Hysteresis Phenomenon ◽  
Stochastic Excitation ◽  
Nonlinear Dynamic Characteristics

In this paper, nonlinear dynamic characteristics of giant magnetostructive nanofilm-shape memory alloy (SMA) composite beam in axial stochastic excitation were studied. Von del Pol nonlinear difference item was introduced to interpret the hysteresis phenomenon of the strain-stress curve of SMA, and the hysteretic nonlinear dynamic model of giant magnetostructive nanofilm-SMA composite beam in axial stochastic excitation was developed. The steady-state probability density function and the joint probability density function of the system were obtained in quasi-nonintegrable Hamiltonian system theory. The result of simulation shows that the stability of the trivial solution varies with bifurcation parameter, and stochastic Hopf bifurcation appears in the process. The result is helpful to stochastic bifurcation control to giant magnetostructive nanofilm-SMA composite beam.

scholarly journals Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil

2018 ◽  
Vol 148 ◽  
pp. 08001
Author(s):  
Chandan Bose ◽  
Sunetra Sarkar ◽  
Sayan Gupta
Keyword(s):  
Fixed Point ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Bifurcation Analysis ◽  
Stochastic Bifurcation ◽  
Stable Limit ◽  
Mean Flow ◽  
Flow Fluctuations ◽  
Flapping Airfoil

The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI) behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO) from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation) analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf) of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.

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.

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