Complex dispersion analysis of viscoelastic effects on elastic waves in three-dimensional single-phase metamaterials

Abstract In this paper, we study the propagation of elastic waves in three-dimensional single-phase metamaterials using the finite element method. Both elastic and viscoelastic scenarios are considered, where the Kelvin-Voigt model is used to describe the solid material viscosity. We explore the influence of material viscosity on the complex band diagrams and the transmission spectra in detail. It is found that the single-phase metamaterials support both the Bragg scattering and locally resonant band gaps. When a small viscosity is introduced, the wave attenuation within the locally resonant band gaps degrades. However, such a small viscosity has negligible effects on the Bragg scattering band gaps. As the material viscosity increases, the wave attenuation is mainly ascribed to the material viscosity rather than the band gap effects. Additionally, the attenuation behavior of evanescent waves can be accurately predicted from the imaginary part of wave vectors identified in the complex band structures. This work provides a reference for the practical applications of viscoelastic metamaterials.