Tunable in-plane topologically protected edge waves in continuum Kagome lattices

Abstract

In this paper, we report the evidence of topologically protected edge waves (TPEWs) in continuum Kagome lattice. According to the bulk edge correspondence principle, such edge states are inherently linked with the topological characteristics of the material band structure and can, therefore, be predicted evaluating the associated topological invariant. Due to the non-trivial band structures shown in the context of quantum valley Hall effect, TPEWs are supported at the interface between two lattices characterized by different valley Chern numbers. The break of lattice symmetry is obtained here, in contrast with other similar works in continuum elastic structures, biasing in the stiffness properties of the unit cell, instead of manipulating mass at sublattice points. This opens new promising possibilities related to waveguide tunability and wave propagation control, exploiting the established techniques for stiffness modulation in elastic structures. A sensitivity analysis of robustness of the supported energy transport is provided, showing the amount of de-localized disorder the waveguide is immune to, and how performances are affected by perturbations in the nominal parameters of the lattice.

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

“…It was found that the topological frequency range was broadened by applying an external electrical field. Riva et al [44] utilized the negative capacitance shunt circuit to adjust the working frequency and control the propagation path of elastic waves. However, these topological effects have only been observed in high-frequency wave modes.…”

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

“…To extend beyond the functionalities available in fixed structures and enable adaptivity to varying operating requirements and external conditions, many recent investigations have focused on introducing tunability to topological metamaterials. The spatial path of topological wave propagation has been demonstrated to be adjustable by applying an external magnetic field (Zhang et al, 2019), modifying mechanical boundary conditions (Darabi and Leamy, 2019;Tang et al, 2019), adding an elastic foundation (Al Ba'ba'a et al, 2020), connecting negative capacitance piezoelectric circuitry (Riva et al, 2018;Darabi et al, 2020), or switching stable states in bistable elements (Wu et al, 2018). The shape and localization of topological edge states have been tuned by exploiting an applied strain field (Liu and Semperlotti, 2018).…”

Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

“…The finite structure is constructed from merging two square AIMs with different μ signs and fixed boundaries with an interface formed from m1 masses (figure 8 a ). Performing standard eigenfrequency analyses of a supercell with an interface reveals a gapless edge state inside the bulk bandgap, as can be predicted from the bulk-correspondence principle [36] (figure 8 b ). This is also inferred from the natural frequencies of the entire structure, as shown in figure 8 b .…”

“…For small values of μ and in line with traditional QVHE systems [34–37], a quantized Cv is achieved and reads Cv±=±12τ boldsgnfalse[μfalse]. One important use of such a topological invariant is to predict the number of topological edge modes at an interface stitching two topologically distinct lattices. Such a number of topological modes can be simply calculated as the absolute difference of the valley Chern number |Cv+−Cv−|=1 [36]. While a theoretical Chern number of ±1/2 provides an excellent measure of the number of such topological modes, the actual value for such a metric deviates from its 1/2 quantization as perturbation becomes stronger, i.e.…”