Hybridization of resonant modes and Bloch waves in acoustoelastic phononic crystals

In phononic crystals composed of solid inclusions distributed periodically in a fluid matrix, Bloch waves are a superposition of acoustic and elastic waves coupled at the boundaries of inclusions. Resonances internal to the unit cell and localized on the solid inclusions, when present, populate the phononic band structure with additional hybridization bands. Comparing the cases of nylon in water and of steel in water, that are conveniently accessible to experiment, we relate the hybridization bands to the resonant modes, also termed quasinormal modes, of a single solid inclusion immersed in water, that are identified numerically using a stochastic excitation technique. To characterize the hybridization of the resonant modes with the continuum of Bloch waves, we compute the complex phononic band structure giving evanescent Bloch waves with acoustoelastic coupling taken into account. In the particular case of hexagonal acoustoelastic phononic crystals, we observe that the acoustic Dirac cone centered at $K$ points of the first Brillouin zone can be severely affected without breaking the symmetry of the crystal.