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In this work, we study the propagation of soundwaves in a honeycombwaveguide network loaded withHelmholtz resonators (HRs). By using a planewave approximation in eachwaveguidewe obtain afirst-principlemodeling of the network, which is an exactmapping to the graphene tight-binding Hamiltonian.We show that additional Dirac points appear in the band diagramwhenHRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edgemodes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interfacemodes located in the band gap, and thesemodes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedombestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also ofmore complex systems.

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves