Homogenization of one-dimensional layered and graded structures
Fluid Dynamics
2022-03-15 v2
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.
Cite
@article{arxiv.2203.05832,
title = {Homogenization of one-dimensional layered and graded structures},
author = {Michael B. Muhlestein and Alexei T. Skvortsov},
journal= {arXiv preprint arXiv:2203.05832},
year = {2022}
}