Nonlinear dynamic characteristics of SMA simply supported beam in axial stochastic excitation

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.