Bloch waves in a periodic dispersive acoustic metamaterial

Abstract

The propagation of mechanical and electromagnetic waves in structures with spatial periodicity has become a relevant field, especially when scientific, technological and innovation aspects are considered. Although the behavior of physical phenomena associated with periodic structures has been consolidated over the last few years, the acoustic case is still a poorly explored field of study and in this sense it is necessary. In this work, we investigate some phenomena underlying the behavior of Bloch waves in a dispersive periodic acoustic metamaterial. The mathematical formalism of the transfer matrix considering the viscothermal losses combined with the onedimensional Bloch-Floquet theorem are adopted and are shown to be sufficiently accurate to describe and extract the characteristics of the periodic structure. Concepts such as sound dispersion, phase velocity and forbidden frequency bands (bandgap) are addressed, and their respective behaviors are supported by experimental results. In addition, a strategy for establishing the location and dimension of these bandgaps is presented. Finally, this study enables a discussion in the field of wave physics, particularly in the behavior of dissipative sound waves that propagate in periodic structures.

Keywords
Acoustic metamaterial; Dispersion relation; Phase velocity; Bloch waves