Hybridization of resonant modes and Bloch waves in acoustoelastic phononic crystals

Abstract

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 quasi-normal 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 acousto-elastic coupling taken into account. In the particular case of hexagonal acousto-elastic 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.

Acoustic Topological Circuitry in Square and Rectangular Phononic Crystals

“…Therefore, by using this coupled acoustoelastic model we take into account the conversion of pressure waves, in the fluid, into coupled shear and longitudinal elastic waves, in the solid. This allows us to include subtle physical effects that would otherwise be missed by simpler models [45]; for example, a model that comprises of the scalar wave equation ( 1) alongside rigid Neumann boundary conditions. We solve the coupled acoustoelastic equations using the finite element method (FEM) following the techniques detailed in Refs.…”

“…We solve the coupled acoustoelastic equations using the finite element method (FEM) following the techniques detailed in Refs. [44,45]. Hereon in, we assume a time-harmonic dependence exp(−iωt) for the pressure field in the fluid phase, and the elastic displacement field in the solid phase, where ω is the angular wave frequency in units of radians per second.…”

Acoustic topological circuitry in square and rectangular phononic crystals

“…Therefore, by using this coupled acousto-elastic model we take into account the conversion of pressure waves, in the fluid, into coupled shear and longitudinal elastic waves, in the solid. This allows for us to include subtle physical effects that would otherwise be missed by simpler models [42]; for example, a model that comprises of the scalar wave equation (1) alongside rigid Neumann boundary conditions. Hereon in, we assume a time-harmonic dependence exp(−iωt), for the pressure field in the fluid phase, and the elastic displacement field, in the solid phase, where ω is the angular wave frequency in units of radians per second.…”

Evanescent Lamb waves in viscoelastic phononic metastrip

“…In addition to evanescent bulk waves [7][8][9] , complex band structures are also widely used for studying evanescent Lamb waves. Some of the investigations are only focusing on flexural waves.…”