Recent technical efforts at Sandia National Laboratories have identified a need for broadband high-frequency vibration isolation spanning a wide range of ultrasonic frequencies. To fill this need, phononic pseudocrystal isolators based upon a structure with cyclic symmetry and radial self-similarity was developed that can potentially suppress frequency transmission across a range far larger than that observed for normal phononic crystals. To enable calculation of transmission characteristics for these articles, boundary conditions enabling half-channel calculations are proposed and their validity demonstrated for both longitudinal and shear waves. These boundary conditions also apply to conventional phononic crystals and can result in significant savings when properly applied for normal incidence longitudinal and shear waves. Additionally, this paper demonstrates and gives formulas for implementing energy density methods that can be used to track wave extinction within phononic pseudocrystals as well as canonical phononic crystal structures.

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