We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and twodimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media with different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.
We report on the experimental observation of topologically protected edge
waves in a two-dimensional elastic hexagonal lattice. The lattice is designed
to feature K point Dirac cones that are well separated from the other numerous
elastic wave modes characterizing this continuous structure. We exploit the
arrangement of localized masses at the nodes to break mirror symmetry at the
unit cell level, which opens a frequency bandgap. This produces a non-trivial
band structure that supports topologically protected edge states along the
interface between two realizations of the lattice obtained through mirror
symmetry. Detailed numerical models support the investigations of the
occurrence of the edge states, while their existence is verified through
full-field experimental measurements. The test results show the confinement of
the topologically protected edge states along pre-defined interfaces and
illustrate the lack of significant backscattering at sharp corners. Experiments
conducted on a trivial waveguide in an otherwise uniformly periodic lattice
reveal the inability of a perturbation to propagate and its sensitivity to
backscattering, which suggests the superior waveguiding performance of the
class of non-trivial interfaces investigated herein.Comment: 18 pages, 7 figures, full length articl
Topologically protected waves in classical media provide unique opportunities for one-way wave transport and immunity to defects. Contrary to acoustics and electromagnetics, their observation in elastic solids has so far been elusive because of the presence of multiple modes and their tendency to hybridize at interfaces. Here, we report on the experimental investigation of topologically protected helical edge modes in elastic plates patterned with an array of triangular holes, along with circular holes that produce an accidental degeneracy of two Dirac cones. Such a degeneracy is subsequently lifted by careful breaking of the symmetry along the thickness direction, which emulates the spin orbital coupling in the quantum spin Hall effect. The joining of two plates that are mirror-symmetric copies of each other about the plate midthickness introduces a nontrivial interface that supports helical edge waves. The experimental observation of these topologically protected wave modes in elastic continuous plates opens avenues for the practical realization of structural components with topologically nontrivial waveguiding properties and their application to elastic waveguiding and confinement.
We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which exhibits edge states to a phononic lattice, thereby developing a family of lattices with edge states. Parameter spaces with topological phase boundaries in the vicinity of the transformed system are illustrated to demonstrate the robustness to mechanical imperfections. A potential realization in terms of fundamental mechanical building blocks is presented for the hexagonal and Lieb lattices. The lattices are composed of passive components and the building blocks are a set of disks and linear springs. Furthermore, by varying the spring stiffness, topological phase transitions are observed, illustrating the potential for tunability of our lattices.
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