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We introduce the concept of effective phononic crystals, which combineperiodicity with varying isotropic material properties to force periodiccoefficients in the elastic equations of motion in a non-Cartesian basis.Periodic coefficients allow for band structure calculation using Bloch theorem.Using the band structure, we demonstrate band gaps and topologically protectedinterface modes can be obtained in cylindrically propagating waves. Througheffective phononic crystals, we show how behaviors of Cartesian phononiccrystals can be realized in regions close to sources, where near field effectsare non-negligible.

Effective Phononic Crystals for Non-Cartesian Elastic Wave Propagation