Broadband Frequency and Spatial On-Demand Tailoring of Topological Wave Propagation Harnessing Piezoelectric Metamaterials

Abstract

Many engineering applications leverage metamaterials to achieve elastic wave control. To enhance the performance and expand the functionalities of elastic waveguides, the concepts of electronic transport in topological insulators have been applied to elastic metamaterials. Initial studies showed that topologically protected elastic wave transmission in mechanical metamaterials could be realized that is immune to backscattering and undesired localization in the presence of defects or disorder. Recent studies have developed tunable topological elastic metamaterials to maximize performance in the presence of varying external conditions, adapt to changing operating requirements, and enable new functionalities such as a programmable wave path. However, a challenge remains to achieve a tunable topological metamaterial that is comprehensively adaptable in both the frequency and spatial domains and is effective over a broad frequency bandwidth that includes a subwavelength regime. To advance the state of the art, this research presents a piezoelectric metamaterial with the capability to concurrently tailor the frequency, path, and mode shape of topological waves using resonant circuitry. In the research presented in this manuscript, the plane wave expansion method is used to detect a frequency tunable subwavelength Dirac point in the band structure of the periodic unit cell and discover an operating region over which topological wave propagation can exist. Dispersion analyses for a finite strip illuminate how circuit parameters can be utilized to adjust mode shapes corresponding to topological edge states. A further evaluation provides insight into how increased electromechanical coupling and lattice reconfiguration can be exploited to enhance the frequency range for topological wave propagation, increase achievable mode localization, and attain additional edge states. Topological guided wave propagation that is subwavelength in nature and adaptive in path, localization, and frequency is illustrated in numerical simulations of thin plate structures. Outcomes from the presented work indicate that the easily integrable and comprehensively tunable proposed metamaterial could be employed in applications requiring a multitude of functions over a broad frequency bandwidth.