可重构力学超材料的设计与波动特性研究  

DESIGN AND WAVE PROPERTIES OF RECONFIGURABLE MECHANICAL METAMATERIALS

作　　者：肖伯雅 杨洮 冯亚菲 刘宇[1,2] 徐文帅 陈猛[1,2] 姜恒 王育人[1,2] Xiao Boya;Yang Tao;Feng Yafei;Liu Yu;Xu Wenshuai;Chen Meng;Jiang Heng;Wang Yuren(NML,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China;School of Engineering Science,Chinese Academy of Sciences,Beijing 100049,China;Unit 92228,People's Liberation Army of China,Beijing 100072,China)

机构地区：[1]中国科学院力学研究所微重力实验室,北京100190 [2]中国科学院大学工程科学学院,北京100049 [3]中国人民解放军92228部队,北京100072

出　　处：《力学学报》2022年第10期2708-2716,I0002,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金项目(11972034,11802213);中国科学院战略重点研究项目(XDB2204301);中国科学院青年创新促进会(2020018)资助。

摘　　要：力学超材料中的弯曲梁双稳态结构由于其主动调控性强且调控精度高等优点近年来受到广泛关注.文章利用中心受压弯曲梁的不稳定性设计了六角型双稳态结构,首先建立了等效弯曲梁模型,基于梁变形微分方程及能量最低原理探明了结构双稳态特性的产生基理,之后利用有限元数值计算研究了结构几何参数对其整体力学性能的影响,分别得到了具备自恢复及双稳态性能的结构几何参数范围,绘制了几何参数与力学性能之间的相图.同时,可重构结构的可控变形能力有助于调整整体的色散特性,利用数值仿真研究了具备双稳态特性的结构在拉伸和压缩两种构型下的色散关系,对比分析了不同结构几何参数及构型转变对结构产生的带隙位置及范围的影响,之后对由不同构型单胞组成的周期性结构进行了频响分析来验证带隙计算的准确性.通过六角型可重构结构的力学特性、色散特性研究及频响分析表明可以通过结构几何参数的设计实现对结构整体性能的主动调控,为可逆向设计的弹性波超材料结构研究分析提供了一条可靠路径.The bending beam bistable structure in mechanical metamaterials has attracted extensive attention in recent years due to its strong active control and high control accuracy. In this paper, a hexagonal bistable structure is designed by using the instability of the centrally compressed bending beam. Firstly, the equivalent bending beam model is established and the basic principle of the bistability of the structure is proved based on the differential equation of beam deformation and the principle of minimum energy. Then, the influence of structural geometric parameters on its mechanical properties is studied by finite element numerical calculation. The range of structural geometric parameters with self recovery and bistable properties is obtained respectively, and the phase diagram between geometric parameters and mechanical properties is drawn. At the same time, the controllable deformation ability of the reconfigurable structure helps to adjust the dispersion characteristics, numerical simulation is used to study the dispersion relationship of the structure with bistable characteristics under the two configurations of tension and compression, and the effects of different structural geometric parameters and configuration changes on the band gap position and range of the structure are compared and analyzed. After that, the frequency response analysis of the periodic structure composed of different configuration cells is carried out to verify the accuracy of the band gap calculation. In conclusion, the mechanical properties, dispersion properties and frequency response analysis of the hexagonal reconfigurable structure show that the overall performance of the structure can be actively controlled through the design of the geometric parameters of the structure, which provides a reliable path for the research and analysis of the elastic wave metamaterial structure with reversible design.

关 键 词：力学超材料 双稳态 色散 带隙 主动调控 

分 类 号：O327[理学—一般力学与力学基础]