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

Abstract

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.