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arXiv · 1811.03007

Acoustic scattering from a fluid cylinder with Willis constitutive properties

Michael B. Muhlestein·Benjamin M. Goldsberry·Andrew N. Norris·Michael R. Haberman
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Abstract

A material that exhibits Willis coupling has constitutive equations that couple the pressure-strain and momentum-velocity relationships. This coupling arises from subwavelength asymmetry and non-locality in heterogeneous media. This paper considers the problem of the scattering of a plane wave by a cylinder exhibiting Willis coupling using both analytical and numerical approaches. First, a perturbation method is used to describe the influence of Willis coupling on the scattered field to a first-order approximation. A higher-order analysis of the scattering based on generalized impedances is then derived. Finally, a finite element method-based numerical scheme for calculating the the scattered field is presented. These three analyses are compared and show strong agreement for low to moderate levels of Willis coupling.

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Michael B. Muhlestein, Benjamin M. Goldsberry, Andrew N. Norris, Michael R. Haberman. 2018-11-02. Acoustic scattering from a fluid cylinder with Willis constitutive properties. https://doi.org/10.1098/rspa.2018.0571

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