基于数值延拓方法的自振荡凝胶周期调控

Self-oscillating gel period regulation based on numerical continuation method

自振荡凝胶是一类由自振荡反应驱动的高分子形变聚合物,其无需外界刺激就会自发地形成周期性的形变,广泛运用于仿生蠕动机器人的研究。自振荡凝胶的化学-力学耦合关系一直是研究的重点,本文基于Ru(bpy)3催化IPAAm(N-isopropylacrylamide)高分子凝胶的力学特征及BZ(Belousov-Zhabotinsky)反应的三维Oregonator模型构造自振荡凝胶的化学-力学耦合动态模型,并构建数值延拓算法分析自振荡凝胶周期性随反应参数和力学参数变化情况。通过本文构建的微分-代数方程组数值延拓方法,可以有效求解自振荡凝胶的极限环,为自振荡凝胶周期调控提供设计基础。

Self-oscillating gels are a class of deformable polymers driven by self-oscillating reactions,which can generate periodic deformation without any external stimulation,and are widely used in the research of biomimetic creeping robots.The chemical-mechanical relation of self-oscillating gels has always been the focus of research.In this paper,based on the mechanical properties of Ru(bpy)3-catalyzed N-isopropylacrylamide(IPAAm)polymer gels and the 3-dimensional Oregonator model of the Belousov-Zhabotinsky reaction,the chemical-mechanical coupling model of the gel was established,and a numerical continuation algorithm was constructed,by which the variation of the self-oscillating gel periodicity with varying parameters is studied.Through the numerical continuation method of differential-algebraic equations constructed in this paper,the limit cycle of self-oscillating gels can be effectively determined,which provides a design basis for the period control of self-oscillating gels.