Phononic band calculations and experimental imaging of topological boundary modes in a hexagonal flexural wave machine

We construct a two-dimensional mechanical wave machine based on a hexagonal lattice to investigate low-frequency flexural plate waves whose propagation mimicks a topological quantum valley Hall system. We thereby demonstrate ‘mechanical graphene’ by extension of the one-dimensional Shive wave machine. Imaging experiments, backed up by simulations, reveal the presence of boundary modes along a topological interface, despite the absence of Dirac cones in the dispersion relation under conditions of spatial inversion symmetry. This work provides an alternative route for the investigation of topological phononic crystals, and should lead to new insights in the design and observation of artificial phononic structures.