Global analysis of stochastic bifurcation in shape memory alloy supporter with the extended composite cell coordinate system method

As an intelligent material, a shape memory alloy has many unique mechanical properties, such as shape memory effect and pseudoelasticity, which have been used in many fields. In this paper, the stochastic bifurcation of the shape memory alloy supporter system subject to harmonic and bounded noise excitations is studied in detail by an extended composite cell coordinate system method. By analyzing the influence of the bounded noise amplitude on stochastic bifurcation, it can be found that there exist three kinds of bifurcation phenomena, including stochastic merging crisis, stochastic boundary crisis, and stochastic interior crisis, which are caused by the collision between an attractor and a saddle within the basin of attraction or the basin boundary. The transfer probability is computed for the first time on the basin boundary and the escaped points within the basin of attraction, which quantitatively explain the phase space structure of the system with stochastic bifurcation. These results demonstrate that the extended composite cell coordinate system method is a powerful tool to reveal the mechanism of stochastic bifurcation and provide a theoretical basis for the operation and design of the shape memory alloy supporter system.

Automated summary

This paper studies the stochastic bifurcation of a shape memory alloy supporter system and identifies three kinds of bifurcation phenomena caused by collision between attractors and saddles. The study calculates transfer probability for escaping points within the basin of attraction, providing a quantitative explanation of the system's phase space structure with stochastic bifurcation. The extended composite cell coordinate system method is shown to be a powerful tool for revealing the mechanism of stochastic bifurcation.