力学超材料带隙调控的胞元折叠方法及带隙变化规律  

Cell folding method and band gap variation analysis for band gap control in mechanical metamaterials

作　　者：裘江海 杨德庆[1,2] 张栗铭 QIU Jianghai;YANG Deqing;ZHANG Liming(State Key Laboratory of Ocean Engineering,School of Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Yazhou Bay Institute of Deepsea Science and Technology,Shanghai Jiao Tong University,Sanya 572024,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院海洋工程国家重点实验室,上海200240 [2]上海交通大学三亚崖州湾深海科技研究院,海南三亚572024

出　　处：《振动与冲击》2025年第2期104-111,共8页Journal of Vibration and Shock

摘　　要：针对减振用的负泊松比力学超材料,提出了基于XOY平面胞元的Z轴维度折叠的带隙调控方法。基于三维折叠胞元的带隙计算方法及对应的三维Bloch-Floquet周期性边界条件,应用有限元法对三类负泊松比超材料构型(箭形、星形和内六角形)的能带曲线与样件的振级落差进行数值计算,并从振动模态角度分析了这类力学超材料的带隙变化原因。不同能带曲线对折叠角度的敏感性体现在胞元对应振动模态的局部刚度上,刚度变化可以产生或消灭带隙。研究表明,将胞元折叠的带隙调控方式应用于三类超材料胞元后,其能带结构均表现出相似的带隙演变规律,通过折叠角度控制胞元的几何形状可以调控能带曲线的移动。在特定折叠角度下超材料的能带结构中可以产生新的方向带隙,原有方向带隙也会消失。以箭形胞元为例,制作了超材料样件,通过扫频试验验证了数值计算结果和带隙变化规律的准确性,其能带结构中第一条方向带隙由3 989.2~4 204.4 Hz变为3 843.4~4 176.5 Hz。A bandgap control method based on XOY plane cell element Z-axis dimension folding was proposed for negative Poisson’s ratio mechanical metamaterials used in vibration reduction.Based on the three-dimensional folded cell element method and corresponding three-dimensional Bloch-Floquet periodic boundary conditions,the finite element method was applied to numerically calculate the band curves of three types of negative Poisson’s ratio metamaterials(arrow shaped,star shaped,and inner hexagonal)and the vibration level drop of the samples.The reasons for the band gap changes of these mechanical metamaterials were analyzed from the perspective of vibration modes.The study shows that the sensitivity of different band curves to folding angles is reflected in the local stiffness of the corresponding vibration modes of the cell,and stiffness changes can generate or eliminate band gaps.When the cell folding method for bandgap control is applied to three types of metamaterial cells,their band structures all exhibit similar band gap evolution patterns.By controlling the geometric shape of the cells through folding angle,the movement of the band curve can be controlled.Under specific folding angles,new directional band gaps can be generated in the band structure of the metamaterials,and the original directional band gaps will also disappear.Taking the arrow shaped cell as an example,a metamaterial sample was made,and the accuracy of the numerical calculation results and the band gap variation were verified through frequency sweep experiments.The first directional band gap in the energy band structure changes from 3989.2-4204.4 Hz to 3843.4-4176.5 Hz.

关 键 词：超材料 负泊松比 带隙调控 折叠胞元 三维带隙计算 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3