Acoustic scattering from a fluid cylinder with Willis constitutive properties. (21st December 2018)

• Record Type: Journal Article
• Authors: Muhlestein, Michael B.; Goldsberry, Benjamin M.; Norris, Andrew N.; Haberman, Michael R.
• Is Part Of: Proceedings. Volume 474:Number 2220(2018)
• Publication Date: 2018-12-21
• Subjects: Willis coupling -- metamaterial -- fluid -- cylinder -- scattering; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0571
• Languages: English
• ISSNs: 1364-5021

Abstract

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 scattered field is presented. These three analyses are compared and show strong agreement for low to moderate levels of Willis coupling.