Wei Wenming, Chronopoulos Dimitrios, Meng Han
State Key Laboratory for Manufacturing Systems Engineering, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Department of Mechanical Engineering & Division of Mechatronic System Dynamics (LMSD), KU Leuven, Ghent Technology Campus, 9000 Gent, Belgium.
Materials (Basel). 2021 Aug 24;14(17):4759. doi: 10.3390/ma14174759.
This paper investigates the influences of nonperiodic rainbow resonators on the vibration attenuation of two-dimensional metamaterial plates. Rainbow metamaterial plates composed of thin host plates and nonperiodic stepped resonators are considered and compared with periodic metamaterial plates. The metamaterial plates are modelled with the finite element modelling method and verified by the plane wave expansion method. It was found that the rainbow metamaterial plates with spatially varying resonators possess broader vibration attenuation bands than the periodic metamaterial plate with the same host plates and total mass. The extension of attenuation bands was found not to be attributed to the extended bandgaps for the two-dimensional metamaterial plates, as is generally believed for a one-dimensional metamaterial beam. The complete local resonance bandgap of the metamaterial plates is separated to discrete bandgaps by the modes of nonperiodic resonators. Although the additional modes stop the formation of integrated bandgaps, the vibration of the plate is much smaller than that of resonators at these modal frequencies, the rainbow metamaterial plates could have a distinct vibration attenuation at these modal frequencies and achieve broader integrated attenuation bands as a result. The present paper could offer a new idea for the development of plate structures with broadband vibration attenuation by introducing non-periodicity.
本文研究了非周期彩虹谐振器对二维超材料板振动衰减的影响。考虑了由薄主体板和非周期阶梯谐振器组成的彩虹超材料板，并与周期超材料板进行了比较。采用有限元建模方法对超材料板进行建模，并通过平面波展开法进行验证。研究发现，具有空间变化谐振器的彩虹超材料板比具有相同主体板和总质量的周期超材料板具有更宽的振动衰减带。衰减带的扩展并非如通常认为的一维超材料梁那样归因于二维超材料板的扩展带隙。超材料板的完整局部共振带隙被非周期谐振器的模式分隔成离散带隙。尽管额外的模式阻止了完整带隙的形成，但在这些模态频率下板的振动比谐振器的振动小得多，因此彩虹超材料板在这些模态频率下可能具有明显的振动衰减，并实现更宽的完整衰减带。本文通过引入非周期性，可为开发具有宽带振动衰减的板结构提供新思路。
