Homogenization of one-dimensional layered and graded structures

TL;DR

This paper introduces a transfer matrix-based homogenization method for one-dimensional layered and graded structures, capable of handling variable cross sections and Willis coupling, with applications to acoustic wave propagation.

Contribution

A novel homogenization approach using transfer matrices that accounts for variable cross-sectional areas and Willis coupling effects in 1D structures.

Findings

Effective homogenized models for layered structures

Application to acoustic wave problems in ducts

Inclusion of Willis coupling in homogenization

Abstract

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.