新型环状谐振径向弹性超材料结构低频带隙机理研究

Low-Frequency Band Gap Mechanism of Radial Elastic Metamaterial with New Ring Resonance

针对具有低频减振带隙的径向弹性超材料结构不易加工,且不能满足工业需求的问题,提出了一种由单一材料构成的新型环状谐振径向弹性超材料结构。相比传统径向弹性超材料结构,这种新型结构由外部八边形以及内部结构通过连接块相连接而构成。有限元计算结果表明,其能带结构图中存在的两个完全带隙与有限周期结构的频响函数曲线中带隙吻合,其中第一带隙位于2171.9~2716.9Hz之间,第二带隙位于4747.5~9067.5Hz之间。通过分析带隙边界处特殊点的本征位移场,可知第一与第二带隙分别是由于内部结构和八边形基体的局域共振所形成。进一步研究了结构参数对带隙位置和带隙宽度的影响,结果表明内部结构半径与连接块宽度参数会影响内部结构的质量以及连接块的等效刚度,进而影响所有带隙的变化,而八边形基体宽度仅对高频带隙影响较大。本研究中径向弹性超材料结构所产生的低频带隙对于工业设备有潜在的应用。

In this paper,theoretical investigation of the new type of ring resonance radial elastic metamaterial plate structure is conducted,which aims at the problem that the radial elastic metamaterial structure with low-frequency vibration damping band gap is not easy to process and cannot meet industrial needs.In contrast to the traditional structure,the proposed new structure is created by an external octagon and an internal structure connected by connecting blocks.Finite element calculation results show that the two complete band gaps in the dispersion relations coincide with the band gap in the transmission spectra of the finite period structure,in which the first band gap is 2171.9-2716.9 Hz and the second band gap is 4747.5-9067.5 Hz.By analyzing the intrinsic displacement field of special points at the band gap boundary the formation mechanism of first and second band gap is attributed to the internal structure and local resonance of octagonal matrix.Furthermore,the effects of the geometrical parameters on the band gaps are further explored numerically.Results show that the internal structure radius and connection block width geometrical parameters will affect the quality of the internal structure and the equivalent rigidity of the connection block,and thus affect all changes in the band gap,while the width of the octagonal matrix only has a large effect on the high frequency band gap.These characteristics of band gap in the proposed radial elastic metamateria can potentially be applied to industrial equipment.