Modeling phononic crystals and acoustic metamaterials to control elastic waves: self-collimation, bi-refringence, forward and inverse design

Das, Debanik

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Modeling phononic crystals and acoustic metamaterials to control elastic waves: self-collimation, bi-refringence, forward and inverse design

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Phononic crystals (PnCs) are periodic arrangements of materials with contrasting elastic properties. These are used to control elastic waves which are responsible for the propagation of sound in the lower frequency and for the conduction of heat in the higher frequency regime. We use the action integral formalism and the finite element method to calculate the band structures of the PnCs. We establish the methodology by studying the conventional hole-based and pillar-based PnCs and corresponding band gaps. Next, we propose a tapered resonator-based PnC to guide out-of-plane elastic waves without a traditional waveguide based on line defects. We show that instead of an absence of the band gap, the out-of-plane wave shows a restricted propagation at a specific frequency. This originates from the standing wave formation at that frequency due to a zero group velocity. Additionally, we model two exotic wave dispersion phenomena, namely self-collimation and bi-refringence. In the self-collimation, the flexural elastic wave shows a diffraction-less propagation. In the bi-refringence, the incoming wave bifurcates into two waves having different group velocity directions. These properties are rare in the conventional single material PnCs. We also show that the self-collimation effect persists for a small variation in the angle of incidence and a perturbative hole at the center of each unit cell. Hence the phenomenon is termed super-collimation. Finally, a reduced Bode expansion scheme is implemented to create an efficient numerical framework for high-throughout phononic band gap generation. Subse-quently, the data is used to solve forward and inverse design problems. Within the classical limit, the scale invariance of the elastic wave equation makes the devices useful in both the low-frequency acoustic regime and high-frequency phononic regime. Therefore the proposed PnCs have potential applications in a wide array of fields, from collimating ultrasonic waves in medical devices to harvesting elastic wave energy using piezoelectric materials.

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