考虑流体作用的超弹性结构的自由振动

The aim of this project is to conduct an in-depth study of the coupled free vibrations of hyperelastic structures that are interacting with fluid media. For small-amplitude vibration superimposed on finite deformations, based on the general nonlinear theory of elasticity, by virtue of the perturbation analysis, a series of theoretically important three-dimensional analytical solutions will be pursued for some isotropic hyperelastic structures with simple geometry interacting with Newtonian fluids. The study is then further broadened by considering the effects of material inhomogeneity and anisotropy, multi-field coupling, viscoelasticity, and non-Newtonian fluids, to help form a relatively systematic and complete three-dimensional analysis of the coupled vibrations of hyperelastic structures. Then, for typical two-dimensional structures such as membranes, plates and shells, high-precise simplifying structural theories will be developed by introducing appropriate assumptions on or directly determining the thickness distributions of stresses and displacements in consideration of the effect of fluid. These simplifying theories are employed to derive approximate analytical solutions of the coupled vibrations of hyperelastic structures. The aforementioned complicate factors will also be incorporated into the approximate analysis. Finally, numerical simulations and experiments will be conducted for the purpose of validation and verification. Through this project, we intend to elucidate the effects of finite biasing field, material inhomogeneity and anisotropy, multi-field coupling, viscoelasticity, and non-Newtonian fluid on the coupled vibrations of hyperelastic structures, to explore the effective approaches to tuning their dynamic responses, and eventually to provide a solid basis for the design, optimization and control of soft robotics and flexible devices.

本项目拟深入研究流体环境下超弹性材料结构的耦合自由振动。针对叠加于有限变形之上的小幅线性振动，首先基于最一般的三维非线性弹性理论，结合摄动分析，考虑具有简单形状的各向同性超弹性结构与牛顿流体的相互作用，获得一批有重要理论价值的三维解析解。然后将研究范畴拓宽至非均匀、各向异性、多场耦合、粘弹性以及非牛顿流体，形成较系统完整的超弹性结构流固耦合振动的三维解析研究体系。其次，针对膜、板、壳等典型的二维结构，考虑流体的影响，针对性地引进或确定位移和应力分布假设，建立高精度的简化结构理论，并逐步将上述多种复杂因素纳入到简化模型之中。最后，拟结合数值模拟和实验测试开展一定的比对与修正研究。通过本项目的研究，将厘清有限偏场、材料非均匀、各向异性、多场耦合、粘弹性、非牛顿流体等因素对超弹性结构流固耦合振动特性的影响，并探索有效的动力学调控方法，从而为软机器和柔性器件的设计、优化与控制提供依据。

超弹性结构与流体的相互作用因其明显的生物医学背景得到了学术界的关注，但其中大多数研究集中于超弹性胶囊。本项目从固体力学的角度深入研究周围流体对超弹性材料结构自由振动的影响，主要考察叠加于有限变形（偏场）之上的小幅线性振动。项目在超弹性结构（包括考虑力电耦合效应）自由振动的三维分析、板壳结构的二维简化建模分析、复杂流体作用解析与典型结构的耦合振动、软弹性周期结构中的波动行为、结构拓扑优化新方法及其应用等方面取得了良好进展，在JMPS、JFM、IJSS、IJMS、JSV等著名期刊上共发表论文36篇，其中SCI收录（或SCI源期刊）论文35篇（含2篇综述论文，分别发表于IJSNM和IJMS）、EI收录论文1篇（综述论文，发表于《力学学报》），获得国家发明专利授权和新型实用专利授权各3项，培养毕业博士生9名、硕士生4名，获中国力学学会优秀博士学位论文奖1篇和提名奖2篇，获2019年度高等学校科学研究优秀成果奖（自然科学奖）二等奖、2021年度浙江省科技进步奖二等奖和2022年度江苏省科学技术奖一等奖各1项，获2022 Lloyd Hamilton Donnell Applied Mechanics Reviews Paper Award 1项。