  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 having different topological invariants. The
topological properties of the considered configurations are predicted by unit
cell and finite strip dispersion analyses. Numerical simulations on finite
structures 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.
