Elastic Metamaterial Design to Filter Harmonic Mechanical Wave Propagation

Abstract

The metamaterial concept was first oriented to electromagnetic field applications and the main objectives were to develop materials with peculiar properties such as negative dielectric constant, negative magnetic permeability and negative refraction index. Gradually, other areas started using parameters that do not exist in the materials found in nature and, classifying them as metamaterials. So, areas such as acoustics, optics and mechanics opened up space for applications of this innovative “material”. Many efforts for an adequate modeling were made searching also for all kinds of possible applications. One example of application in optics is the use of conformal transformation to design devices with new functionalities from non-homogeneous isotropic dielectric media. The mirages created in the desert are the result of these non-homogeneities. These studies are supposed being helpful to develop invisible cloaks using metamaterials. The present work deals with elastic metamaterial application in mechanical engineering. It is well knowing that metamaterials are able to filter harmonic wave propagation and many works present this capability caused by a bandgap that appears in some range of frequency due to the system’s features. However, it is not very clear how the parameters used for the metamaterials design should be defined. The purpose of this work is to propose a methodology to design an optimized metamaterial component to filter the mechanical wave propagation in a finite chain of masses. It is also in the scope of this work to analyze the borders of the bandgap of the studied chain of masses and how the propagated wave is attenuated along this region.