Comparisons of two effective medium approaches for predicting
sound scattering by periodic arrays of elastic shells

Umnova, O; Krynkin, A; Chong, AY; Taherzadeh, S; Attenborough, K

Abstract

Two effective medium models are presented and used to predict complex reflection and transmission
coefficients of finite periodic arrays of resonant elastic shells as well as their effective density
and bulk modulus at low frequencies. Comparisons with full multiple scattering theory and
measurements show that the self-consistent model fails to correctly predict the shape of the
transmission/reflection curves when scatterer resonances are close to the first Bragg bandgap. The
low frequency grating model, which neglects the evanescent modes and considers scattered wave
propagation only in the same direction as the incident one, gives a much better agreement with
both measurements and the full multiple scattering theory. Moreover, because it does not require
the wavelength to strongly exceed the size of scatterers, the model gives reliable predictions even
at frequencies around the first periodicity related bandgap. In contrast to the self-consistent model,
the low frequency grating model is applicable when the resonant scatterers have more than two
low frequency resonances.

Citation

sound scattering by periodic arrays of elastic shells. ˜The œJournal of the Acoustical Society of America (Online), 134(5), 3619-3630. https://doi.org/10.1121/1.4824340

• Journal Article Type: Article
• Publication Date: Nov 1, 2013
• Deposit Date: May 28, 2015
• Journal: The Journal of the Acoustical Society of America (JASA)
• Print ISSN: 0001-4966
• Peer Reviewed: Peer Reviewed
• Volume: 134
• Issue: 5
• Pages: 3619-3630
• DOI: https://doi.org/10.1121/1.4824340
• Publisher URL: http://dx.doi.org/10.1121/1.4824340
• Additional Information: Funders : Engineering and Physical Sciences Research Council (EPSRC)