Stochastic Nonlinear Dynamic Characteristics and Control of Fe-Ga Cantilever Nanobeam with Nonlocal Effect

The nonlinear dynamic characteristics of Fe-Ga cantilever nanobeam subjected to stochastic excitation are studied in this paper where the nonlocal effect is considered. Nonlinear differential terms are introduced to explain the hysteretic phenomena of the Fe-Ga alloy’s strain-magnetic field intensity curves, and the nonlinear dynamic model of Fe-Ga cantilever composite nanobeam subjected to stochastic excitation is developed. The system’s nonlinear dynamic characteristics are discussed, and the optimal control strategy is proposed to enhance the system’s reliability. Numerical simulations show that the nonlocal effect can influence the system’s stochastic Hopf bifurcation; the boundary of the system’s safe basin has fractal characteristics, the area of safe basin decreases when the intensity of the noise increases, and it increases again through stochastic optimal control. The results of this study are helpful for the application of Fe-Ga composite nanobeam in engineering fields.