Michael B. Muhlestein

arXiv2022

Homogenization of one-dimensional layered and graded structures

The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional area and for Willis coupling, which couples the stress-strain and momentum-velocity constitutive relations. The homogenization method is then demonstrated by considering acoustic waves normally incident upon a rigidly-backed double-layered wall and plane waves propagating in a duct with a section of exponentially-growing cross-sectional area.

physics.flu-dyn↗

arXiv2018

Acoustic scattering from a fluid cylinder with Willis constitutive properties

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.

physics.comp-ph↗