Low frequency topologically protected wave transport in sinusoidal lightweight acoustic metamaterials

Topological phononic crystals and acoustic metamaterials have attracted enormous research attention in recent years due to the presence of robust and disorder-immune wave propagation. In this study, a sinusoidal lightweight elastic topological insulator with protected interface modes is investigated at a subwavelength frequency region. By a wave dispersion study, the dual Dirac cones are observed at a subwavelength frequency region due to the employment of two distinct cylinders connected with sinusoidal ligaments. Both cylindrical masses and sinusoidal ligaments are found responsible for opening low-frequency bandgaps that manipulate elastic wave wavelengths almost 30 times larger than the lattice size. Consequently, the subwavelength bandgap closing-and-reopening phenomenon with phase transitions is further captured and opposite signs of the valley Chern numbers are obtained for different structural parameters. A supercell structure is constructed based on the phase transition, and dual topologically protected interface modes (TPIMs) are captured with different quality factors. The comparison of topologically protected interface modes shows that TPIM I is in a higher and wider frequency range, while TPIM II is positioned in a comparatively narrow and extremely low-frequency range. Finally, the robust elastic wave propagation along various designated paths is demonstrated. The proposed lightweight topologically protected phononic lattice may spark future investigation of topological edge states in metadevices at a subwavelength frequency region.