Experimental observation of transverse and longitudinal wave propagation in a metamaterial periodically arrayed with nonlinear resonators

Elastic wave propagation in solids composed of elastic metamaterials always exists as both transverse and longitudinal waves simultaneously. By using the Hamilton principle, Bloch theorem, and finite-element method, an approach is proposed to explore the band energy structures of the metamaterial, this is observed in an experiment on an ultralow frequency metamaterial periodically positioned nonlinear resonators and this means the broadband isolation of both longitudinal and transverse waves was verified. Comparison of the propagation of transverse and longitudinal waves in the ultralow frequency metamaterials, the Bragg band-gaps (BBGs) and local resonance band-gaps (LRBGs) differ with both the frequency of the bandwidth and the depth of the band-gap.