Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

• Published in: New journal of physics Vol. 19; no. 2; pp. 25001 - 25018
• Main Authors: Pal, Raj Kumar, Ruzzene, Massimo
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.02.2017
• Subjects: Backscattering; Computer simulation; Configurations; Continuity (mathematics); Edge waves; Elastic plates; elastic waveguides; Electromagnetism; Energy gap; Finite strip method; hexagonal lattice; inversion symmetry; Lattices (mathematics); Numerical prediction; Periodic structures; Physics; plates with resonators; Quantum Hall effect; quantum valley Hall effect; Resonators; Topology; Unit cell; Wave propagation
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/aa56a2

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 two-dimensional 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.