Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Abstract

Elastic wave propagation characteristics of elastic metamaterial plates embedded scatterer with various lattices are explored numerically and experimentally in this study, for the attenuation of in-plane longitudinal and out-of-plane flexural waves in the subwavelength frequency region. Firstly, the mathematical models of the elastic metamaterial plates are established, and the dispersion relations are derived by the plane wave expansion (PWE) method based on Bloch's theorem. Furthermore, the applicability of the irreducible Brillouin zone (IBZ) for different lattices is also investigated through iso-frequency contours. The analysis of the bandgap formation mechanism indicates that the proposed metamaterial plates can enlarge the bandgaps (BGs) in the low-frequency range by coupling Bragg and local resonance BGs. Moreover, the influences of the scatterer shapes, geometric and material parameters on the BGs are investigated, and which combination of parameters has positive significance for opening low-frequency broadband is also discussed. The results show that the vibration transmittance obtained by experiment and numerical calculation is in good agreement with the predicted results of band structures. Therefore, the elastic metamaterial plates should be promising in the application of low-frequency wave mitigation.