Manipulating Elastic Waves in Topological Mechanical Metamaterials

Abstract

Due to the recent discovery of topological insulators in condensed matter physics, a new notion of topology has emerged in association with the intrinsic dispersion behavior of a structure. In this work, we have taken this notion of topology and have shown some novel wave manipulation capabilities in one- and two-dimensional (1D and 2D) elastic systems. In particular, we have taken four different type of elastic systems. First, a 1D elastic system made of a highly tunable chain of granular particles, in which we analytically, numerically, and experimentally demonstrate an in situ topological band transition and existence of a topologically-protected vibration mode. Second, we take a 1D time-dependent system made of a granular chain, in which nonreciprocal wave dynamics is invoked. Using numerical simulations, we show that this nonreciprocity can be quantified by a topological invariant of 2D, i.e., Chern number. Third, we consider a 2D discrete lattice consisting of units inspired by the Stewart platform. By harnessing the bistability of the unit, we show the capability of in situ manipulation of wave path in this tunable 2D topological structure. We also demonstrate the uniqueness of topological waveguides in comparison to conventional (nontopological) waveguides in this platform. Lastly, we propose a continuum structure, i.e., a thin plate, with systematically arranged local resonators on its top. We show numerically that by judiciously arranging the local resonators, we can create a subwavelength topological waveguide in the system, which can robustly guide flexural waves along a path with sharp bends. In principle, this is analogous to the quantum spin Hall effect discovered in condensed matter physics. We employ a ubiquitous design of a bolted plate to experimentally demonstrate waveguiding capability of this plate. These results show that the new notion of topology -- emerging from topological insulators in electronic and optical systems -- can provide a fresh outlook towards manipulating elastic waves in mechanical structures, such as directional propagation, filtering, and localization of wave modes. These novel effects investigated in this study can be exploited for engineering applications such as impact mitigation, vibration isolation, smart sensing, and energy harvesting.