The maths of a photo induced hydrogel swimming robot: nonsmooth forcing dynamics

主讲人：宣辰 西交利物浦大学副教授

时间：2024年4月7日9：30

地点：三号楼332室

举办单位：数理学院

主讲人介绍：宣辰，西交利物浦大学副教授，荷兰乌得勒支大学的客座教授。主要从事多物理场下连续体的本构理论，固体应力诱导相变，智能材料力学和软体机器人等领域的研究，在相关课题上取得了重要研究成果，目前已在 American Physical Society, International Liquid Crystal Elastomer Conference, British Liquid Crystal Society, ICTAM等国际重要学术期刊上发表论文多篇。

内容介绍：Certain hydrogel is light sensitive, since light provides heat and hydrogel shrinks under high temperature thus making the hydrogel photosensitive. When light shines on the hydrogel, the hydrogel shrinks and as light propagates through the hydrogel shrinks less thus bending towards the light. This hydrogel beam undergoes a vibration, governed by a wave PDE with a second derivative in time and 4th derivative in space coupled with a diffusion equation, a result of a competition between the elasticity of the beam and the photo induced bending. This photo induced vibration enables the hydrogel beam to swim in water. Based on dimensional energy analysis, we determine the stable vibration amplitude and construct phase diagrams for the increase and decrease of the oscillation amplitude, which are further confirmed experimentally. It is found that resonance can occur and damping plays an important role in determining the conditions for resonance. A mass-spring-damper ODE system subjected to a displacement dependent excitation force is developed to investigate the features in generalized self-excited oscillating systems. The prototypical PDEs can be well understood by the above simplified ODE model. This work lays a solid foundation for understanding self-excited oscillation and provides design guidelines for self-sustainable soft robots. It also puts forth another interesting question of whether chaos is involved in future work.