  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.
