Demonstration of Topological Boundary States in Mechanical Metamaterials

Abstract

In the past few decades, using metamaterials to control energy flow was a popular topic and attracted lots of researchers to devote to this field. Indeed, metamaterial has been shown that it is a potential avenue to tailor the wave propagation; however, how to guide the energy through desired paths with minimum energy loss via metamaterials had remained a challenge until the discovery of topological insulators. Topological insulator, in short, is a material that behaves like an insulator in the interior; whereas, the outer surface acts like a conductor and the flow of electrons can transport freely without backscattering. The non-trivial property was first discovered in condensed matter physics and it can be interpreted by topological invariant predicted from band structures. Recently, experimental demonstrations of the topological insulators have successfully shown that the waves are highly immune to the backscattering. It grows researchers' attentions because it overcomes the disadvantage (energy dissipation due to the backscattering) from the traditional technique in the wave control. The conception of topology opens a new direction for guiding waves. In light of that, we try to implement and realize the topological idea in the mechanical regime. Specifically, we target the thin plate structure and we focus on the most dominating motions in the thin plate, i.e., flexural waves. The goal is to provide a design principle that allows us to empower the waves in an artificial structure immune to back-scattering. Furthermore, we have freedom for controlling the topological waves to be localized at the desired location of the plate structure. In this dissertation, we select the bolted plate structure as the tabletop device to numerically and experimentally demonstrate three types of topological boundary modes (one-dimensional edge mode, zero-dimensional bound state, and zero-dimensional corner mode) through different mechanisms (mechanical analogue of quantum spin Hall effect, mechanical version of Majorana-like mode, and mechanical counterpart of second-order topological insulators). In conclusion, all results suggest that the revolutionary topological design benefits the wave dynamics field and makes huge improvements towards applications such as directional wave propagation, energy harvesting, vibration isolation, or signal processing. The findings in this dissertation shed the light on the advanced control of wave propagation.