Multiband Pure Topological States in Elastic Structures

Abstract

Inspired by notions of topological physics, recent years have witnessed the rapid development of mechanical metamaterials with novel properties of topological states. However, most of the current investigations have either focused on discrete mass-spring lattices, with topological states limited to a single operating band, or on various elaborate continuous elastic systems, enduring the drawbacks of modal couplings. It remains largely unexplored how to design topological elastic systems that naturally possess multiple operating bands and are free from modal couplings. In this study, we design an elastic system based on fundamental mechanical elements (beams, rods and nuts), which is capable of supporting multiband pure topological states. Through an equivalent beam-spring model with lumped masses together with finite element analysis, we demonstrate that our proposed structure exhibits multiple Dirac points (DPs) at different frequencies. We show that simply adjusting the heights of nuts fastened on beams can lift the degeneracies, giving rise to two kinds of valley Hall phases characterized by opposite valley Chern numbers. The dispersion diagram of the supercell formed by unit cells with different topological indices shows that there simultaneously exist perfectly pure interface modes (i.e., no other modes coexist) within two frequency ranges. Furthermore, numerical simulations demonstrate that the domain wall formed by structures with distinct topological properties supports topologically protected interface waves over dual frequency ranges. Our results have potential for the design of mechanical systems that need to work under changeable working frequencies and may have significant impact on many diverse fields such as vibration control, energy harvesting and seismic isolation.