Title: Asymptotic modeling of Helmholtz resonators including thermoviscous effects
Abstract: We systematically employ the of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded in a rigid surface, each resonator consisting of an arbitrarily shaped cavity connected to the external half-space by a small cylindrical neck. The bulk of the analysis is devoted to the problem where a single resonator is subjected to a normally incident plane wave; the model is then extended using Foldy's method to the case of multiple resonators subjected to an arbitrary incident field. As an illustration, we derive critical-coupling conditions for optimal and perfect absorption by a single resonator and a model metasurface, respectively.
Publication Year: 2020
Publication Date: 2020-01-25
Language: en
Type: preprint
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