Sound Wave Propagation through Periodic and Nonreciprocal Structures with Viscous Components

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Acoustic properties of periodic elastic structures have been a subject of active research for more than a century. Here, I derived and analyzed the dispersion equation for sound waves propagating in a periodic layered heterogeneous structure containing at least one viscous fluid as a constituent. The derivation of the dispersion equation is based on the Navier-Stokes equation for sound wave and the boundary conditions of continuity of fluid displacement and stresses at the interfaces with Bloch periodic boundary condition. The obtained dispersion equation is very general, it is valid for different combinations of elastic layers, any direction of propagation, and … continued below

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Shymkiv, Dmytro May 2024.

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  • Shymkiv, Dmytro

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Acoustic properties of periodic elastic structures have been a subject of active research for more than a century. Here, I derived and analyzed the dispersion equation for sound waves propagating in a periodic layered heterogeneous structure containing at least one viscous fluid as a constituent. The derivation of the dispersion equation is based on the Navier-Stokes equation for sound wave and the boundary conditions of continuity of fluid displacement and stresses at the interfaces with Bloch periodic boundary condition. The obtained dispersion equation is very general, it is valid for different combinations of elastic layers, any direction of propagation, and frequency of sound. In the case of superlattice consisting of narrow layers with high viscosity fluid and layers of ideal fluid, an acoustic analog of the Borrmann effect is predicted. In the other part of my dissertation, I study the nonreciprocal wave propagation in phononic crystals induced by viscosity. Using Fourier-transformed wave equation, I proved analytically that for an infinite phononic crystal with broken PT-symmetry dispersion relation remains the same switching the direction of the wave propagation, while Fourier components of velocity are nonreciprocal. I optimized shape of the scatterer to reach the highest value of the nonreciprocity in a two-dimensional finite phononic crystal. Sound propagation through crystals with various unit cells is numerically simulated with COMSOL Multiphysics to create a dataset of transmission values. For each introduced parameter the optimized scatterer's geometries are obtained utilizing machine learning techniques. I found parameters of the crystal, which may serve as a linear non-resonant passive acoustic diode.

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  • May 2024

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  • June 19, 2024, 6:26 a.m.

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  • July 5, 2024, noon

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Shymkiv, Dmytro. Sound Wave Propagation through Periodic and Nonreciprocal Structures with Viscous Components, dissertation, May 2024; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc2332612/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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