In this paper, nonlinear dynamic characteristics of shape memory alloy (SMA) simply supported 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 SMA simply supported beam in axial stochastic excitation was developed. The local stochastic stability of the system was analyzed according to the largest Lyapunov exponent, and the global stochastic stability of the system was discussed in singular boundary theory. 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 SMA simply supported beam.
About this article
12 July 2012
04 September 2012
30 September 2012
shape memory alloy (SMA)
Copyright © 2012 Vibroengineering
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.