Study of three-dimensional elastic metamaterials based on a lattice system

In this paper, a three dimensional (3D) mass-in-mass lattice system is proposed to understand how elastic waves propagate through 3D metamaterials. In our model, we included spring elements that protrude in all three dimensions, along with spring elements protruding in only one or two dimensions to properly analyze the system’s elastic properties. Due to the dispersion equation containing four variables, it must be graphed in three different perspectives to produce plots in which the stop bands’ values can be interpreted with ease. In essence, the stop bands are produced by aligning the graphed structure along each orthogonal plane. By modifying the spring elements’ constants, each of the stop bands can be shifted into higher or lower frequency ranges independent of each other, theoretically providing complete control over how a wave propagates through the metamaterial. From this, real world applications can be developed such as absorbing elastic waves in undesired directions, focusing elastic waves to specific points, guiding waves along complicated paths, and creating elastic superlenses.