Low-frequency and multiband elastic wave propagation in a 3D topological metamaterial

Elastic metamaterials that are engineered with topological phases contain waveguides that are protected from unwanted scattering in the presence of imperfections, enabling robust and omnidirectional control of elastic wave propagation. Recently, three-dimensional (3D) topological elastic metamaterials have been developed that support waveguides with planar and layer-selective transport behavior. These 3D topological elastic metamaterials operate in a singular frequency band that is often in the ultrasonic regime (>20 kHz). Thus, an unexplored opportunity exists to explore 3D topological elastic metamaterials that operate in multiple frequency bands in a low-frequency range (<20 kHz). To address this gap, this research proposes to advance the state of the art through the synthesis of a subwavelength 3D topological elastic metamaterial that harnesses multi-modal local resonance for multiband wave control. The novel 3D metamaterial is configured to obtain multiple low-frequency Dirac degeneracies by exploiting local resonance and the elastic analog of the quantum valley Hall effect. Theoretical and experimental findings reveal topological surface states with various polarizations in multiple low-frequency bands. The 3D metamaterial created in this study could serve as a macro-scale platform to explore novel multiband and subwavelength topological transport phenomena, while the research findings open a path to new frequency- and polarization-dependent wave control capabilities.