Controlling cylindrical waves using effective phononic crystals

Phononic crystals (PCs) are periodic media that can exhibit novel wave propagation behaviors. The analysis of PCs relies on the Bloch theorem, and the application of which implies that certain canonical behaviors can be supported, e.g., band gaps. The Bloch theorem assumes plane wave propagation; however, this is not always the case, e.g., for cylindrical or spherical wave fronts. Here, we redefine material properties in PCs in the presence of cylindrically propagating waves, such that the resulting wave equations contain periodic coefficients. In this sense, an equivalent system can be defined on which Bloch theorem can be applied to predict its wave response. This talk will discuss our recent work on effective phononic crystals, which are PCs that are not geometrically periodic but whose material properties result in periodic coefficients in the wave equation. We demonstrate these concepts using radially-propagating torsional waves and use finite element method models to solve for material properties that result in Bragg scattering-based band gaps, locally resonant band gaps, and topologically protected interface modes. Finally, we conduct experimental validations on 3D printed samples fabricated with multi-material polyjet printing. This work has applications to mitigating damaging torsional vibrations in rotating machinery such as turbines, compressors, and engines.