周期新型超材料板多阶弯曲波带隙研究

Multi-flexural wave band gaps of a new periodic metamaterial plate

利用了声子晶体带隙性质的概念,结合局域共振原理,提出了一种新型周期超材料板结构。这种结构是由具有负等效模量的声学超材料子结构作为共振单元,周期排列在薄板上形成的。在共振单元的作用下,不仅在低频范围内产生带阻特性,还引起了部分弯曲波发生波型转换并产生相应的多阶带隙,使得在多个频段范围内阻断波的传播,扩大了抑制振动传递的频率范围。利用平面波展开方法分析了结构的弯曲波带隙,并且和有限元方法得到结果进行比较,得到了一致的频散关系。对有限超材料板的振动传递损失也进行了分析,数值计算结果证明了所求频散关系的正确性以及本文提出的隔振结构对振动衰减的有效性。除此之外,研究了局域共振单元的参数和单胞尺寸对结构带隙性质产生的影响,为选取合适的参数满足特定隔振要求(低频,宽带等)的超材料板结构提供了参考依据。

A new periodic metamaterial plate was proposed based on the concept of the phononic crystal and local resonance mechanism. The proposed structure consists of negative modulus acoustic metamaterial microstructures acting as local resonators. The structure not only exhibits low frequency stop band characteristics,but also provides multi-flexural band gaps,and leads to the transformation of partially flexural waves. Since no wave energy propagation is allowable in the multi-frequency domain,the frequency domain for vibration transmission mitigation in the structure is broadened. The dispersion relation was acquired by using the plane wave expansion method. A comparison between the results obtained by the plane wave expansion and finite element method was presented and a good correspondence between the results of both methods was found. The vibration transmission loss of a finite metamaterial plate was calculated to validate the band gap,demonstrating the efficiency of the vibration isolation. Moreover,a parametric study was implemented to investigate the effects of parameters of the local resonators and unit cell on the band gap property,which makes it possible to satisfy the specific requirements（ low frequency,wide band gap,etc） of metamaterial plates for vibration isolation.