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physics.flu-dyn2022
Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator
M. J. A. Smith, P. A. Cotterill, D. Nigro +2
Using a combination of multipole methods and the method of matched asymptotics, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator i…
physics.flu-dyn2022
Two-dimensional Helmholtz resonator arrays. Part II. Matched asymptotic expansions for specially-scaled resonators
M. J. A. Smith, I. D. Abrahams
We present a solution method which combines the method of matched asymptotics with the method of multipole expansions to determine the band structure of cylindrical Helmholtz reson…
physics.flu-dyn2022
Two-dimensional Helmholtz resonator arrays. Part I. Matched asymptotic expansions for thick- and thin-walled resonators
M. J. A. Smith, I. D. Abrahams
We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining e…