Nonlinear Dynamic Characteristics Of Shape Memory Alloy Tracheal Stent

Shape memory alloy(SMA)tracheal stent is the most popular therapy technology for tracheal stenosis.It has excellent corrosion resistance and biocompatibility,and the treatment effect is remarkable with few complications.In this paper,we use the hysteretic nonlinear differential equations theory to develop the hysteretic nonlinear constitutive models of SMA based on its stress-strain experimental data.Considering the influence of temperature on stress-strain hysteresis curves of SMA material and applying modern statistical regression method,we study the SMA’s coupling characteristics of stress,strain and temperature.Combined with the specific environment of tracheal stent,the nonlinear differential equations of a SMA tracheal stent subjected to cough excitations,radial pressure and airflow friction are studied.For the deterministic system,we obtain the conditions for the stent to remain stable in the tracheal through analyzing the stability of the system.Using Mathematica mathematical software for simulation,we can see that there are equilibrium points,limit cycles in different conditions.Considering the effect of random disturbance,we develop the nonlinear stochastic dynamical model.The system’s stability is determined by both the largest Lyapunov exponent and the theory of singular boundary.The stent system’s SPDF and JPDF are determined by FPK equation.We study the critical conditions of the occurrence of stent system’s stochastic Hopf bifurcation,and adjust the system’s parameters to avoid stochastic Hopf bifurcation and improve the stability of the stent system.Considering the strongly nonlinear factors of the system and the time-delay characteristics of SMA material,we establish the strongly nonlinear time-delay stochastic dynamics model of the system.Using the energy function method,we modify the system’s nature frequency under strongly nonlinear condition;get the expressions of the improved drift coefficients and diffusion coefficients,and obtain the high-precision time-delay dynamics response of the system under strongly nonlinear condition.From analysis results,we find that the time-delay constant has great influence on the system’s dynamic characteristics,and two periodic motions with different amplitudes may appear in the system,which are decided by the initial conditions.Jumping phenomena between the two vibration amplitudes appears with the change of time-delay constant,which is a new stochastic bifurcation,.This paper’s result will be useful for the future application of the Ti-Ni SMA tracheal stent in both theoretical and engineering fields.