Inertial amplified topological metamaterial beams

Abstract

To break the limitation of large mass required for low-frequency topologically protected interface modes (TPIMs), a novel inertial amplified topological metamaterial beam is proposed in this work. Detailed analytical and numerical studies are conducted to investigate the dynamic characteristic of this system. The Dirac cone (DC) is formed at the boundary of the Brillouin zone through the zone-folding method. Thanks to the inertial amplification mechanism, the lower-frequency DC and wider local resonance bandgaps (LRBGs) are obtained without sacrificing total stiffness or increasing total mass. Besides, the DC and LRBG can be tuned effectively by the arm length ratio of the lever. In order to realize the TPIM, two topologically distinct supercells are constructed by space modulation of resonators. Transmission simulation confirms the existence of TPIM between two domains with different topological properties. The energy concentration of TPIM is quantified by the quality factor. Moreover, the tunability and robustness of TPIM are also verified. Besides, to further enlarge the response area of TPIM, the sandwich structure is proposed. Although the peak displacement is reduced with the enlargement of response area, the displacement is still well confined within the sandwich layers. This novel inertial amplified topological metamaterial beam is expected to promote the application of topological devices, especially in the low-frequency lightweight challenging conditions.